







Simultaneous equations with fractions 
20181214 

From zaheer: solve simultaneous equations and give answer in fractional form
3x  2 = 4y +5/3
y + 7 = 2x + 4
would really appreciate some help on this please Answered by Penny Nom. 





A line cuts a curve 
20181111 

From roxanne: Hello, i need to ask a question, do you mind explaining and writing the formula of how to solve equations such as "find the set values of k for which the line y2x5 cuts the curve y=x^2 +kx+11" please Answered by Penny Nom. 





The pointslope equation for a line 
20180923 

From Sally: The equation of the line in pointslope form for the line passing through the point ( 4, 6) and parallel to the line y = 6x + 2. Describe the steps. Answered by Penny Nom. 





Linear feet and cubic feet 
20180716 

From Dave: How do I convert: 1 foot wide x 15 inches high x 19 inches deep
We are trying to figure out how to convert the linear footage into cubic footage
the above are the figures represent just 1 linear feet of several thousand
Any thing helps,
Thanks in advance
Dave Answered by Penny Nom. 





More on the curvature of the Earth 
20180423 

From will: the formula for figuring the earth's curve goes against logic, looking at a fixed point and backup 1mi. the point drops 8" then 16" in the next mi. and 32" in the third mi. why shouldn't it be 24" why is the 8" per mi. squared can you tell me in laymens terms why this is it goes against logic it would seem the correct wat would be to add up 8" per mile as you back up from the fixed point 8" 16" 24" 32" not 8/16/32/64" Answered by Harley Weston. 





Dividing a region in half 
20180224 

From mandy: There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the xaxis into two regions with equal area. What is the slope of that line? Answered by Penny Nom. 





The slope of a line 
20180222 

From Steve: my current slope is 6%. I want to know how many inches higher I will be at 18'
Thanks Answered by Penny Nom. 





The equation of a line 
20180123 

From Gloria: Write the equation of a line in standard form through the point (1, 6) and perpendicular to the line 2x –y = 9. Answered by Penny Nom. 





The product of the coordinates of a point on a line 
20180117 

From Sophia: For any point on line l, the product of the xcoordinate and the ycoordinate is less than or equal to zero , what is the answer? Answered by Penny Nom. 





The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





Simultaneous equations with fractions 
20170909 

From Farah: Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g  f = 10 Answered by Penny Nom. 





A pair of linear inequalities 
20170808 

From Hempstone: Solve the inequalities 3x5<2x+5>4x+9 Answered by Penny Nom. 





Catherine, Molly and Tom 
20170719 

From liezel: what is the answer of this problem, If Catherine and molly has 320pesos altogether, Molly and tom have 360 in all. Tom and Catherine have 240pesos altogether.How much does each of them have? Answered by Penny Nom. 





Parallel and Perpendicular lines 
20170717 

From Karen: Find an equation for the line with the given properties. Perpendicular to the line 7x + 2y = 6; containing the point (2, 1)
Find an equation for the line with the given properties. Parallel to the line 5x  3y =6; x intercept = 3 Answered by Penny Nom. 





Simultaneous equations with fractions 
20170602 

From Jamal: 1/x + 1/y =5 and 1/y  1/x =1 Answered by Penny Nom. 





Two wires between two buildings 
20170511 

From Bill: I need to find the height of the intersection point of two building wires< br />
Building A is 860 feet high and building B is 480 feet high. The wires existent from the top of one building to
The bottom of the other < br />
The distance between is 32 feet Answered by Penny Nom. 





What is the grade of the incline? 
20170312 

From Jon: If I am climbing 16 feet in elevation over 80 feet horizontal. What is the grade of the incline Answered by Penny Nom. 





Five equations 
20170116 

From Muhammed: A x 4 = E
B ÷ 4 = E
C + 4 = E
D  4 = E
___________
& A + B + C + D = 100
what is the value of E Answered by Penny Nom. 





Simultaneous equations with fractions 
20161221 

From Kimi: I am stuck on this,can someone please help me????
1/2x+1/3y=11
8x+2/5y=102
Can someone please explain how to solve questions like these??
Or else I will never learn...
Thank you Answered by Penny Nom. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





Simultaneous equations 
20161125 

From Rohan: x2/3 + y  1/4 = 13/12
2x/2 + 3 + y/3 = 11/6 Answered by Penny Nom. 





Parallel lines 
20161026 

From Jordan: (7,5) 3x 4y=5 Answered by Penny Nom. 





y = mx + c and Ax + By + C = 0 
20161018 

From Erick: please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o form. Answered by Penny Nom. 





A linear relationship 
20161016 

From Bianca: x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it? Answered by Penny Nom. 





The equation of a line 
20161001 

From Miriam: write the equation of the line that passes through (6,7) and is perpendicular to 3x+5y=0 Answered by Penny Nom. 





The length of stock on a roll 
20160923 

From Ken: I have a roll that is 13.5 inches wide ( OD) , and is wound on a 3 inch core. the thickness of the material is 3.5 thick.
Do you know of a formula that can calculate the linear feet on that roll?? Answered by Harley Weston. 





The equation of a ski slope 
20160831 

From Hannah: The information provided is
A ski slope has a slope of 0.2. You start at an altitude of 10,000ft.
Then the question is "Write the equation giving altitude (a) as a function of horizontal distance moved (d).
I know this is probably a very simple question but I didn't take a math class my senior year and now I'm a freshman in college, so some of it is very frustrating to me.
Any help is much appreciated, thank you! Answered by Penny Nom. 





The dimensions of a rectangle 
20160725 

From Krunox: A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width. Answered by Penny Nom. 





The temperature inside and outside a greenhouse 
20160722 

From Mehzad: Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?
a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same Answered by Penny Nom. 





Two equations with fractions 
20160722 

From kanesh: p/2+q/3=3
p/4+2q/3=3 Answered by Penny Nom. 





Simultaneous equations 
20160625 

From sena: 2x/3+3y/2=1
4x5y=22
simultaneous equation Answered by Penny Nom. 





A pair of equations with fractions 
20160511 

From tiya: hello, i want to know how to solve this question.
m/6+2n/3=6
m/10=2n/5=2 Answered by Penny Nom. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





Corrosion inhibitor in a pipeline 
20160302 

From Edu: I have a 12 in pipeline and 5 miles long. I need to coat it with corrosion inhibitor how much chemical will I need Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 Answered by Penny Nom. 





Perpendicular lines 
20160214 

From Brendon: points A (4; 6) , B (1;2), C (5;3) and D (4; 1) are given
prove that AC and BD are perpendicular to each other Answered by Penny Nom. 





Two equations in two unknowns 
20160213 

From Anumba: 4x + 2y = 4
7x  y = 11 Answered by Penny Nom. 





The equation of a vertical line 
20160207 

From Kagiso: The equation for a vertical line that goes through the point (7; 3) is? Answered by Penny Nom. 





A system of linear equations 
20160124 

From kareem: my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





A graph of the water level of a river 
20160105 

From emoni: Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Answered by Penny Nom. 





Constructing simultaneous linear equations 
20151228 

From Deborah: Linda thinks of a twodigit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?
Thank you! Answered by Penny Nom. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





The line of intersection of two planes 
20151209 

From Rabz: Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom. 





A tangent line to a parabola 
20151202 

From pei: Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Answered by Penny Nom. 





A tangent line to a circle 
20150903 

From Jamie: Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Answered by Penny Nom. 





A tangent to y = x^3 
20150531 

From Brayden: Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





A region defined by three lines 
20150316 

From Lucinda: find the area of the figure formed by the line y=5x+9 and the xaxis and yaxis. Answered by Penny Nom. 





Two equations with fractions 
20150226 

From Pulane: Hi math centre I've been trying to solve these equations for days now please help
(6/x)(1/y)=4
(9/x)+1=(2/y)
Please help me solve them simultaneously
Thank you Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





A line segment of length root 5 
20141215 

From angela: On the dot grid below, draw and label a line segment with length square root 5
the dot grid is 8 by 10 Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Two equations in two variables 
20140918 

From Susan: (28x + 36y)  [20000  .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





Three collinear points 
20140828 

From jhanavi: p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





Two regression lines 
20140614 

From catherine: Given a set of data values ,we can get two regression lines .Explain. Answered by Robert Dawson and Penny Nom. 





The equation of a line 
20140516 

From Michael: Find the equation of a line that passes through (2,1); the sum of the x and yintercepts is 2. (There are two answers) Answered by Penny Nom. 





A question concerning two lines 
20140509 

From Hela: The equation of the line L is 6x+5y=3, and the equation of line Q is 5x6y=0, which statement below about the line is true?
A) same y intercept
B)parallel
C) Same x intercept
D)perpendicular Answered by Penny Nom. 





A trig problem 
20140425 

From srishti: Consider the points P= (sin(ab),cosa), Q=(cos(ab),sina), R=(cos(ab+c),sin(ac), where 0 Answered by Chris Fisher. 





Simultaneous equations with fractions 
20140419 

From Maryam: I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:
x/8  y = 5/2
3x + y/3 = 13 Answered by Penny Nom. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





A circle which is tangent to two perpendicular lines 
20140309 

From MJ: I'm a College Student taking up Bachelor of Secondary Education on Math Subject.
And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:
"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"
But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle.
Thanks in advance! :) Answered by Penny Nom. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 Answered by Penny Nom. 





The slope of the line y=2x+5 
20131229 

From victoria: what is the slope of the line with the equation y=2x+5 Answered by Penny Nom. 





Distance from a point to a line 
20131228 

From Sue: I need to find the distances from the west line on 1st Take Point and 2nd
Take Point.
Thanks,
Sue Answered by Penny Nom. 





A linear equation 
20131226 

From khushboo: A farmer sowed wheat and paddy in two fields of total area 5000 sq.m. Write a linear equation and draw a graph to represent the same? Answered by Penny Nom. 





How do I graph y=2x1? 
20131207 

From cindy: How do I graph y=2x1? Answered by Penny Nom. 





What is the slope of this line? 
20131201 

From Charlene: What is the slope of this line? Answered by Penny Nom. 





A line through (5, 1) 
20131008 

From allison: find an equation in standard form for line passing through point (5,1) and perpendicular to line x=4 Answered by Penny Nom. 





Two perpendicular lines 
20130815 

From Hanna: The problem says, "Write the equation in standard form for the line that is perpendicular to the graph of y=5x+1 with a yintercept of 4." I have no clue how to do this. Please help me! Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





Simson line 
20130523 

From Nazrul: From any point p lying on the circumcircle of the triangle perpendiculars
PD , PE are drawn on BC,CA respectively. The line segment ED intersects at
the point 0 ; prove that PO ⊥ AB ( PO is perpendicular to AB ). Answered by Chris Fisher. 





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





The equation of a line 
20130404 

From Miranda: My coordinates provided are (6, 6) and (8, 9) and i need to put this into ax=bx=c format. I remember the equation to find the slope of y2y1/x2x1 to get the slope. However when i put that back into the y=mx+b format it still leaves me with a lot of variables. Please help :) Answered by Penny Nom. 





The distance between 2 lines in 4D 
20130401 

From samane: how can i measure the distance between 2 lines in 4D?? Answered by Chris Fisher. 





Tangents to the curve y = x^3 
20130324 

From Ethan: How many tangent lines to the curve y = x^33 pass through the
point (2, 4)? For each such line, and the exact coordinates of the point of
tangency on the curve. Answered by Penny Nom. 





A linear programming problem 
20130227 

From Kelley: A manufacturer of skis produces two types: downhill and crosscountry. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing is increased to 48 hours.

Downhill 
Crosscountry 
time available 
manufacturing time per ski 
2 hrs 
1 hr 
40 hr 
finishing time per ski 
1 hr 
1 hr 
32 hr 
profit per ski 
$70 
$50 

Answered by Penny Nom. 





Is a line lying in a plane an open or a closed region? 
20130213 

From pardeep: please help with this question on the open and closed intervals ::
Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? Answered by Harley Weston. 





A geometry word problem 
20130124 

From Matthew: "G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"
How would you solve this? Answered by Penny Nom. 





A word problem involving a fraction 
20121012 

From Derrick: If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do? Answered by Penny Nom. 





A problem that yields a linear equation 
20121007 

From Eshraj: one fourth of a whole number is three more than one fifth of the next whole number.find the whole number Answered by Penny Nom. 





Row echelon form 
20120905 

From Jennifer: Hello, my name is Jennifer. I am a 12th grader in PreCalculus and I was wondering if you may help me with Row Echelon Form.
x + 2y  3z = 5
2x  4y  6z = 10
3x + 7y  2z = 13 Answered by Penny Nom. 





A tangent to f(x) = 1/x 
20120904 

From Steven: Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Answered by Penny Nom. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





John's electronic store 
20120725 

From Jora: Electronic Store
John opened an electronic store in December. During his first month,
He sold 10 LCD TVs and 20 Plasma TVs. His income during that
month was $12800. In January, he sold 25 LCD TVs and 40 Plasma
TVs for an income of $27600.
In February he projects to sell 30 LCD TVs and 50 Plasma TVs.
If John expenses are $28900 in February, how much money will he
have after paying the expenses? Answered by Penny Nom. 





2x+underroot2=3x43underroot2 
20120709 

From Eshraj: 2x+underroot2=3x43underroot2 Answered by Penny Nom. 





An equation of the form y=mx 
20120417 

From Samiya: what would be an equation of the form y=mx with the points (2, 6) and (1, 3) for the line? Answered by Penny Nom. 





The equation of a line 
20120326 

From Danielle: Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (2,0) and (0,3)?
Thank You! Answered by Penny Nom. 





A vertical line passing through (10,4) 
20120316 

From Isabelle: Hi! My question is this:
Write the equation of each line described:
A vertical line passing through (10,4)
I would really appreciate your help!
Thanks,
Isabelle Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





The curvature of the earth 
20120208 

From sean: Question from sean, a student:
Two people 1.8 metres tall walk directly away from each other until they can no longer see each other (due to the curvature of the earth, which has a radius of about 6378 km).
A) Find a function relating the height of two identical objects with the distance between them using the scenario above as an example.
B) Sketch this function (you may use Graphmatica if you wish). Over what domain and range does the function exist?
C) Describe this relation in practical terms. Answered by Harley Weston. 





Four apples and two oranges cost Rs. 30... 
20120113 

From nasr: Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost? Answered by Harley Weston. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





A straight line distance 
20120106 

From Margaret: If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line? Answered by Penny Nom. 





Augmented matrix 
20111214 

From Britney: Write Augmented matrix and use row reduction to solve.
I need major help with this problem! Tomorrow is my semester test and I have no idea how to do this.
2x+5y=8
yx=10 Answered by Robert Dawson. 





Lines tangent to y^2=4x 
20111111 

From Reuchen: Find equations of the lines tangent to y^2=4x and containing (2,1). Answered by Penny Nom. 





The slope of a line 
20111110 

From Sara: Line k lies in the xyplane.
The xintercept of line k is 4.
And line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0).
What is the slope of line k?
Give the answer as a fraction. Answered by Penny Nom. 





Linear equations 
20111006 

From Hannah: I am confused about a question on my homework, here is an example on what I need to do:
You own a sightseeing boat tour. Kids' admission costs $5, adults' admission costs $8.
During that day you get (madeup number) $521 with 71 admissions.
How many of each passenger boarded?
I tried something like
5x + 8y = 521
x + y = 71
But, I still don't understand how to solve it! Help? Answered by Penny Nom. 





Two line segments in the plane 
20110815 

From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.
Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points. Answered by Chris Fisher. 





An equation in the form Ax+By=C 
20110728 

From Mike: I need to write an equation in the form Ax+By=C
The points I was given are (5,0) and (3,5)
I know how to find the slope I got 5/8 and wrote it out as y=(5/8)x+b however I'm not quite sure where to go from here.
Any help would be greatly appreciated. Answered by Penny Nom. 





A linear equation with fractions 
20110713 

From Simon: I would like to ask if you would be able to explain : linear equation: 2 1/2 (X1)  x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) .
Thanks for your help. Answered by Penny Nom. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





A transversal 
20110330 

From Jillian: I don't understand finding angels in a transversal Answered by Penny Nom. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You! Answered by Penny Nom. 





The number of points on a line is equivalent to that of a surface 
20110324 

From Gary: I I was reading about how the number of points on a line is equivalent to that of a surface. This was done by taking any point on a line then taking alternating digits and making them as points on an x and y axis therefore points on a surface.The problem is as i see it if you just take a line then hold it over a surface you have just put the points on the line in a one to one correspondence with the points directly under it on the surface.Now you have all the rest of the surface which cannot be mapped onto the line since it is already used up.What am i missing? Answered by Penny Nom. 





A camera's line of sight 
20110226 

From MJ: A rocket that is rising vertically is being tracked by a ground level camera located 3 mi from the point of blast off when the rocket is 2 mi high its speed is 400mph At what rate is the (acute) angle between the horizontal and the camera's line of sight changing Answered by Penny Nom. 





Points on a graph 
20110215 

From Maggie: Which set of ordered pairs can be used to graph y = 2x1.
A.(5,9),(1,3),(4,9) B. (2,5),(1,1),(5,9)
C.(2,5),(0,1),(4,3) D. (5,9),(2,3),(4,9)
I cannot figure it out. Could you help me? Answered by Penny Nom. 





The nearest one and a half and the nearest inch 
20110202 

From Miranda: REASON:sarah gave the same answer when asked to round 4 seven eighth inches to the nearest one and a half and the nearest inch. explain why sarah is correct? Answered by Penny Nom. 





The angle between a line and a plane 
20110112 

From tom: what are the angles of the diagonal of a rectangular parallelepiped 2in by 3 in by 4 in
makes with the faces...
You know this is a problem that I can't figure out ...I don't know where
the angle and the diagonals where? can you help me with this one? Answered by Penny Nom. 





Line segments 
20110104 

From Izsak: What is the formula to find the number of segments that can be named by a given number of points on a line? Answered by Penny Nom. 





A tangent line 
20110103 

From Amanda:
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Answered by Penny Nom. 





What is the speed of each car? 
20101104 

From Jennifer: two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea? Answered by Stephen La Rocque. 





An exponential equation 
20101019 

From Sandi:
Question from sandi, a student:
I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)Population
0500
1600
2720
3864
41037
51244
61493
71792
82150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days. Answered by Penny Nom. 





The equation of a line 
20101019 

From Sava: I have to write an equation and sketch a graph for the line that meets the given conditions:
A line with slope 15/5 that passes through the point (2.5,4.5) Answered by Penny Nom. 





A linear system 
20101015 

From Sandy: HARD!! algebra (Linear Systems) question?
An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady from the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane).
Part A
Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance travelled each way
Part B
When solving the system of equations graphically, what equations would you enter into the equation editior (to make graphs on your calculator)
Part C
Indicate what the X and the Y represent Answered by Stephen La Rocque. 





A strip of land 
20100915 

From Walter: How many linear feet of strip of land 15 feet wide does it take to make 1 acre? Answered by Penny Nom. 





A linear relationship 
20100622 

From Laura: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $300 to drive 480 miles and in June it cost her $460 to drive 800 miles.
Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. Answered by Robert Dawson. 





4 > 3m7 >= 2 
20100605 

From pamela: The question is
4>3m7>=2 Answered by Penny Nom. 





x/a +y /b =a+b : x/a^2+ y/b^2 =2 
20100530 

From smithu: x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method ,
cross multiplication, substitution method Answered by Penny Nom. 





Graphing a linear inequality 
20100526 

From Valeie: When graphing a linear inequality, how do you know if the inequality represents the area above the line. Answered by Penny Nom. 





Line of sight 
20100506 

From David: I live in St. Joseph, Michigan and there is an ongoing argument regarding lineofsight over the horizon.
Standing on a 200 foot high bluff here, people swear they can see the top of the Willis (nee Sears) Tower in Chicago, which is about 1653 feet high.
It is my contention that this is actually a "refracted reflection" and not directlineofsight.
So, to settle the argument, I'd sure like some simple explanation for this, even ifand I hope notI am incorrect.
David Answered by Harley Weston. 





A tangent line to a circle 
20100415 

From Rhonda: The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Answered by Penny Nom. 





Exactly two lines of symmetry 
20100411 

From debbie: i am looking for a quadrilateral with exactly two lines of symmetry. please help! thank you. Answered by Tyler Wood. 





A system of equations 
20100330 

From samantha: the equations of two lines are 6xy=4 and y=4x +2.what is the value of x in the solution for this system of equations? Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





The angle of intersection between two lines 
20100325 

From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher. 





The line passing through (2,6) and (2,9) 
20100324 

From antoinette: the equation of a line passing through the points (2,6) and (2,9)? Answered by Penny Nom. 





A quadratic equation 
20100315 

From rachelle: under certain condition, it is found that the cost of operating an automobile as a
function of speed is approximated by a quadratic equation. use the data shown
below to find the function. then use the function to determine the cost of operating
the automobile at 60mph.
speed
(in miles per hour) 
operating cost
per mile(in cents) 
10 
22 
20 
20 
50 
20 
Answered by Penny Nom. 





The line joining (3,4) and (5,6) 
20100306 

From Patric: Find the condition that the point (x,y) may lie on the line joining the points
(3,4) and (5,6) Answered by Penny Nom. 





A linear relationship 
20100224 

From Mel: This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
h (cm) 
120 
340 
480 
600 
1040 
T (degrees C) 
14.28 
12.96 
12.12 
11.4 
8.76 
Find the gradient and vertical intercept of the function. Write the formula for T. Answered by Penny Nom. 





Substitution method 
20100217 

From Melodie: 7x  4y = 10
4y= x2 Answered by Tyler Wood. 





Can a line segment curve over two planes? 
20100214 

From Graham: I am working on a math fair project.
Can a line segment curve over two planes?
Such as, if I had a three dimensional L bracket and I drew a line segment
on it with a marker starting on the bottom of the L and had it curve
around the corner and up the top, would it still be considered one line
segment? Or is that two line segments?
Is there a rule that a line segment can only occupy one plane?
Thank you.
Graham Answered by Chris Fisher. 





Substitution 
20100214 

From Izayah: what is 3 ways to find the meeting point of y=2x+4 and 3x+y=7
by making 2 table and using a graph Answered by Stephen La Rocque. 





The angle at which the road is inclined 
20100210 

From abeth: a mountain road drops 5 m for every 22 m of road. Calculate the angle at which the road is inclined to the horizontal to the nearest degree. Answered by Penny Nom. 





Linear growth 
20100127 

From S.: I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.
Choose the amount of population growth each year = 200
(Hint: Choose a whole number for your growth rate, rather than a percent.)
a) Fill in the following chart:
Year (t) Population (P)
t = 0
(2010) 1000
t = 1
(2011) 1000+200=1200
t = 2
(2012) 1000+400=1400
t = 3
(2013) 1000+600=1600
b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.
. . .
Answered by Melanie Tyrer. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





A linear equation with the variable on both sides 
20100116 

From dog: 4x9=7x+12 Answered by Penny Nom. 





A linear equation with fractions 
20091231 

From Michelle: How would I solve: (2)(1/2x + 5) = (2)(8)? Answered by Penny Nom. 





Linear programming using the Simplex Method 
20091228 

From William: A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running,
at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to
process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day.
Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the
amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B
yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to
maximize the amount of gold extracted subject to the above constraints?
I need a linear programming solution or algorithm of the simplex method solution.
Not a graphical solution. Thanks. Answered by Janice Cotcher. 





The acute angle formed by intersecting lines 
20091217 

From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x  2y = 2. Was is necessary to find the intersection point? Answered by Robert Dawson. 





Airline routes 
20091201 

From Kapilan: Please answer the following question:
From A to B there are four possible air routes. From B to C there are five
possible air routes. From C to D there are three possible air routes. How many
different trips can be taken from A to D and back without taking the same route on any
section of the return trip? Answered by Penny Nom. 





A line through the yintercepts 
20091201 

From Rogerson: Find the equation of the line through yintercept of the lines 3x + 4y = 12 and 3x  y = 9. Answered by Penny Nom. 





The point of intersection of the pair of straight lines 
20091119 

From Stephanie: Find the point of intersection of the pair of straight lines:
y=3x9
y=4x+2
x = _______ and y = ________
I am totally confused. Please help Answered by Robert Dawson. 





The intersection of two graphs 
20091030 

From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. Answered by Penny Nom. 





Is it a rectangle? 
20091029 

From sefora: The coordinates of the vertices of quadrilaterals are given.
Draw each quadrilateral on a grid.
Determine whether it is a rectangle (show your work)
P(5,1), Q(4,4), R(6,2), S(3,5) Answered by Penny Nom. 





Two non zero vectors 
20091027 

From Nazrul: Given that a and b are two non zero vectors and ma+nb=0 where m and n are two scalars. How can I prove that m=n=0. Answered by Robert Dawson. 





A word problem 
20091024 

From Ryan: Two times one number plus 7 times another number is equal to 17. the first number plus the second number is equal to 25. What are the two numbers? Please Help! Answered by Penny Nom. 





Forming a square 
20091021 

From christianah: Two parallel lines have the equations y=x+4 and y=x2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines.Explain and justify your reasoning. Answered by Penny Nom. 





A linear system 
20091020 

From marissa: Solve this linear system
2xy=5
3x+y=9 Answered by Penny Nom. 





A line and a circle 
20091019 

From Renson: Determine whether the line x2y=0 cuts,touches or fail to meet the circle x^2+y^28x+6y15=0.If it touches or cuts ,find the coordinates of the point(s) of contact Answered by Harley Weston. 





$6.25 in nickels quaters and dimes 
20091010 

From miriam: a piggy bank contains $ 6.25 in nickles quaters and dimes.
there are 65 coins all together and there are four times as many nickles as quaters
find the number of coins of each kind Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





Elimination method 
20091008 

From Kenty: How do I solve this problem using the elimination method?
3x7y=0
6x+4y=0
I am not sure how so if someone can show me a similar problem (instead of
solving this one for me) that would be fantastic. Answered by Penny Nom. 





The method of substitution 
20090917 

From laura: ok! i really need help with this question plz help!!
x=  4y +5
x+2y = 7 Answered by Penny Nom. 





10x8 /3 =6x+24 /5 
20090916 

From Heidi: 10x8 /3 =6x+24 /5.....I know the answer is 7/2 but how do I get there? Answered by Penny Nom. 





The slopeintercept form 
20090911 

From Shelby: Write an equation in slopeintercept form of the line that is parallel to the graph of 3y4x=1 and passes through (0,6) Answered by Penny Nom. 





Airline overbooking 
20090903 

From Nikita: An airline company knows that 8% of it's passengers will not show up for their scheduled flights. A plane has 175 seats.
a) What is the probability that 10 passengers or fewer will not show up?
b) What is the probability that 10 to15 passengers will not show up?
c)What is the probability that exactly 10 passengers will not show up?
d) What is the probability that more than 19 passengers will not show up? Answered by Robert Dawson. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





Linear equations 
20090823 

From shwetha: The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased by 6 cm then area increases by 168 cm square. Find the length and breadth of the rectangle. Answered by Stephen La Rocque. 





Graph 2x3y+15=0 
20090820 

From Diem: Graph 2x3y+15=0 Answered by Leeanne Boehm. 





Two equations in two unknowns 
20090730 

From Alicia: I need help with the following equation please show me the steps to complete so that I will know how to do this my self.
2xy=2 5x+y=5 Thanks for the help Answered by Penny Nom. 





Circular Measures 
20090724 

From onyeka: find the equation of a circle with point [3,7][5,5] and wich center lies on the line x4y=1 Answered by Robert J. Dawson. 





Finding the Line Joining Perpendicular Feet 
20090716 

From mukulu: Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x3y4= 0 and 3x+y6=0. Answered by Janice Cotcher. 





Parallel lines 
20090701 

From chris: Write the slope of a line that is parallel to each line.
1.y=2x5
2.y=x+2
3.3x+y=10
4.5xy=11
5.x+2y=6
6.2x3y=9
7.4x+y=3
8.x+2y=14 Answered by Brennan Yaremko. 





The product of gradients between 2 perpendiculars lines 
20090611 

From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to 1.... Answered by Penny Nom. 





Two equations 
20090531 

From tony: y = 1.2x  32.7,
y = 0.7x + 46.15
can you please solve this for me? i am not able to figure it out... thank you
tony Answered by Penny Nom. 





(x + 1) / 3 + (x + 2) / 7 = 2 
20090522 

From MzDonna: Question from MzDonna, a parent:
We can't seem to get an answer for this problem:
X + 1 X + 2
_____ + _____ = 2
3 7
The book gives the answer as 10 ; But, we struck. Please help us.
___
21
Thanks in advance for your assistance. Answered by Stephen La Rocque. 





Two equations 
20090518 

From Bob: solve the system:
x/2  2y= 8
3x + 2/3y= 10 Answered by Stephen La Rocque. 





Finding an Array to an Integer Linear Programming Problem 
20090512 

From Debbie: how to make an array for 3 box of juice for 25 students and 2 teacher. 1 pack of juices
hols 3boxes the answer is 9 packages but how do you make array for this Answered by Janice Cotcher. 





Solve 1<52x<10 for x 
20090512 

From Helen: solve the following inequality for x
1<52x<10 Te less then sign by the one, should be less then or equal to. Answered by Stephen La Rocque and Penny Nom. 





Perpendicular lines 
20090507 

From shabnam: the line presented by y= 3x2 and a line perpendicular to it intersect at R(1,1). Determine the equation of the perpendicular line Answered by Stephen La Rocque. 





Stairway construction 
20090502 

From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs.
Rule 1: x+y=43 and x+y=46 (cm)
Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length)
I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe.
Did i explain it ok? Thanks for your help.
olivia Answered by Penny Nom. 





A perpendicular line in standard form 
20090421 

From Kristy: Can you help me with this equation?
Find the equation, in standard form of the line perpendicular to 2x3y=5 and passing through
(3,2) With the equation in standard form with all integer coefficient. Answered by Stephen La Rocque. 





Parallel and perpendicular lines 
20090408 

From Blake: I need to know what the formula for working a problem. I need to know how to find if i line is parallel or perpendicular by only looking at the equation. i know you must know the slope but how do i find slope? Answered by Stephen La Rocque. 





An infinite number of solutions 
20090324 

From Sean: this is a linear equations problem;
first:
3535.5 + Fbd (.866) + Fbc (.5)  Fab (.5) = 0
and
3535.5  Fab (.866)  Fbc (.5)  Fbd (.5) = 0 Answered by Harley Weston. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





A dead fly is stuck to a belt that passes over two pulleys 
20090321 

From Jules: A dead fly is stuck to a belt that passes over two pulleys 6 inches and 8
inches in radius. Assuming no slippage,how fast is the fly moving when
the large pulley (8 inches) makes 21 revolutions per second ? How many
revolutions per second does the small pulley make ?
How long will it take the dead fly to travel 1 mile ? Answered by Penny Nom. 





A plane cuts a line segment 
20090317 

From Manis: Find the ratio in which the line joining (2,4,16) and (3,5,4) is divided by the plane 2x3y+z+6=0. Answered by Robert Dawson. 





A linear system 
20090313 

From Rasanga: Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1 Answered by Harley Weston. 





The equation of a line 
20090311 

From Teresa: Write an equation in slopeintercept form that has a horizontal intercept of 7/3 and a vertical intercept of 7/9 Answered by Harley Weston. 





The graph of y = 6 
20090221 

From Barb: I was given the problem that says "graph the line y = 6" how do I find all the set points that have a y coordinate of 6? I am so lost lost and have no clue how to start. Can you help me please? thanks. Answered by Penny Nom. 





Find an expression for the nth term 
20090220 

From Dawn: Find an expression for the nth term:
x= 1 2 3 4...n
y=11 8 5 2...?
I think it's a linear relation but don't know the equation that goes with it. Answered by Stephen La Rocque. 





Linear systems 
20090220 

From Rose: I have been having trouble trying to figure out these three math problems , I need help breaking them down so I could understand them better please help.
1. x = 7  x
2 x  y + 8
2. 8 x + 5 y = 1 8 4
x  y = 3
3. y + 2 x = 3
y + 2 x = 4
I can't figure out how to break them down in the right order. Answered by Penny Nom. 





The substitution method 
20090218 

From Nicolette: I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7 y=x3 How can i solve this using the substitution method? Answered by Penny Nom. 





A line parallel to a given line 
20090218 

From Lisa: I'm having a hard time understanding the concept of how to write an
equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y=mx+b.
(7,9); 2x+5y=4. i would appreciate it alot if someone can show ne how
to do this. Thank you, Lisa Answered by Penny Nom. 





Cubic feet gas to grams of gas 
20090211 

From tim: I was trying to convert cubic feet gas to grams of gas. Is there a formula to complete this task? Answered by Robert Dawson. 





Solving an equality 
20090210 

From Deborah: 2(v+10)<18 Answered by Penny Nom. 





Are these lines parallel? 
20090206 

From Conor: are these lines parallel?
y = 3x 2 and 6y = 3x +2 Answered by Stephen La Rocque. 





Congruent line segments 
20090205 

From casie: marica drew oneline segment on a graph with endpoint of (0,9) and (0,4). she drew another line segment with endpoints (1,1) and (6,1). are the line segment congruent?explain Answered by Penny Nom. 





A point on 8x^2+5xy+y^3=149 
20090204 

From Vivian: Consider the curve defined by 8x2+5xy+y3=149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k Answered by Harley Weston. 





The intersection of two lines 
20090130 

From kaylee: how do you find and graph the intersect of these two equations:
y=2x4 (and) 2y=x
thanks,
kaylee Answered by Stephen La Rocque. 





The vertical line test 
20090126 

From bob: what is a Vertical line test Answered by Stephen La Rocque. 





Linear speed 
20090126 

From Hom: A semi is driving cross country at 70mph. The tires on the semi have a 3 foot diameter. What is the linear speed in feet per minute? Answered by Robert Dawson. 





Using y = mx + b 
20090126 

From Caroline: How do you write a symbolic representation using the y=mx+b method? Answered by Robert Dawson. 





20 miles of gasoline 
20090118 

From Roger: I used the volume formula and found that a cylinder with a 3" radius X 8.75" height yields just over 231 cu. in. (one gallon) doesn't seem right, but that's what I got. Then found the percent that 8.175" is to one foot and multiplied that into the number of feet in 20 miles. I'm not good at math, so I'm starting to lose myself here. The short story is I get a cylinder that is 20 miles long and only .0000387" in diameter. Is this even close to the mark? Answered by Harley Weston. 





The point of intersection of the straight lines 
20090118 

From Kieran: Find the point of intersection of the straight lines
y=2x+4, and y+2x16=0 Answered by Robert Dawson and Penny Nom. 





Solve for x 
20090116 

From maritza: 5=3(x2)= Answered by Penny Nom. 





0.0708 lbs per linear yard 
20090116 

From Kevin: If I know that my product is .0708lbs per linear yard how do I calculate how many Linear yards are in a lb? Answered by Penny Nom. 





A line is perpendicular to another line 
20090116 

From Greg: A line is perpendicular to the line y=2x+3 and has the same xintercept as x+3y+10.
Find the equation of this line. Express your answer in the form of y=mx+b. Justify your answer. Answered by Robert Dawson. 





The table of values for y=3x10 
20090109 

From Jade: How can I know the value of x for y=3x10 in this table of values pls. include the deatails
if x=2 y=16
if x=3 y=1
but how if y=2 what is x Answered by Penny Nom. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





A line in slope intercept form 
20081208 

From laurie: the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3 Answered by Penny Nom. 





The sides of a rectangle 
20081208 

From Mitchell: The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y60=0
Point C is at (18, 14).
What is the length of segment AD? Answered by Penny Nom. 





Solve 3x +5= 4x10 
20081122 

From Nikko: HELP please how do I solve these type of questions? 3x +5= 4x10 or 4x +10= 6x8 Answered by Penny Nom. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





What is 5x+3y=24? 
20081113 

From Robert: What is 5x+3y=24??????? Answered by Stephen La Rocque. 





A belt drives a pulley 
20081103 

From Rebecca: A point on a belt is moving at the rate of 30 ft/sec and the belt drives a pulley at the rate of 200 rpm. What is the radius of the pulley? Answered by Penny Nom. 





A circle tangent to a line and with its centre on another line 
20081101 

From liza: Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Answered by Chris Fisher. 





Tangent line 
20081027 

From Maddie: Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C. Answered by Stephen La Rocque and Victoria West. 





A linear system 
20081022 

From Tiffany: solve:
x + y + z = 4
2x  3y  z = 1
4x + y  2z = 16 Answered by Penny Nom. 





The slope of a tangent line 
20081018 

From Amanda: If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Answered by Stephen La Rocque. 





Two equations in two unknowns 
20081017 

From Dushayne: Please help me in solving this problem:
a. 3x4y=32
5x+2y=10
b. 2x+3y=11
4x+3y=10 Answered by Penny Nom. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





Using the augmented matrix 
20081017 

From Karlena: I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically
x+y+2z=30
2x+3y+2z=53
x+2y+3z=47 Answered by Harley Weston. 





A tangent line to f(x) = 1/(x  1) 
20081016 

From Amanda: If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Answered by Harley Weston. 





Perpendicular lines 
20081016 

From Hailey: In the xyplane,
the line with equation 2x + y = 3
is perpendicular to the line with equation y = mx + b,
where m and b are constants.
What is the value of m? Answered by Penny Nom. 





Linear and Angular Velocity 
20081010 

From Matthew: The pedal and gear relationship of a bicycle is shown. The radii of the gears are r(sub1) = 5 cm and r(sub2)= 12 cm. The radius of the wheel is r(sub3) = 30 cm. How many rotations per minute of the pedal gear will produce a racing cyclist's speed of 60 km per hr.
For a diagram: http://bikepedalsgears.weebly.com/ Answered by Stephen La Rocque. 





A linear equation with fractions 
20081007 

From Christopher: 1/6(x18)+1/8(x+8)=x9 Answered by Penny Nom. 





The rise over the run 
20081007 

From Mak: what is the ratio of the rise to run? Answered by Penny Nom. 





Lines that pass through a point 
20080930 

From Abigail: what is the name for a point that a group of lines pass through that contains the letters c e n p i l? Answered by Penny Nom. 





The vertices of a triangle 
20080927 

From T.: how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x3y17=0,4x9y+13=0? Answered by Harley Weston. 





The standard form Ax+By=C 
20080926 

From Susan: I am having difficulty changing the pointslope form of the equation of the line yy1=m(xx1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way. Answered by Penny Nom. 





5 units from (1,2) and 5 units from yaxis 
20080926 

From Shaun: Find the points (x,y) in the plane that are 5 units from (1,2) and 5 units from yaxis.
I am more interested in the approach, in general terms, than the numerical values. Answered by Penny Nom. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





Collinear 
20080908 

From Patrick: On page 17 of my son's 9th grade math book Geometry by Jurgensen, Brown, and Jurgensen (copyright 2004),
the authors state from the diagram that you can conclude the points A, B, and C are collinear.
In the diagram, the points A, B, and C appear to be situated on a straight line; however,
nothing in the diagram states that it is a straight line. I told him that you can't conclude they are collinear
because angle ABC could be 179.9 degrees instead of 180 degrees since nothing in the diagram states otherwise.
His teacher marked his answer incorrect on a test but I still believe that I am correct. How do conclude points are
collinear if nothing tells you that they are situated on a line? Answered by Harley Weston. 





A tangent to a circle 
20080906 

From Jake: Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Answered by Penny Nom. 





Parallel and perpendicular lines 
20080906 

From C: Can you help me determine whether these lines are parallel, perpendicular or neither and why?
Problem 1: y=3x+2
y=1/3x  4
Problem 2: y=1/3x + 1/2
y=1/3 x 2 Answered by Penny Nom. 





A line parallel to y= 1/2x + 5 
20080903 

From Michelle: Find the equation of a line parallel to y= 1/2x + 5 if the required line passes through ( 3,4) Answered by Penny Nom. 





A word problem with three numbers 
20080902 

From Wanda: "Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers." Answered by Victoria West. 





Function or Not? 
20080822 

From Katie: Determine whether y is a function of x:
[(x^2)y](x^2)+(4y)=0
....thx Answered by Janice Cotcher. 





Angular & Linear Speed from a Sine Graph 
20080819 

From Kim: Kim, a student:
I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer. Answered by Janice Cotcher. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





A linear function 
20080807 

From Warren: What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function?
How will you transform y=square root of 3 x + 1 in standard form Ax+By=C? Answered by Penny Nom. 





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





Simultaneous equations 
20080723 

From Franco: Solve
3 D + E  F = 10
2 D  F = 4
3 D  4 E  F = 25
Franco Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20080722 

From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom. 





A reflected line segment 
20080714 

From Peter: Segment AB has endpoints A(1,2) and (3,1). Segment AB is reflected over the yaxis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'? Answered by Janice Cotcher. 





Overbooking flights 
20080710 

From DON: Overbooking by Airlines
This is a simplified version of calculations used by airlines when they overbook
flights. They realize that a certain percentage of ticketed passengers will cancel
at the last minute. Therefore, to avoid empty seats, they sell more tickets than
there are seats, hoping that just about the right number of passengers show up.
We will assume that the noshow rate is five percent.
For a flight with 220 seats, the airline wants to find how sensitive various
probabilities are to the number of tickets it issues. In particular, it wants to
calculate
a) the probability that more than 225 passengers show up
b) the probability that more than 220 passengers show up
c) the probability that at least 215 seats will be filled
d) the probability that at least 210 seats will be filled.
To assess the benefits and drawbacks of issuing various numbers of tickets on an
airline flight with 220 seats, create a table showing as many different scenarios
as possible (table only on one page when printed) and use a second page for
your analysis and recommendation to the airline. Which are the good cases,
which are the bad cases for the airline? Answered by Janice Cotcher. 





A rectangular room 
20080630 

From Peter: A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side? Answered by Penny Nom. 





A line which is perpendicular to another line 
20080618 

From Emily: How do you solve perpendicular bisectors with a slope and a point? Answered by Penny Nom. 





Substitution method 
20080530 

From taquicia: 2yx=3
x=5+y Answered by Janice Cotcher. 





x/4 = 3 1/2 
20080530 

From Kelsey: How do you solve for "X" in the problem below?
X
 = 3 1/2
4
Kelsey Answered by Victoria West. 





Elevation gain 
20080518 

From Mark: How do you calculate elevation gain on a treadmill? e.g. 5.0 miles (26,400ft) @ 15% incline.
I have been estimating it as 26,400 x .15 = 3,960 ft of elevation gain.
Hopeful Mount Rainier Climber Answered by Victoria West. 





How old are the sisters? 
20080511 

From George: Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice as old as her sister.
Find the present age of the two siblings. Answered by Penny Nom. 





A linear model 
20080509 

From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of 25,195 per year with t represents the number of years since 1994? Answered by Penny Nom. 





15 + 0.10n = 0.25n, solve for n 
20080424 

From monica: 15 + 0.10n = 0.25n
Solve for n. Answered by Penny Nom. 





x/3 5 = 3(x2) 
20080420 

From Mrs: I am having trouble helping my son solve the following equation:
x/3 5 = 3(x2) Answered by Penny Nom. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





The slope intercept form 
20080411 

From Dave: Hi, why is there a yintercept in the slope intercept form?What does the yintecept have to do with the equation? Answered by Penny Nom. 





The shortest distance from a point to a line 
20080403 

From Katherine: How do I find the shortest distance from the point (3,5) to the line x = 2 Answered by Stephen La Rocque. 





A linear system 
20080310 

From sandhiya: one group of people purchased 10 hotdogs and 5 soft drinks at a cost of
$12.50. a second group bought 7 hotdogs and 4 soft drinks a ta cost of $9.00
find the cost of a single hot and a single soft drink.(using the row echelon form to solve) Answered by Penny Nom. 





Two perpendicular lines 
20080307 

From Daphne: Does anyone know how to find a line perpendicular to 3x=4y=20 and
passes through the point (12,0)? Answered by Stephen La Rocque and Penny Nom. 





Simultaneous equations 
20080229 

From CONOR: I was wondering if you could help me with this problem
7x  5y = 1
3y = 4x Answered by Penny Nom. 





A line drawn between 2 vertices 
20080226 

From Arshad: what is a line drawn between 2 vertices which are not next to each other called. Answered by Penny Nom. 





The equation of a line 
20080217 

From Jennifer: Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form ) Answered by Penny Nom. 





The slope intercept form of a line 
20080217 

From chris: find the slope and y intercept of the line (2x+4)3y=11(x1)
is this equation in slope point form. Answered by Penny Nom. 





A inear system 
20080203 

From Kelly: is (1,5) a solution of each system? y=x+4 y=1/5x Answered by Penny Nom. 





Two equations in x and y 
20080201 

From leslie: 6x+8y=40 4x+5y=25 Answered by Penny Nom. 





The standard form of a line 
20080130 

From Thomas: I'm attempting to get this in standard form
slope=3;(1,5) Answered by Penny Nom. 





Linear feet to metres 
20080125 

From Jillian: i have a measurement of something in linear feet. i dont know what a linear foot is so i want to convert it to meters to have an idea.
how do i convert. Answered by Penny Nom. 





The standard form of a line 
20080124 

From James: I need to put it in Standard from ax+by=c the problem is
(4,0); parallel to y=2+1 how can I put this in Standard from Answered by Stephen La Rocque. 





Find the slope of the line with equation 73y=2x 
20080123 

From nell: Find the slope of the line with equation 73y=2x Answered by Stephen La Rocque. 





A linear system 
20080122 

From Lisa: I am supposed to use augmented matrices to solve this system of equations. x  3y = 5; 4x  12y = 13. I think it is unsolvable but I want to be sure I am not just giving up. Thanks in advance for your help! Lisa. Answered by Stephen La Rocque and Brennan Yaremko. 





The equation of a line 
20080120 

From Sara: The question is:
Write the equation of a line that is parallel to y=3x2 through the point (5,9).
I think the correct equation for this is y=3x+24.
But I have to write it in standard form, and I can't seem to figure out how to do that. Please answer soon! Thanks! Answered by Stephen La Rocque and Penny Nom. 





The line through (22 ;1) and (23, 2) 
20080120 

From Zachery: i have a slope that equals 1/1 and my coordinates are (22;1) and (23;2) and i am trying to change it into the equation y=mx+b and the farthest that i've gotten is y=1x_ (i can not find out how to find b.) So i was wondering if you could help me find out what b is because i have got no clue!!!!! Answered by Penny Nom. 





How many rolls of stock do I need to buy? 
20080116 

From Dan: How many rolls of stock do I need to buy?
Given:
The rolls are 40" wide, 20" roll o.d., 4" core o.d., gauge is 0.008"
I need to cut these master rolls in 6" strips (4" of waste per master roll)
and I need 1,270,500 linear feet of this strip. Answered by Stephen La Rocque. 





Linear systems 
20080110 

From Sandra: I have two questions. Please solve both. Thank you.
1.) In your chemistry class, you have a bottle of 5% boric acid solution and a bottle of 2% boric acid solution. You need 60 milliliters of a 3% boric acid for an experiment. How much of each solution do you need to mix them together?
2.) You plant a 14inch hemlock tree in your backyard that grows at a rate of 4 inches per year and an 8 inch blue spruce that grows at a rate of 6 inches per year. In how many years after you plant the trees will the trees be the same height? How tall will each tree be?
Thank you. I did not understand neither problem, so I could not show any work. Please help. Answered by Stephen La Rocque and Harley Weston. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





Donuts and bagels for the first period class 
20080108 

From Karen: Mr. Pace bought breakfast for his first period class. Ten donuts and fifteen bagels
cost a total of $15.75. Mrs. Pace bought breakfast for her class. Five donuts and twenty
bagels cost a total of $17.00. Set up and solve a system of linear equations to determine the cost
of one donut and one bagel. Answered by Penny Nom. 





What is the speed of the plane in still air? 
20080105 

From oscar: A plane flies 400 miles with the wind and 340 miles against the wind
in the same length of time. If the speed of the wind is 24mph, what is
the speed of the plane in still air? Answered by Penny Nom. 





The shortest distance to a line 
20080104 

From nana: 3y+4x12=0 is the equation of the line AB on a graph......the line AB joins both y and x axises together.....point A is on y axis and its value is 3....point B is on x axis and its value is 4.....Question : from point O(0,0).find the point ont the line AB Answered by Stephen La Rocque. 





Finding the equation of a line from its graph 
20071225 

From ken: I have a graph and it is asking me to find the slope of each line, and
then write its equation. the graph show a negative slope. Would
appreciate the answer if you could show me how to do this question.
Kind regards: Ken Answered by Stephen La Rocque. 





Linearize a graph 
20071219 

From Justene: My daughter has a physics lab where she must linearize a graph of acc vs. mass. I have no idea how to help her. Answered by Stephen La Rocque. 





Plotting a function 
20071206 

From Paula: My son has a problem that says plot the point:
2x3y=9
I have explained to him that there must be a function for y in order to plot that point, but he doesn't think so. The question above that one says find the function for y, and I assume we should use that function. Am I wrong? Can we plot a point without a y function. Answered by Stephen La Rocque. 





An augmented matrix 
20071129 

From Beth: I am having troubles fiinding this augnmented matrix. I know how to do it
but everytime i do it it get a different answer and its not the right answer.
Could you help me to make sure I do it right?
Here is the problem:
4x  3y = 5
2x +9y = 6 Answered by Harley Weston. 





Straight lines 
20071126 

From Divyansh: hello
i am in eleventh class and am, preparing a project on straight lines
i cant really find uses of straight lines and its equations in daily life
i am also thankful to you in advance and am waiting for your answer eagerly because i need to submit my project only this week
thanking you Answered by Penny Nom. 





Two lines 
20071118 

From Kate: represent qraphically the equations of these lines and their intersecting points
xy=2
3x+y=11 Answered by Penny Nom. 





Why do they use the letter b in y=mx+b? 
20071115 

From virginia: why do they use the letter b in y=mx+b?
im asking this because my math teacher said he will give extra points to anyone who finds this out first
and i was hoping you guys would be the ones who could help. Answered by Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





I have a piece of material 44 inches by 78 inches 
20071102 

From Marianne: I have a piece of material 44 inches by 78 inches. How many linear yards can I get from it? Answered by Penny Nom. 





collinear points 
20071026 

From Carl: the points H,S,D,K,L, and B are collinear.
KS+SB=KB
DH+HS=DS
DH+HK=DK
point L and B are not between any other labeled points on the line.
<> Answered by Penny Nom. 





A line parallel to a given line 
20071020 

From Samaira: Given Y=2/3 + 3/4x
Give the equation that is parallel to the given one and which touches the xaxis in x=3 Answered by Leeanne Boehm and Stephen La Rocque. 





Domain and range 
20071012 

From Dawn: Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help. Answered by Penny Nom. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Equation of a tangent line to a function 
20071004 

From Princess: If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Answered by Stephen La Rocque. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





The incline of my yard as it slopes away from my house 
20070922 

From Janet: I need to calculate the degree (or is it percent?) of incline of my yard as it
slopes away from my house. Do I visualize a right angle formed by a
level line from the bottom of the slope to the side of the house, and then
compare the line of the slope against the right angle to get the degree?
Or is an incline calculated by the measurement of the rise in 100 feet? For
instance, if the ground rises 3 feel in a distance of 100 feet, is that a 3%
incline? And if it rises 4 feet in a distance of 25 feet, is that a 16% incline?
Thanks so much. Answered by Stephen La Rocque. 





Two equations in two unknowns 
20070922 

From Mary: Having problems doing this problem, looking for a solution with the work. I would like to see how you got your answer, to see what I was doing wrong.
solve using the substitution method, is there "no solution" or "infinitely many solutions"
4x+y=4
2x+8y=0 Answered by Stephen La Rocque and Leeanne Boehm. 





Segments on a line 
20070910 

From Cathy: This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments. Answered by Penny Nom. 





The slope of a line 
20070906 

From Danielle: Hello. I need some help with this: i am supposed to find the equation of a line with a point
(2/3,5) and (5/6,4) the answer in the book says y=6x+1. My question is how did they get
for the slope? Answered by Penny Nom. 





Perpendicular lines 
20070906 

From dinesh: we know that for two perpendicular lines
m1*m2=1perpendicular
but this is not true for xaxis and yaxis? Answered by Harley Weston. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





Two coplanar lines 
20070821 

From Robin: I am going two show that the two lines are coplanar:
(x5)/4=(y7)/4=(z+3)/5
(x8)/7=y4=(z5)/3
I know I have to find a point that lie on both lines, but dont really get it. Answered by Stephen La Rocque and Penny Nom. 





Pointslope form 
20070816 

From jenny: write an equation in the pointslope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,1)
slope= 5,passing through (4,2)
slope= 2,passing through(0,3) Answered by Leeanne Boehm. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





A nonlinear system 
20070814 

From Marsia: Explain how the solution of a nonlinear system could be just a point, or two points. Sketching these may make it easier Answered by Penny Nom. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





Equation of a perpendicular line 
20070728 

From Marina: Find the equation, is standard form, with all integers coefficients, of the line
perpendicular to x+3y=6 and passing through (3,5) Answered by Stephen La Rocque. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





A linear system 
20070629 

From Kim: solve for x,y,z
xy+z=4
2x+2yz=2
x2y+2z=7 Answered by Harley Weston. 





The substitution method 
20070623 

From mary: solve the system by the method of substitution:
5x+2y=15
4xy=9 Answered by Stephen La Rocque. 





Factor X^6  64 
20070620 

From Krystal: How do I Factor X^6  64 into linear factors? Answered by Penny Nom. 





A system of linear equations 
20070614 

From Alfredo: A student club sponsored a jazz concert and charged $3 admission for students, $5 for faculty, and $8 for the general public. The total ticket sales amounted to $2542.
Three times as many students bought tickets as faculty. The general public bought twice as many tickets as did the students. Set up the equations that determine how many
tickets were sold to each group and solve. Answered by Stephen La Rocque and Penny Nom. 





Two tangent lines to y=x^3 
20070607 

From stephanie: find the equations of two tangent lines to the y=x^3 function through the point (2,8) Answered by Penny Nom. 





What happens when you have zero's on both sides? 
20070605 

From Lily: On the substitution method what happens when you have zero's on both
sides of the equation? Is that considered no solution or infinitely many? Answered by Stephen La Rocque and Penny Nom. 





Equation of a line 
20070603 

From Mahrukh: Hi i would like to know how to find the equation of a line, when you are given a piont (3, 1) and the x intercept which is 1? Answered by Penny Nom. 





The intersection of two planes 
20070531 

From Sarim: How to find a intersection of two planes? Answered by Penny Nom. 





y=mx+b 
20070529 

From molly: Im having a problem with the y=mx+b for our homework we have a table that goes from 0 to 6 , 1 to 7 and 2 to 8 and we have to make a equation of that. Please help. Answered by Penny Nom. 





The distance between parallel lines 
20070528 

From Kristie: I can't figure out how to determine the distance between parallel lines I am taking
linear algebra and vector geometry. I was given two lines in the form #x+#y =#
told they were parallel and asked to find the distance between them??
Please help
Thanks Answered by Penny Nom. 





Find the equation of a line passing through two given points 
20070512 

From Kenzie: I am having problems solving an equation of the line passing through (2,4) and (6,0) Answered by Penny Nom and Stephen La Rocque. 





Linear growth 
20070511 

From Rebecca: What is the definition of linear growth? Answered by Penny Nom. 





The substitution method 
20070508 

From A student: I need help on these two problems( substitution method)
2x+7y=10
x3y= 3
and
6x8y= 12 3x+4y=9 Answered by Penny Nom. 





Slicing a doublenapped cone with a plane 
20070507 

From Andrew: I am writing a paper about creating parallel lines by slicing a doublenapped cone with a plane. I have found out how it can be shown by algebra that the equations for parallel lines are generated from the degenerate case of a second degree polynomial in two variables, but I have yet to find a source with a visual representation of this case. Do you know if it exists? Answered by Chris Fisher. 





Road incline grades 
20070507 

From cecil: convert grade percent to degrees Answered by Stephen La Rocque. 





The vertices of a triangle 
20070502 

From natakie: Find the coordinate of the vertices of a triangle whose sides lie on the following three lines.
2x+5y16=0, 4x3y6=0 and 3x+y+2=0 Answered by Penny Nom. 





Two equations 
20070429 

From lavon: I'm having trouble figuring out a linear equation, can you help?
 3x + 2y = 8
3x + 2y = 8 Answered by Penny Nom. 





Finding out if two line equations are parallel or perpendicular 
20070428 

From Vincent: Can you determine if the two lines are parallel, perpendicular, or neither
1/2x+4y=3/5
y/1 + 10/5= 8x
I think there perpendicular but how would you solve the equations Answered by Stephen La Rocque. 





A line parallel to a given line 
20070428 

From vince: write an equation of the line satisfying the given conditions
Through (2,3) parallel to 2x=3y+5 and graph both equations Answered by Penny Nom. 





A line parallel to a given line 
20070426 

From vincent: I forgot how to write the equation of the line satisfying the given conditions
through (2,3) parallel to 2x=3y+5
and how would you graph this Answered by Penny Nom. 





Two parallel lines 
20070425 

From prasanna: Let me know the Equation of a line which is parallel to some other line at a distance of Dmts. Answered by Penny Nom. 





A linear system 
20070425 

From Tee: 2x y =5
2x +=y =5
and also
3/7x + 5/9y =27 (fractions)
I have to find the addition method to both problems Answered by Penny Nom. 





Linear programming 
20070424 

From Sylvia: What is graphing linear programming? Answered by Penny Nom. 





Two lines intersect at a right angle 
20070420 

From ellen: The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point
(4,6). Determine the values of a, b & c. Answered by Stephen La Rocque. 





Ax + By = C 
20070418 

From Diana: find an equation in general form Ax + By = C with the following properties passing through points (a,b) and (2a, 2b) Answered by Penny Nom. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





Solving QuadraticLiner Equations algebraically 
20070412 

From Hector: Solving QuadraticLinear Equations algebraically.
y=x^24x+3
y=x1 Answered by Stephen La Rocque. 





No solution to a linear system 
20070409 

From Ryan: When is it possible to get no solution when solving a linear system? Answered by Leeanne Boehm, Steve La Rocque, Penny Nom and Melanie Tyrer. 





Slopes of perpendicular lines 
20070327 

From Mykolyn: How do you find the slope of a line that is perpendicular to the graph of:
y= 1/2x+4? Answered by Leeanne Boehm and Sara Ulmer. 





Solve for x and y 
20070327 

From anthony: solve y=4x and x+y=5 Answered by Sara Ulmer. 





A linear system 
20070323 

From Adam: Solve the system by graphing: 4y>6x
3x+2y<6 Answered by Stephen La Rocque and Penny Nom. 





Graphing a line 
20070323 

From mitchell: Graph each equation.
y = 2x + 4 Answered by Jaymi Peterson and Haley Ess. 





A line that is perpendicular to another line 
20070316 

From Jesse: How do you write an equation of a line that is perpendicular to
y+2x+3 and passes through (3,4); I don't understand the steps
of how to do this???? Answered by Stephen La Rocque and Penny Nom. 





Statistics data 
20070308 

From Parnini: The following table shows the expenditure on different household items by a family. Draw a line graph for the following data: Items : Food Rent Cloth Education Saving Others Expenditure : 2000 2.500 1.500 1.200 4000 3.500 Answered by Stephen La Rocque. 





Prove that the triangle ABC is isosceles 
20070305 

From Lisa: I am stuck on this problem... If AB = CD (parellel line), and Answered by Stephen La Rocque and Penny Nom. 





Simultaneous equations with fractions 
20070228 

From Alyca: Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =)
*For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?* x y 2    =   3 6 3 x y 1    = 1 12 4 2
Answered by Steve La Rocque and Ashley Mang. 





The intersection of two lines 
20070228 

From Tamara: I was told to make a graph to help solve this question. I was given two equations. One was x2y=3 and the other was 2x+y=4. We have to change it to the equation of the line format. Then we graph the line and find the point where they meet. I've been trying to do that, but when i check the answer, It turns out wrong. It's meeting in the wrong spot. I need help please. Answered by Penny Nom. 





Parallel lines 
20070227 

From Jennifer: How to you decide whether the graphs of these two equations are parallel linse: y=3x+2, y=1/3x+4 Answered by Stephen La Rocque and Penny Nom. 





A common tangent line 
20070220 

From chris: I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Answered by Chris Fisher. 





An augmented matrix 
20070213 

From Mary: I've been trying for quite some time now to figure this out. I have to solve this by using the GaussJordan Method: 3x  y = 15 2x + 3y = 10 Can anyone help me? Answered by Penny Nom and Gabriel Potter. 





Dividing money unequally 
20070206 

From Linda: I have a total of $13,826.48. It is to be divided by 15 kids  2 of the kids only get half of what the other 13 do  how much do the 13 get and how much does the 2 get? Thanks Answered by Haley Ess and Steve La Rocque. 





Nickels, dimes and quarters 
20070205 

From Avinash: Mary has 48 coins made up of nickels, dimes and quarters with a total value of $5.10. She has 4 more dimes than nickels and quarters combined. How many coins of each kind does she have? Use matrix to solve the system Answered by Stephen La Rocque. 





Patrick's new job 
20070202 

From kathy: patrick has been offered jobs by two different automobile repair shops. his income from the first shop will be $1,200 per month plus 3% of the monthly sales. the second shop will pay patrick $1,500 per month plus 2% of the monthly sales. part a let s equal the amount of monthly sales and i equal patrick's income in dollars. write a system of two equations that could be used to determine the monthly income from either shop. part b solve the equation to determine what amount of monthly sales for each shop would result in patrick earning the same monthly income, i, from both shops Answered by Penny Nom. 





The substitution method 
20070131 

From Victoria: how do i solve this problem using the substitution method? 2x5= 14 7x+14y= 5 Answered by Stephen La Rocque. 





The elimination method 
20070131 

From Addrianna: x2y=2 3x5y=7 Answered by Stephen La Rocque. 





A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 
20070127 

From Liz: A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current. Answered by Stephen La Rocque. 





The sum of the digits of a twodigit number is 13. 
20070127 

From Liz: The sum of the digits of a twodigit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number. Answered by Penny Nom. 





An algebra exercise 
20070124 

From Clara: Given x + 2y = 2 and x  2y = 18, find: a) x^2  4y^2 b) x^2 + 4y^2 Answered by Stephen La Rocque and Penny Nom. 





Line segments on dot paper 
20070121 

From Khaori: The three line segments below are drawn on centimeter dot paper.
a. Find the length of each segment to the nearest tenthousandth of a centimeter. b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not. Answered by Penny Nom. 





Points of intersection 
20070118 

From Mark: Find the points of intersection of the given pair of curves. 2x  3y = 8 and 3x  5y = 13 Answered by Steve La Rocque and Haley Ess. 





A line through the point (4, 7) and parallel to the line y=2 
20070114 

From Chasity: i am suppose to write an equation of a line through the point (4, 7) and parallel to the line y=2. please help me Answered by Penny Nom. 





A line perpendicular to another line 
20070113 

From Dusty: Find an equation for the line perpendicular to: 3x  4y + 1 = 0 passing through (4,7) Answered by Leeanne Boehm and Penny Nom. 





Write the equation of a vertical line passing through (6,2) 
20070109 

From Alex: Write the equation of a vertical line passing through (6,2) Answered by Penny Nom. 





x + 2y < 6 
20070106 

From Mike: I understand solving by graphing, but i am having trouble with the graphing of in equalities. i solved : x + 2y<6 Answered by Penny Nom. 





A linear system 
20070104 

From Harold: System A (4, 2/3) 2x3y=6 and x3y=2
I approached this problem using the addition method.
Could i have found the answer using the graphing method? Answered by Penny Nom. 





Linear inequalities 
20061201 

From Susan: how would I graph a linear inequality of y>3. Answered by Stephen La Rocque. 





An equation for a line 
20061116 

From Jessica: (3,4) m=undefined write an equation for each line given the slope and a point on the line. show your work Answered by Stephen La Rocque. 





How high is the satellite above the earth? 
20061113 

From Naomi: If the linear speed of a satellite in synchronous orbit is 1000 mi/h, how high is the satellite above the earth? Answered by Stephen La Rocque. 





The slopeintercept form 
20061108 

From Kilihea: I need to graph this equation but first need to turn it into a slopeintercept form. 6x  3y = 3 I would really appreciate it if you could help me turn it into a slopeintercept form. Answered by Penny Nom. 





The distance from a point to a line in 3 space 
20061029 

From Marie: find the distance from the point (1, 2, 3) to the line x = y = z2 Answered by Penny Nom. 





Solving a linear equation 
20061012 

From Eriona: 6p5=17. I have to solve the equation. Answered by Penny Nom. 





Plotting a linear equation 
20061009 

From Jennifer:
I am having problems explaining how to do these problems to my child .
graph:2=xy
graph the equation: 2y+x=3
Answered by Penny Nom. 





How many line segments are necessary? 
20061004 

From Varun: If you place 35 points on a piece of paper so that no three are collinear, how many line segments are necessary to connect each point to all the others? Answered by Stephen La Rocque. 





Family of lines 
20060929 

From Sasha: could a "Family of Lines" have both parallel and intersecting equations that aren't related directly but otherwise related by each other to create a curve Answered by Chris Fisher. 





a _________________ line forms a 90 degree angle with another line 
20060924 

From Lisa: a _________________ line forms a 90 degree angle with another line is this to it
what fills in the blank? first letter is E third letter is R and has 13 letters Answered by Stephen La Rocque. 





Linear systems 
20060921 

From Alexander: Hello, i have a math assignment due tonight at midnight and i need some help please
It is using the addition method to solve linear systems Answered by Penny. 





Convert a standard form to a slope intercept form 
20060914 

From Maiko: I need to know step by step procedures to convert a standard form to a slope intercept form? Answered by Penny Nom. 





Rays 
20060831 

From Natasha and daughter: My daughter, Natasha, is in 4th grade. She had the following homework question about rays that confused us:
Name as many rays as you can in the figure below. Answered by Penny Nom. 





An angle in a parallelogram 
20060813 

From Sam: Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC =30 degrees find the size of angle ADE. Answered by Stephen La Rocque. 





I want to calibrate a glucose meter 
20060727 

From John: If I have 3 glucose control solutions having:
Low  50 mg/dl
Normal  100 mg/dl
High  330 mg/dl
I want to calibrate a glucose meter but I need more than these 3 data points. How can I mix these up to get different concentrations in between 50 and 100, 100 and 330. I would like to mix up different concentrations and put them in test tubes or whatever to do some calibration work. Like 70 mg/dl, 90 mg/dl, etc. More data points should be in between say 50 and 100 since this is normal, 90 mg/dl is considered close to normal.
Answered by Stephen La Rocque. 





How old is y = mx + b? 
20060705 

From Beckie: I am taking intermediate algebra this summer (Math 95), and have a question for you. My instructor will award extra credit points to any of us who find out how old the formula
y = mx+b is. Would you happen to know the answer? Answered by Penny Nom. 





Square feet and linear feet 
20060610 

From Richard: Need to know how many linear ft are in 2800 sq.ft Answered by Penny Nom. 





Three people go to a store where there is a sale 
20060530 

From Geocee: Three people go to a store where there is a sale. One person buys two shirts, one pair of pants and one sweater. The second person buys one shirt, two pairs of pants and two sweaters. The third person buys three shirts and four pairs of pants. Find the price of each item if the first person spent $155 and the second and third person spent $235 each. Answered by Stephen La Rocque. 





How do you graph 3x + 6y = 9 by axis intercepts? 
20060522 

From Crystal: How do you graph 3x + 6y = 9 by axis intercepts? Answered by Penny Nom. 





Absolute Value vs. Standard Deviation ? 
20060424 

From Sonia: Why we don't just take the average of the absolute value of difference scores (use the mean deviation) to describe variability instead of calculating the standard deviation? Answered by Claude Tardif. 





Equation of a line in Ax + By = C form 
20060419 

From Christopher: How do you write the equation of a line with a slope of 3/8 and passing through (4,6) in Ax+By=C form? Answered by Stephen La Rocque. 





Finding the inverse of a function 
20060412 

From Sam: If g(x) = 2x+3/5 then how do I find the inverse? Answered by Walter Whiteley. 





Equations of two lines 
20060405 

From Wael: Determine a cartesian equation of the line passing through A and V as a direction vector?
1 A (2;1) and V = j
2 A (2;3) and V = i Answered by Penny Nom. 





x7=20 and 2x+5=17 
20060404 

From Janette: I'm trying to help out my daughter, it has been much too long since I've been in school. The question is x7=20 and the other question is 2x+5=17. What are the formulas? Answered by Penny Nom. 





2x+5y=3 And x+3y=7 
20060403 

From Lloyd: simplify 2x+5y=3 And x+3y=7
Answered by Penny Nom. 





Angular velocity 
20060328 

From Ben: How do you (a) express angular speed in terms of linear speed and (b) express linear speed in terms of angular speed? Answered by Stephen La Rocque. 





A line parallel to a plane 
20060328 

From Ryan:
I was wondering how I would prove the following theorem. I am completely lost at this point and all my other ideas have been extremely complicated and somewhat blurry.
"Through a point outside a given plane, there is at least one line parallel to the given plane."
Answered by Chris Fisher. 





Linear feet on a paper roll 
20060320 

From Vishal: I WOULD WISH TO KNOW OF A STANDARD FORMULA BY WHICH I CAN CALCULATE THE LINEAR FEET OF A PAPER ROLL AS PER THE FOLLOWING DETAILS:
THICKNESS: 150 GSM (GRAMS PER SQUARE METER)
REEL WIDTH: 85 CM
REEL DIAMETER: 140 CM
REEL INNER CORE: 10 CM
REEL WEIGHT: 946 KG's
Answered by Stephen La Rocque. 





2x+3y=0 and 3xy=0 
20060314 

From Lisa: my name is lisa I am doing math for work and i have a math problem to solve and i need help with it here is the question 2x+3y=0 and 3xy=0 this is one question can you help me please Answered by Penny Nom. 





The graph of y = 2x + 1 
20060223 

From Geneva: I'm having trouble with graphing equations like y=2x+1 which is my homework I'm not sure how to graph it. I'm in the 8th grade taking a 9th grade course algebra I. Answered by Penny Nom. 





Brokenline graphs and histograms 
20060216 

From George:
1. What is the main difference between a brokenline graph and a histogram? Both represent continuous variables.
2. What is the correct way to read a multiplication array: xaxis first and then yaxis, other way around or it doesn't matter?
Answered by Penny Nom. 





Two parallel lines 
20060122 

From Marbara: On my math homework I have a problem where it says find the value of x so that L is parallel to M
on one of the there are three lines. the top one is horizontal which is L. the bottom one is also horizontal directly under L which is M. there is another line that is diagonal going through the middle sections of L and M.
To the right of the diagonal line and right under line L is an equation 5x10
to the right of the diagonal line and right above line M is an equation 8X5
I tried to find what X is but I can't because it never matches both equations no matter what way I try to do it. Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Answered by Penny Nom. 





Intercepts and slope 
20060115 

From Anthony: Given 1.7x + 0.8y=7.1:
(a) state the intercepts and slope for the graph
(b) Draw the graph Answered by Penny Nom. 





y  y1 = m(x  x1) 
20060108 

From Greg: How do you change 2x + 3y = 7 into y  y1 = m(xx1)?
Answered by Penny Nom. 





Simultaneous Equations 
20051221 

From Matt: I have these two equations,
336 = 60a + 10b
and
432 = 84a + 6b
Am I right in saying both a and b are 4.8? Answered by Penny Nom. 





5(x3)/4 =x+1 
20051214 

From Jennifer:
I have two problems i am stumped on I don't know how to help my daughter.
5(x3)/4 =x+1
3(x+12)/5 =x +2
Answered by Penny Nom. 





2/n +4 = 10 4/3n 
20051211 

From Jennifer:
2/n +4 = 10 4/3n
5(x3/4) = x+1
Answered by Penny Nom. 





Solve for x 
20051204 

From Lisa: 5(x4)=3(23x) Answered by Penny Nom. 





Express t as a function of d 
20051130 

From Matthew:
I have a problem on my homework I cant seem to figure out. Basically it gives me this Linear Regression Equation:
ln t=1.5 ln d0.8954
and it wants be to transform the equation expressing t as a function of d. For some reason I keep getting it wrong. Anyone got an idea of how to do this?
Answered by Penny Nom. 





Graphing two lines 
20051120 

From A student: About y = 5x + 24 and y = 3x  8
1. Graph both equations on the same set of axes. When you made your graph, how did you choose the range of x and y values?
2.Find the point of intersection for the graphs.
3. Test the point of intersection you found by substituting its coordinates into the equations. Do the coordinates fit the equations exactly? Answered by Penny Nom. 





Solving a pair of equations 
20051110 

From Steven: what is answer to
2 x + y = 1
y = ^{1}/_{3} x  4 Answered by Penny Nom. 





What is the angle between 2 noncollinear parallel lines? 
20051017 

From Ben: What is the angle (if any) between 2 noncollinear parallel lines? Answered by Chris Fisher and Walter Whiteley. 





2x  5x + 6.3 = 14.4 
20051016 

From Leslie: How do we solve 2x  5x + 6.3 = 14.4 Answered by Penny Nom. 





A piecewise function 
20050915 

From Duncan: A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Answered by Penny Nom. 





Graphing a linear inequality 
20050826 

From Gina: When graphing a linear inequality, how do you know if the inequality represents the area above the line? Answered by Penny Nom. 





Labour efficiency 
20050823 

From Rob:
The problem, on the surface, seems very simple and yet has created some controversy among a group of accountants. The problem itself has to do with labour efficiency rates and only involves two variables; standard working hours, and actual working hours. The difficulty lies in deriving an efficiency % from these two numbers.
Standard working hours or the targeted number of labour hours required to produce one widget, which I will represent as "s". Actual working hour or the actual number of labour hours require to produce one widget, which I will represent as "a". Labour efficiency I will represent with "E". The prevailing calculation with which I have a problem with is this:
s/a=E or if s=3000, and a=4000 then 3000/4000=75%
What bothers me about the calculation is that the standard hours get represented as a percentage of the actual hours and in my opinion changes the focus of the calculation from standard or target, where it should be, to the actual hours. I cannot define why, but this just seems inherently wrong to me.
The calculation that I use:
(1+((sa)/s))=E or if s=3000, and a=4000 then (1+((30004000)/3000))=66.67%
My calculation is like a %change from standard calculation. However, there is something that also concerns me about my calculation.
If you substitute 100 for a and 50 for s, then you come to a quandary, because if you plug those numbers into the second equation the result is of course zero % efficient which doesn't sit right with me either. If you plug them into the first calculation you get 50% efficiency which doesn't really seem to work either, because you require 100% more hours to do the same work in this case. ???
Is the first calculation correct? Am I missing something altogether? Are both calculations off base? Answered by Harley Weston. 





The substitution method 
20050628 

From Addie: how do i know where to began the substitution method? how do i solve
y = x + 1
2x  y = 1 Answered by Penny Nom. 





Angle of incline 
20050515 

From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom. 





Ax + By = C 
20050403 

From Farzana: I was wondering if you could please explain to me how I would write the equation of line through the given points [(3,7), (0,5)] in Ax+By=C form. Answered by Penny Nom. 





The shortest distance from a point to a line 
20050330 

From carly: Find the shortest distance from the point (15, 2.5) to the line 5x+6y=30. Answered by Penny Nom. 





Gasoline in a cylindrical tank 
20050323 

From Jennifer:
Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l".
I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is.
Also, the part I am really confused on is this one,
E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal?
Answered by Penny Nom. 





1 pied linéaire 
20050218 

From Christiane: Pouvezvous m'indiquer 1 pied linéaire égale quoi? 3 pied....? Answered by Claude Tardif. 





A line segment connecting two vertices of a polygon 
20050202 

From James: What is a line segment (not a side) connecting two vertices of a polygon called? Answered by Penny Nom. 





Two intersecting lines 
20041218 

From James: Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes! Answered by Harley Weston. 





The tangent line at an inflection point 
20041128 

From Louise: the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Answered by Penny Nom. 





An ODE 
20041110 

From David: I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Answered by Harley Weston. 





The point slope form of a line 
20041026 

From Jack: Given a set of ordered pairs, ie (1,1) (2,4) (3,7), how does one determine the rule f(n) other than by trial and error Answered by Penny Nom. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





Pizza for Jack? 
20040916 

From Grace: Jack is playing pool with Jim for $1 a game. He has only $2 and decides to play until he goes broke or has $5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have $(i1)after one game is he starts with $(j1). For example, a23  .40 since there is a 40% probability that Jack will end up with $1 after a game is he starts the game with $2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have $4 after one game if he had $1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates $5, a11 and a66 are both 1.
Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has $2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, $0$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value. Answered by Penny Nom. 





Solving an equation 
20040614 

From Anthony: I was hoping that you could help me with this problem. I believe that this is a high school level problem but as an adult who has forgotten the "rules", I am stuck.
the equation is this: x=t2/(t1t2)
we know that x=5.73
t1=303
we must solve for t2 Answered by Penny Nom. 





The equation of a line 
20040430 

From Amy: Write the equation of the line that contains the point (4,6) and is perpendicular to the line y=5x+100. Answered by Penny Nom. 





The line through (4,2) and (4,8) 
20040417 

From Kim: Write an equation for the line.
Given points (4, 8) and (4,2) are on the line.
I believe m=undefined.
How do I solve for b when m is undefined, and then plug in the values for m, b, and y?
Answered by Penny Nom. 





Graphing lines 
20040208 

From A student: how do you solve y=1\3x+3 and y=1\3x3 by graphing? Answered by Penny Nom. 





The incline of an exercise machine 
20040202 

From An exerciser: This is a question about incline percentage. On an exercise machine if the elevation is raised 3 and one half inches from a level position then what would be the incline percentage? Answered by Penny Nom. 





Intersecting a line and a curve 
20040129 

From Senthil: between line and curve how can i
find intersection point?
could you write me the formula and explanation also sir. Answered by Penny Nom. 





Solving an equation 
20040103 

From A student: the question is to solve and check equations and the question is
2n + 3n + 7 = 41 Answered by Penny Nom. 





Making a windmill 
20040102 

From Matthew: I am a farmer in Ontario. It has been almost 20 years since high school. I am toying with making a windmill. The output chart for the the old generator I have is shown below. Before I tear it appart I would like to develop a formula from the chart that can predict the output at various speeds. Answered by Penny Nom. 





How far can you see? 
20031215 

From Judy:
How far apart, assuming no obstacles, can two people stand and still see each other?
i know this deals with the curvature of earth, but i can't figure out the formulas involved.
Answered by Chris Fisher. 





Mr.Carter is very cautious 
20031126 

From Bob: Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo $650 form my investments? Answered by Harley Weston. 





A point and a line 
20031119 

From Meenakshi:
Given a line segment L(x_{1},y_{1})
to (x_{2},y_{2}) and a Point P(x_{3},y_{3}).
I need the formula to find a point on the line L that is closest to
the point (x_{3},y_{3}). Answered by Penny Nom. 





Lines 
20031114 

From A student: What is a name that a group of lines pass through? Answered by Chris Fisher. 





A least squares line 
20031109 

From Michelle: Hooke's Law asserts that the magnitude of the force required to hold a spring is a linear function of the extension e of the spring. That is, f = e0 + ke where k and e0 are constants depending only on the spring. The following data was collected for a spring; e: 9 , 11 , 12 , 16 , 19 f : 33 , 38 , 43 , 54 , 61 FIND the least square line f= B0 + B1x approximating this data and use it to approximate k. Answered by Penny Nom. 





Intercepts 
20031104 

From A student: I am totally confused on how to determine intercepts of an equation and then to graph the line. For example, how to determine the intercepts of 2x3y12=0. Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





Two line segments and a plane 
20030911 

From Laura: Do all figures made up of two segments lie in a plane? Answered by Penny Nom. 





The incline of a road 
20030803 

From A driver: incline % grade as to degree. ie 6% hwy grade= what degree of incline? Answered by Penny Nom. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





The substitution method 
20030414 

From Patty:
I need help with the following: 5x  4y = 13 2y + 3x = 1 Answered by Penny Nom. 





A number line 
20030227 

From Shery:
My seventh grader problem of the month 0__________1______________5____> This is a arrow, the number should be below A.Mrs Decker created an arrow representing a number line shown above. She wanted to find points and label them with a heart (G) for Valentine's Day so that the fraction 5/g is less than 1. (be sure to mark the G and not the fraction 5/g). She pondered, "Are there any other locations for G?" Is so help her description the location of all these points. If not why not? Answered by Penny Nom. 





Two investments 
20030207 

From A student: you have $7200 in principal and invest different sums @ 10% and 14%. You receive 920 at end of term. (one year)What amounts are invested at what rate? Answered by Penny Nom. 





Two equations in two unknowns 
20030206 

From Patrick: What are all ordered pairs of real numbers (x, y) for which: y^{x2  7x + 12} = 1 and x + y = 6? Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





The intersection of conics 
20021219 

From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston. 





x + y=80 and x + z=100 
20021128 

From PJ: x + y=80 x + z=100 can you solve for x, y or z? Answered by Penny Nom. 





A two stage rocket 
20021126 

From Hoda: a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex). Answered by Claude Tardif. 





Performance reviews 
20021121 

From Lara: Perhaps you can help. He's doing performance reviews at work. The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year. The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year. How do I solve for the other performance review numbers. Answered by Penny Nom. 





The substitution method 
20021115 

From A student: Solve by using the substitution method. x = 3y  1 x + 2y = 9 Answered by Penny Nom. 





Determining a parabola 
20021106 

From Shelley: let (0,3) and (1,9)and (1,1) be given points in a parablola. Determine a b and c Answered by Penny Nom. 





A linear function 
20020909 

From Chad: If y = 9x  13 does it represent a linear function? And if it does what is its slope and is it a direct variation? Answered by Peny Nom. 





Mixing gas and oil 
20020827 

From Sherry: how do I calculate the correct fuel ratio for a boat motor? 50:1 the oil containers only say how many ounces to add to 5 gallons of fuel to make a 50:1 ratio.(13 ounces to 5 gallons of fuel) I have a 20 gallon tank so what if I add 11.6 gallons of fuel, what formula would I apply to get the correct measurement of oil to add? Answered by Penny Nom. 





Parallelograms 
20020821 

From Moorthy: 11 parallel lines are intersected by another 9 parallel lines.Then how many parallelograms are formed? Answered by Walter Whiteley. 





Two equations 
20020726 

From Derek: 1. 3x + 2y = 4 2. 7x + 2y = 24 finding x and y. Answered by Penny Nom. 





Linear programming 
20020527 

From Jes: A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of $8 on each Part I and $5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit? Answered by Claude Tardif. 





25m = 100 
20020422 

From Megan: If 25m = 100, Then m equals what number? Answered by Penny Nom. 





Lines of symmetry 
20020422 

From Cindie: How many lines of symmetry do the following figures contain? trapezoid: rhombus: hexagon: pentagon: Answered by Walter Whiteley. 





An augmented matrix 
20020420 

From A student: Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is a+2b+c=0 2a+5b+4c=1 ab9c=5 Answered by Penny Nom. 





3/4n6=12 
20020407 

From Diane: I am in 6th grade advanced math and I just started Algebra. My teacher tries to explain it to me but I just can't get it. I am having difficulty understanding it. Please HELP!!! I will type a problem, if you could answer it and show your work so i can understand it that would be great. Please explain in simple terms. here is a couple problems I am having trouble with, PROBLEM #1 3/4n6=12 Answered by Penny Nom. 





Pairs of equations 
20020404 

From A student:
high school level student is asking
y=4x x=4y
x+y=5 3x+2y=20
y=x1 3xy=4
x+y=3 2x3y=9
x+5y=4
3x+15y=1
. . .
Answered by Penny Nom. 





If the matrix A is inverible and AB =AC, then B = C 
20020327 

From Vikki: i hope you can help i am soooo stuck here goes: a)
A= 0 1 B= 1 1 c= 2 5 0 2 3 4 3 4
A,B and c are matrices Evaluate AB and Ac (which I can do) then
b) I need to prove that if the matrix A is inverible and AB =AC, then B = C. Why does this not contradict what happened in part a)? Answered by Leeanne Boehm. 





The slope of a tangent line 
20020304 

From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston. 





The substitution method 
20020224 

From Joe: whats the answer to this question? 3x+y=11 x+2y=3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom. 





Linear regression 
20020116 

From Murray: If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]m*x[m]b) is at its absolute minimum. Answered by Harley Weston. 





Algebra review questions 
20020114 

From A student:
 A wildebeast was observed racing a distance of 86.4m in 4.8 seconds. Find the speed of the wildebeast in m/s.
 8x  7  5x = 23
 7 z  3 (z + 2) = 26
Answered by Penny Nom. 





Simultaneous equations 
20011217 

From Matthew: 4x + y = 4 2x  3y = 5 what is x and y Answered by Penny Nom. 





A 1 m by 1 m square box in the xyplane 
20011215 

From Murray: Inside a 1 m by 1 m square box in the xyplane, there are finitely many line segments, whose lengths sum to exactly 10 m. Show that there exists a straight line in the plane which crosses at least six of these line segments. (Hint: first, show that there exists a straight line in the plane which crosses at least five of these line segments.) Answered by Claude Tardif. 





y = zx  x  c 
20011211 

From Andrew: Could you please help me work out the value of x where: y = zx  x  c Answered by Penny Nom. 





Normal lines 
20011211 

From Kristie: Why are perpendicular lines called normal lines? Answered by Chris Fisher. 





Two equations in two unknowns 
20011204 

From Courtney: y = 3x + 2 y = 4x  5
solve for x Answered by Penny Nom. 





Slope intercept form 
20011127 

From A student: what is slope intercept form? Answered by Penny Nom. 





Matrix 
20011121 

From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom. 





A tangent line 
20011121 

From A student: write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Answered by Harley Weston. 





3x1/2(x4)+5= 3 
20011113 

From Tausa: 3x1/2(x4)+5= 3 Answered by Penny Nom. 





Lines in the plane 
20011021 

From Greg:
*If the line with equation 3x4ky= 16 has yintercept 2, find k. *Write the equation of the line passing through (2,5) and perpendicular to the line passing through (2,4) and (6,1) Answered by Penny Nom. 





A function or not a function? 
20011018 

From Christian: Which are the following are not functions?  y = x^{2}
 y = x^{3}
 x = y^{2}
 y = 3
Answered by Leeanne Boehm. 





A line in 3 dimensions 
20011017 

From Murray: I'm working on a complicated proof and i need the equation for a line in 3 dimensions. Answered by Claude Tardif. 





A linear inequality 
20010917 

From Eric: How can I solve x + y + x  y< =6? Answered by Penny Nom. 





Linear regression 
20010801 

From A student and a mother: My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation rxy and standard estimate of errorSy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related. Answered by Chris Fisher and Penny Nom. 





The best linear model 
20010729 

From Rebeca: I am a student (senior) summer hire working for Dept of the Army Resource Management. I've been assisting the Analyst in developing a model to predict training costs. The technique we used was simple linear regression. Now I've been asked for my opinion in choosing the best model I feel is better. I've chosen #1. Garrison Training but I want a second opinion before I give my choice. I've taken basic statistics last year in high school and will probably be taking more this year. Could you look over the information and give me a reason my choice would not be best? The dep variabley, is Training costs in dolars per day. Model  Ind Variable X  a  b  r  sy.x  1.  Garrison Training  126.31  0.982  0.9055  117.2  2.  Local Training  212.16  1.37  0.7937  142.7  3.  Man Rig Area  116.38  2.47  0.6481  175.6  4.  Major Training  346.12  4.67  0.7280  167.2  Answered by Andrei Volodin. 





Matrix reconstruction 
20010719 

From Guy: Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix? Answered by Walter Whiteley and Patrick Maidorn. 





The shortest distance from a point to a line 
20010605 

From Kat: Find the shortest distance from the given line. Round to the nearest tenth. (2,1) and x+5y+20=0 Answered by Penny Nom. 





Common solution 
20010602 

From Samantha:
 Solve for common solution: x+y=6 2x3y=2
 Solve for y in terms of x: 3xy=4
Answered by Penny Nom. 





Solving some equations 
20010416 

From Justin: Solve the following equations for x  x+7=10
x=
 x7=10
x=
 3x=7
x=
 x/3=10
x=
 .
 .
 .
 .
Answered by Penny Nom. 





Where do the lines y=2x4 and y=x1 intesect? 
20010406 

From Bryce: solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x4 and y=x1 intesect? Answered by Penny Nom. 





Matrices 
20010326 

From Peg: What are some applications of matrices, basic trigonometry, and linear systems in the real world? I'm writing and Algebra report about where these topics are used outside of the classroom. Answered by Judi McDonald and Walter Whiteley. 





Systems of equations 
20010316 

From joy: How do u solve problems using systems of equations? ~ finding x and y~ ex:
26 = 3x  2y 42 = 4x + y Answered by Penny Nom. 





The substitution method 
20010305 

From A student: Solve each system of equations by the substitution method. Show your work.  y = 8
7x = 1  y
 y = x  1
4x  y = 19 Answered by Penny Nom. 





Solving Equations 
20010223 

From Stephanie: Do you know who came up with solving equations? Do you have any websites that can give me good information on solving equations? Do you know any history on solving equations? Do you know what solving equations is used for? And finally............Sorry about all of the questions :) Has the form of solving equations changed from the time it came out to now? Answered by Juci McDonald. 





Linear equations 
20010213 

From Jamie: I have a question how do you do linear equation? Answered by Penny Nom. 





Kinds of lines 
20010209 

From Robyn: What are the different kinds/types of lines? Answered by Leeanne Boehm. 





Partitioning of an arbitrary line segment 
20010208 

From David: Did Euclid's Geometry include a construction for the regular partitioning of an arbitrary line segment? Answered by Chris Fisher. 





Vitamins A and B 
20010114 

From Sara: A diet is to include at least 140 mg of Vitamin A and at least 145 mg of vitamin B. these requirements are to be obtained from two types of food. type X contains 10 mg of vitamin A and 20 mg of vitamin B per pound. Type Y contains 30 mg of vitamin A and 15 mg of vitamin B per pound. if type X food costs $12 and Type Y $8 per pound, how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost? Answered by Claude Tardif and Harley Weston. 





Blood flow and age 
20010111 

From Gayle: I don't understand the second part of this problem Here is the first part that was correct. A 35yr old has 100% blood flow. A 65yr old has 64% blood flow. Find the rate of change per yr in the percent of blood flow. (This part is correct) m=(64100)/(3565)= 36/30= 1.2 per year of blood flow. Now, here is the second part I DON'T UNDERSTAND! .Let b represent the percent of blood flow and a represent a person's age. Write an equation that you could use to predict the percent of blood flow for a person of any age over 35. Answered by Penny Nom. 





Networks of satellites and linear spaces 
20001208 

From David: Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.  There are at least two distinct satellites.
 For each pair of satellites there is exactly one network containing them.
 Each network contains at least two distinct satellites.
 For each network, there is a satellite not in it.
What is the least number of satellites. what is the least number of networks? Answered by Penny Nom. 





A piecewise linear equation 
20001124 

From Jacky: There is a light bulb and it is given that the light bulb cost $0.75 and the cost of operating it is $0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph. Answered by Harley Weston. 





Solving an equation 
20001114 

From Heather: 4x3 = 3x+4 these kinds of problems i dont get but everything else in my math class i have got. i just dont understand it. Answered by Penny Nom. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





Pillows and Cushions 
20000927 

From Fiona:
The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day. Answered by Harley Weston. 





Buying art supplies 
20000918 

From Travis: An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50 Sketch Pads $3.00 Paint Sets $10.00 Answered by Denis Hanson. 





Two linear equations 
20000914 

From David Dean: 2a + 1b = 3.39 3a + 3b = 6.59 What formula do I use to find what a = ? Answered by Harley Weston. 





How many planes contain a line and a point? 
20000830 

From Harold: How many planes contain each line and point? Answered by Harley Weston. 





Three points on a line 
20000825 

From Casey: I am trying to find the slope and yintercept of an equation. I have THREE x values and THREE y values. How do you do it? Help! Answered by Penny Nom. 





Slope 
20000819 

From John K. DePonte: My question is to why the variable "m" was chosen to represent the slope of a linear equation. I always told my class to think of "m" for "m"ountain slope. But what is the real reason for this? Answered by Penny Nom. 





Two linear systems 
20000801 

From A student: please help me with this homework question. 5/x + 6/y= 19/6 3/x + 4/y =2 hint: let a = 1/x and b = 1/y substitute these expressions into the system to find a and b. Then find x and y. This is a question I answered wrong on a test: solve the given system for x, y, and z. Express your solutions in terms of a, b, and c. Answered by Penny Nom. 





Lines on an oscilloscope screen 
20000620 

From Janis Watson: What are the proper names for the vertical and horizontal lines on a graph? I am trying to explain an oscilloscope screen, and I don't know what to call these, except "vertical lines" and "horizontal lines." Answered by Penny Nom. 





The equation of a parabola 
20000522 

From Ian Forsyth: Given the points A(0,0) B(60,10) C(24,d) find the equation of the parabola. leave the equation in terms of x, y and d if the general form of a quadratic is y = ax^{2} + bx + c. Answered by Penny Nom. 





Graphing a linear function 
20000517 

From Chelsea: I need help with grahing linear functions.If you could email me back the basics and how tos I would be much appriciative. Answered by Penny Nom. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Parallel and perpendicular lines 
20000508 

From Jimmy Lumpkins: Need a method for solving the following problem: Find the equation of a line through point P that is parallel or perpendicular to another line. Answered by Paul Betts. 





Taxis in Chicago 
20000327 

From A high school studenthigh school student: Suppose that taxis pick up and deliver passengers in Chicago, which is divided into three zones. Records kept by the drivers show that of the passengers picked up in Zone 1, 50% are taken to a destination in Zone 1, 40% to Zone 2, and 10% to Zone 3. OF the passengers picked up in Zone 2, 40% go to Zone 1, 30% to Zone 2, and 30% to Zone 3. Of the passengers picked up in Zone 3, 20% go to Zone 1, 60% to Zone 2 and 20% to Zone 3. Suppose that at the beginning of the day, 600 of the taxis are in Zone 1, 100 in Zone 2, and 300 in Zone 3. What is the distribution of taxis in the various zones after all have had two riders? Answered by Harley Weston. 





A system of equations in five unknowns 
20000320 

From Will: I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives . . . Answered by Penny Nom. 





Systems of linear equations 
20000310 

From Ann Marie Devereux: hi there!!, I guess I have a problem!!! 3x+4y=10 (over) 4x+y=9 2x=5y+3 (over) x=3y+1 Answered by Penny Nom. 





Angle of Intersection of Two Lines 
20000302 

From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston. 





Midpoints and endpoints 
20000215 

From Jessica Sipes: I need to know how to find and endpoint using the midpoint and the other endpoint. Answered by Penny Nom. 





Ax + By = C 
20000118 

From Fatiha Khanboubi: I was wondering if you could please explain to me how I would write the equation of line through the given points [(4,1), (6,3)] in Ax+By=C form. Answered by Harley Weston. 





Parallel lines 
20000112 

From Lori: Find an equation of the line parallel to the given line containing the given point. x + y = 2; (1,2) We know parallel line have the same slope and we know the answer y = x + 3. Answered by Penny Nom. 





Parallel planes 
20000110 

From Hugo Alvarez: When two parallel planes are cut by a third plane, the lines of the intersection are? Answered by Claude Tardif. 





Systems of equations 
19991206 

From Roger Hornbaker: I am having problem figuring out x and y solutions.  5x + y = 4
3x  y = 4  3x + 2y = 6
 3x + y = 0 Answered by Penny Nom. 





The elimination method 
19991202 

From Jennifer: Could I get an answer to this one: 2x+5y=36 3x+2y=32 I have to use the Elimination method, as I already know how to do Substitution. How do I begin and show my work? I'm attempting to eliminate the values for y. Answered by Penny Nom. 





Linear models 
19991109 

From Helen Moreno: What is a linear model? Answered by Harley Weston. 





Broken line graphs 
19991019 

From Lori Samara, Kristi Cameron and the 4th grade students: Students in Ms. Cameron's grade 4 class were wondering if a broken line can be used anywhere in the range on the y  axis when creating a broken line graph? They understand that the broken line can be used at the 0 on the broken line but what if there is a large gap in the data from 100  200? What do we do? The text book and mathematics dictionary do not answer these questions. Answered by Penny Nom. 





Length of a line 
19991010 

From Dagmara Sarudi: My question has to do with the length of a diagonal. This problem came up when I thought about the shortest distance between two points, for example walking from one point to another in my neighborhood. I can choose a zig zag route and assuming the blocks I walk are exactly the same length, it shouldn't matter what route I took, the distance I travel should still be the same when I reached my goal. If, on the other hand I could travel in a diagonal line, the distance would be shorter. But what if, in my zig zag motion, the sections get so small the route approaches a diagonal. Shouldn't it be that each separate section added together equals the value of the two original sides? Or would it suddenly equal the value of the diagonal (which, of course was shorter than the two sides added together)? What gives? Answered by Chris Fisher and Harley Weston.






Why is slope designated m? 
19990818 

From Peter Komlos: Why is the slope of a line is designated by the letter "m"? Answered by Penny Nom. 





Parametric Equations 
19990806 

From Nicholas Lawton: Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is : yc/p=xp^2cp^3 Answered by Harley Weston. 





Slopes of curved lines 
19990609 

From Stephen Ehrler: When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Answered by Harley Weston. 





Graphing a linear equation 
19990527 

From Dylan Bradley: Im in Grade ten and am doing linear equations, I cann't figure out how to make a chart for questions like y = 2x + 3 Answered by Penny Nom. 





Parallel and perpendicular lines 
19990423 

From Crystal Pilling: My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x  5y= 16, (5,6) I have to find a line that is perpindicular to this line on a graph. HELP ME PLEASE!!!!! Answered by Penny Nom. 





Shopping at Wegman's 
19990422 

From Stan: Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of $13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of $16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of $25.09. .... Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables. Answered by Penny Nom. 





y=mx+b 
19990415 

From Selena Royle: When solving a problem on slopes,and in the formula y=mx+b what do the M and B stand for? Why M and B? Answered by Penny Nom. 





Dividing a Circle 
19990412 

From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example  1 line divides the circle into 2.
 2 into 4.
 3, however into 7.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom. 





Linear programming and optimization 
19990409 

From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom. 





0/11 
19990309 

From Jacob: What is the term applied to 0 divided by a number. In calculating slope problem my answer was 0 divided by 11. I don't know what to do with this answer or how to interpret it. Answered by Jack LeSage and Penny Nom. 





Fitting a Curve 
19990119 

From Kirk Doward: Hello my name is Kirk from Scarborough, Ontario. I have been out of a formal education system for thirty years. I program microcontrollers in my spare time. I have built a temperature sensing device ready to go but, thermistors are very nonlinear. I do know that there is a way to calculate the input condition of the thermistor and display the correct temperature in degrees C. I am sending a file to show my progression so far. Answered by Harley Weston. 





Linear Equations 
19990116 

From Casie Tomney: My dad and I have been trying to figure, how to solve for x on any of these problems my teacher gives us. The problem is: 2h/3 + 1/2 = 5h/6  3/4 Thanks!!!!!!!! Answered by Jack LeSage. 





Intersection of Planes 
19981203 

From Lindsay Fear: My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes x + ay + bz = 0 ax  y + cz = 0 bx + cy  z = 0 have a line in common is that a^2 + b^2 + c^2 + 2abc = 1 Answered by Walter Whiteley. 





Algebra 
19981125 

From Casey: yeah my son brought home a math worksheet and he was wondering and me too if u could help him and me out . he has problems like this 4n+9=7n+2= ??? and he has to show work so if u could help us out that would be great Answered by Jack LeSage. 





Intersection of planes 
19981122 

From Dave Rasmussen: I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Coordinate Geometry. I have been teaching my students to write equations of planes and lines,  to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me? Answered by Walter Whiteley and Harley Weston. 





Linear systems of equations 
19981116 

From Crystal Girvan: My name is Crystal Girvan.Im in grade 11. I have a question.We are solving linear systems of equations: comparison method. My questions is. it says a)use the method of comparison to solve this system a=b1, 3a+ b=3 b) verify your solutin in a I dont understand it. please help Answered by Jack LeSage. 





A Linear System 
19981008 

From Jason Bussey: The linear systems with the following pattern all have the same solution. Is their some kind of reasoning as to why this is so? 2x+3y=4 3x+4y=5 4x+5y=6 5x+6y=7 The solution is always x=1, y=2 Thank you Jason Answered by Penny Nom. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 





A Horizontal Line 
19980923 

From Tess Warer: Find the equations of a line through (1,5) and parallel to the Xaxis. Answered by Harley Weston. 





Concurrent Lines in a Triangle 
19980810 

From Chris Woolf: The question is Name four types of concurrent lines, rays, or segments that are associated with triangles. Answered by Chris Fisher. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





Seed Problem 
19980326 

From Jody A. Johnson: Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall.  Write the particular equation giving the height as a function of time.
 Find the intercepts and explain them.
 What would be the height in one year?
 How long would it take for the plant to grow to a height of 1km?
I'm having a problem with this equation. Could you please help. Thank you. Answered by Penny Nom. 





Yintercept 
19980227 

From Don Trumpet: What is the Yintercept for the problem:Y = 2(x+2) + 9 Answered by Harley Weston. 





Intersecting Lines. 
19980210 

From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, 4186) and (770, 1816) respectively. How can that be? Answered by Penny nom. 





Calculating the Intersection Point. 
19971210 

From Milton Parsons: Given 2 lines through (x1,y1),(x2,y2),and (x3,y3),(x4,y4). Can you give me a good formula for calculating the intersection point. I would greatly appreciate it.Thanks. Answered by Chris Fisher and Penny Nom. 





How many intersections? 
19971008 

From James: (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Answered by Chris Fisher. 





Equation of a line 
19970408 

From Susan Gregson: I am a secondary school teacher. My students and I would like to know why the letters m and b are traditionally used to stand for slope and Yintercept in the standard form of an equation. Was this an arbitrary choice? Who made it? Are the letters from Greek ot Latin words? Answered by Harley Weston. 





Could you tell me the name for the bar in a division problem? 
19961021 

From Linda: Could you tell me the name for the bar in a division problem. Not the line with dots on either side but the line that divides the two numbers? My name is Linda. I am asking for my niece who is in 8th grade. Answered by Chris Fisher. 





Prove that these two lines are parallel. 
19960529 

From Adam Piekarzewski: Using parallel line theorems and side angle side etc. in triangle acd a line is drawn from point b on ac and point i on ad. another triangle fliped vertically and joined at d is named fdh, a line is drawn from point e on fd and point g on fh. ab = fg, ai = fe, ac  fh prove that bi  eg / / Answered by Harley Weston. 





Les unités linéaires 
20021112 

From Sandy: je me demande qu'est ce qu'une unité linéaire, mesures de surface et des mesures de volume. je voudrais aussi savoir quelle est la règle de transformation pour les unités linéaires, les mesures de surface et les mesures de volume Answered by Claude Tardif. 





Espaces vectoriels 
20020818 

From Bacar: Comment montrer que trois (ou plus que trois) sous espaces vectoriels sont en somme directe. Answered by Claude Tardif. 

