







Weighing stars and hearts 
20190225 

From Zach: Two stars and one heart weigh 38 units. One star and one heart weigh 27 units what is the weight of each? Answered by Penny Nom. 





A linear equation 
20190211 

From Nick: What's a linear equation? Answered by Penny Nom. 





Solve for x in Y=1.5x + log (1+x) 
20181223 

From Asadollah: Please restate below expression in terms of y
Y=1.5x + log (1+x)
Thanks Answered by Penny Nom. 





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 puzzling equation 
20181204 

From Manny: Hello,
Can you explain why this is wrong:
1 = (1)^3 = (1)^{6/2} = ((1)^6)^{1/2} = (1)^{1/2} = 1 ??
Thank you 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. 





Are those two equations the same? 
20180605 

From Francisco: Solve for y: 2(x+3)=y x=5
Solve for y: (x+3)2=y x=5
Are those two equations the same? Answered by Penny Nom. 





The mass of a durian 
20180414 

From REEVASSHINIE: A watermelon with a mass of 5 kg and two durians with the same
mass are placed on an electronic balance.If the reading shown on the
balance is m kg,write an expression for the mass of a durian Answered by Penny Nom. 





The intersection of a curve and a line 
20180308 

From lola: find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points 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. 





Heat equation 
20171123 

From Max: What does du\dt=a(triangle)^2u mean. Can it be solved for t. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20170915 

From sumit: what is the area (in sq. unit) of an equilateral triangle inscribed in the circle x^2+y^24x6y23=0. 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. 





Simultaneous equations 
20170902 

From keto: xy=2,x^2+xy=12 Answered by Penny Nom. 





The equation of a circle 
20170703 

From Chen: Find the center radius and equation of a circle in standard form given the following conditions:
1. Tangent to 3x+2y=0 at the point (0,0) and passing through (1,1) and (6,0) 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. 





Algebra 
20170528 

From Kerim: I need to solve this equation.
y=at^2  2at
x =2a√t
Express y in terms of x and a
Give in the form y=(x^p/ma^3)  (x^q/na) where p,q,m and n are integers Answered by Penny Nom. 





Quadratic Equations 
20170328 

From Natalie:
Hi Maths Central,
I am having trouble with quadratic equations. The question is:
Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.
1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.
Thank you so, so much for your help, Maths Central! Answered by Penny Nom. 





Solve 3x^219x14=0 for x 
20170315 

From nick: I'm an 8th grader and am quite confused with this equation:
3x^219x14=0
The answer is:
2/3 , 7
But I'm not sure how to solve for it. 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. 





Form the quadratic equation which has given roots 
20170116 

From Tharshini: Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots
3a1 and 3B1 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. 





Joining a fitness center 
20161218 

From Salem: A fitness center offers a special price for groupclass students. The cost of registration is 30 dollars and then you have to pay 25 dollars per month. What is the rule of the equation in the light of c=m+? 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. 





An equation with fractions 
20161109 

From Tina: How do you solve x+1/3=x+2/5. X+1 divided by 3= x+2 divided by 5. What's x= 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. 





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 equation of a circle 
20160930 

From Trent: write the equation of circle B with center B(2,3) that passes through (1,2) Answered by Penny Nom. 





Two equations 
20160917 

From Nilesh: How to solve (xy)^1/2 + 3(xy) = 30 ; xy + 3(xy) = 11? Answered by Penny Nom. 





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. 





A cubic equation 
20160725 

From Chinmay: x³2x²7x+5 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. 





An equation involving pi 
20160626 

From Diaz: How would you solve :
( pie*X)/ 4 = pie/2
I have no idea.what to do! Answered by Penny Nom. 





Simultaneous equations 
20160625 

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





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





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. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





When does sqrt(x^2+y^2)=x+y? 
20160330 

From Margret: when does sqrt(x^2+y^2)=x+y Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 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. 





A quadratic equation with equal roots 
20160123 

From abdiwahid: X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a? 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. 





Find the quadratic equation whose roots are 4 and 7 
20160103 

From sadiya: Find the quadratic equation whose roots are 4 and 7 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. 





A quadratic equation with known roots 
20151101 

From Awudu: Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and 2/3,find the values of a,b and c. Answered by Penny Nom. 





The flight of a ping pong ball 
20151013 

From Abigail: Hello,
Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.
Not sure whether I would have to look at it from a different perspective.
Thanks,
Abi Answered by Harley Weston. 





2p^2+4p=16. How do i get p? 
20150922 

From Dohie: How do i solve this?
2p^2+4p=16. How do i get p?
Thanks Answered by Penny Nom. 





Four equations in 3 unknowns 
20150823 

From damien: solve:
S x U  T = 44
T  U x S = 36
U + T  S = 7
U x U / S = 4 Answered by Penny Nom. 





Manipulating an equation 
20150605 

From Leigh: Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=ymx. Could you please assist me with this 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 word problem with fractions 
20150409 

From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.
If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.
Let x be the numerator and let y be the denominator of the original fraction.
Write down two simultaneous equation in x and y.
Solve these equations to find two possible values for the given fraction. Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. 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. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 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. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? 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. 





A quadratic equation 
20140920 

From Najah: (E): (m2_1)x2 _ (m+3)x+4_m2=0
A) for what values of m is the equation (E) quadratic?
B) for what value of m is the real number 1 a root of (E) Answered by Penny Nom. 





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. 





The equation of a circle 
20140814 

From jennifer: hi there My name is Jennifer and residing in Denmark. I am a student and I wrote to you because i am having trouble in finding out the equation for the circle using
(xa)^2 + (yb)^2 =3D r^2.The diameter of this circle is d=3D 44,514 cm.
I have attached a drawing of my problem..thanks 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. 





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 quadratic equation given the roots 
20140423 

From Sarah: How do you find the quadratic formula when you're given just the roots ... X=3 X= 1/3
Thanks ! Answered by Robert Dawson. 





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. 





Manipulating an equation 
20140412 

From Paul: S=4wl+2wh and solve for h Answered by Penny Nom. 





The equation of a circle 
20140307 

From Balraj: I have to draw a circle x^2+y^2 =8x . please tell me how to understand these coordinates ? please elaborate , on how to understand these types of equations. Answered by Penny Nom. 





Paul is making banana bread 
20140217 

From John: Paul is making banana bread. The number of cups of bananas he uses is proportional to the number of loaves of bread. Paul uses 11 1/4 cups of bananas to make 5 loaves of bread. Which equation represents the relationship between c, the number of cups of bananas, and b, the number of loaves of bread?
A) C=4/9 b
B) C=2b
C) C= 2 1/4 b
D) C=5b Answered by Penny Nom. 





Simultaneous fractional equations 
20140215 

From benjamin: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic
here is the question:
using substitution method, solve the simultaneous equation.
(x+1)/(y+2)=0.5
(x2)/(y1)=1/3 Answered by Penny Nom. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 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. 





f(x)= a+b*lnx 
20131204 

From Kevin: How do I find the curve, algebraically on paper, for f(x)= a+b*lnx with data points
(6,1303) (9,1639). I can do it with LnReg on a calculator but I want to know how
to get the same results or close to the same results by working it out on paper.
When I run it through the LnReg on the calculator I get, f(x)=181.792+828.678 Ln x.
How did it achieve this solution? Answered by Penny Nom. 





A quadratic equation 
20131127 

From corinanna: Hi,
How do you find a quadratic equation given the domain & range,
& or the yintercept? Answered by Penny Nom. 





Solve 0=2(x5)^2+4 
20131117 

From Leila: How do you find the solution to 0=2(x5)^2+4 Answered by Penny Nom. 





Substitution type simultaneous equations 
20131103 

From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^23x+4 and 3x2y=1
I have rearranged 3x2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you. Answered by Penny Nom. 





An equation with fractions 
20131022 

From Bill: 1/5n= 9
Solve this equation in simple steps! 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. 





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. 





Four equations 
20130808 

From may: HI how to solve this 4 equations?
A+C = 0
4A+B8C+D=1
3A+16C8D=29
12A+3B+16D=5 Answered by Robert Dawson. 





A quadratic with no real roots 
20130715 

From Pranav: If ax^2+bx5=0 has no real roots. Then d sign of 1) a+b5
2) (25a5b5)(4a+2b5) will be what ?? Answered by Penny Nom. 





Simultaneous equations 
20130710 

From Warren: solve this simultaneous equation: xy=4
2x+3y=14 Answered by Penny Nom. 





An equation in two variables 
20130514 

From Steve: Verify solutions to an equation in two variables. 4x2y=8 (3, 2) Answered by Penny Nom. 





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. 





Simultaneous equations with fractions 
20130331 

From Terence: 5/x6/y=1
17/x+30/y=16
I been spending whole day to solve this question. Would be very grateful if you can help I try
The denominator value is a equations term which make is simultaneous equations so hard. Answered by Penny Nom. 





f(x) + f ''''(x)=0 
20130305 

From Andreea: Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something. Answered by Brennan Yaremko. 





The tangent to a circle at a point on the circle 
20130222 

From Andrew: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Answered by Penny Nom. 





A word problem involving toys 
20130214 

From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls? Answered by Penny Nom. 





A curve in 3space 
20130214 

From pardeep: we have to show that the curve r(t)=(cos t)i+(sin t)j+(1cos t)k ,0<=t<=2pie;
is an ellipse by showing it to an intersection of a right circular cylinder and a plane.
i got the eqn. of the cylinder but did not get the eqn of plane. Answered by Harley Weston. 





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





The equation of a circle 
20130211 

From mhd: Complete the equation of the circle centered at(0,4) with radius 3 Answered by Penny Nom. 





Simultaneous equations 
20130210 

From Michael: 2P + 1/3V =8
3P  2/V=5 Answered by Penny Nom. 





7x1/41/3[2x 1x/2]=19/3 
20130203 

From M: 7x1/41/3[2x 1x/2]=19/3 Answered by Penny Nom. 





The zeros of a fourth degree polynomial 
20130123 

From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^45x^3+7x^2+3x10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^33x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it. Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 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. 





Minutes and seconds 
20120829 

From Casey: I have to write a variable equation. The questions says there are 60 seconds. but we need to write and equation to solve for minutes. Is it 1/60 or 1/s Answered by Robert Dawson. 





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. 





2x+underroot2=3x43underroot2 
20120709 

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





A quadratic function 
20120608 

From Salehah: Hi there, i dont know how to do quadratic equations. So how do i do the question,
that says: xint 4 and 2, and yint of 4? and we are to maek a quadratic function with this information.
Please help!
Thank you very much!
Salehah Answered by Robert Dawson. 





Solve for x 
20120512 

From Desiree: 3x 5^2=8 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. 





Parametric equations 2 
20120225 

From Kathy: If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you! Answered by Harley Weston. 





8(3x+4)+6x=4(x8 )+4x 
20120118 

From bianca: 8(3x+4)+6x=4(x8 )+4x Answered by Penny Nom. 





An equation with fractions 
20120106 

From Balkees: 3/4(48x)=2x2/3(612x) Answered by Penny Nom. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





Three consecutive numbers 
20111129 

From Michael: Find three consecutive numbers such that the second number squared
is equal to the first and third added together 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. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





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. 





U(n+1) = 2Un + 1 
20110522 

From Cillian: In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence Answered by Claude Tardif. 





The equation of a sphere 
20110416 

From kanika: equation of sphere and how to know its center Answered by Penny Nom. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





Tony and his friends 
20110321 

From Mieke: Using the following statements and the information given, how much money did each friend have.
Mike says, "I have $41.00 more than Tony."
Jessica says, "I have 6 times as much as Tony plus $2.00."
Ashley says, "I have 13 times the amount Tony has."
Sara says, "I have the 8 times the amount Tony has."
The total together they had was $304.00 Answered by Penny Nom. 





The equation of a circle 
20110214 

From Cristela: find the equation and all the information in General Form and Standard Form of the Circle that will passed trough the point (2,3) (6,1) (4,3) Answered by Stephen La Rocque. 





The equation of a sphere 
20110209 

From kelly: what is the equation of a sphere if one of it's diameters has a giving end point of (4,4,4), (8,8,8)? Answered by Penny Nom. 





Throwing a football 
20110208 

From Janet: a football is thrown into the air from 2 meters high. After 1 second it is 6.9 meters high. After another second it is 2 meters high. How high is it after 1.02 seconds and .05 seconds? when will it reach 5.136 meters? I am not sure how to extract the numbers I need and what equations to use them in? Answered by Stephen La Rocque. 





The greatest value of 5 –  x – 3 
20110116 

From pranav: What is the greatest value of 5 –  x – 3  for any integral value of x.
< br />
PRANAVM Answered by Penny Nom. 





2x = 2+2x 
20110115 

From james: 2x=2+2x can you help me find what x epauls? Answered by Penny Nom. 





Simultaneous equations 
20101205 

From ryan:
Question from ryan, a student:
3 4
   = 1 (1)
x y
7 2 11
   =  (2)
x y 12 Answered by Chris Fisher and Stephen La Rocque. 





Two girls agree to mow a lawn 
20101123 

From Milorad: Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by
cutting a uniform strip around the lawn. How wide a strip should the first girl cut?
I've been struggling with the question above, mainly with the equation and I have
set it up as 2400=(602x)(802x), if this is incorrect I would like to know where I've
gone wrong and also would like a full answer to see it properly done. I need an algebraic
answer and not one with a diagram. 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. 





sin14.5/a = sin150/280 
20101026 

From ken: how do you do the steps to this equation. sin14.5/a = sin150/280 the text book answer is 140.21 miles ,but how do the steps? Answered by Penny Nom. 





The equation of a circle 
20101020 

From Silvan: Hi, I just want to find the x,y values for the circumference of a circle...
Lets take a clock having its centre at (0,0) in a graph.
I just want to know how to find the (x,y) coordinates for the curved path or the surface of the circle..
Is there any formula to directly align the curved path or the circumference of the circle in a graph for a known radius of a circle..
I feel it will be useful for me to draw a clock in a graph... :) Answered by Penny Nom. 





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. 





Find the point of contact of the circles 
20100920 

From Sandra: If the center of circle A = (1,3) and the radius of it is √20,
the center of circle B = (5,9) and the radius of it is √80.
Find the point of contact of the circles A and B. Answered by Janice Cotcher. 





The circle centered at (2,4) with radius 3 
20100918 

From lupe: Consider the circle centered at (2,4) with radius 3. Write the equation
of this circle sketch its graph, and find the exact coordinates of its intercepts.
xintercept
yintercept using the quadratic equation? Answered by Penny Nom. 





An algebraic equation with fractions 
20100910 

From leah: If 6/x  (x1)/2 = 4
then the LCD is 2x, right?
so you get 12/2x  (x2x)/2x = 8x/2x, right?
then what do you do with the 2x when you turn it into a quadratic equation? Answered by Penny Nom. 





A logarithmic equation 
20100908 

From Rohit: x^2 + k*ln(x)  c  k = 0
Where k and c are constants. Answered by Penny Nom. 





Algebraic Equations 
20100810 

From Justin: the amount of money that Mika has if she has some quarters
how fast Rya runs if she runs 5 mi/h slower than Danae
please help,
thanks, justin Answered by Robert Dawson. 





A rational equation 
20100802 

From Bailey: 3/x
+
x/x+2
______
2/x+2 Answered by Penny Nom. 





The suspension cables of a bridge 
20100729 

From Mike: what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span Answered by Robert Dawson. 





The equation of a parabola 
20100629 

From Tiffany: Find the equation of a parabola that passes through the points (2,3), (1,1) and (1,9) Answered by Stephen La Rocque. 





The equation of a circle 
20100623 

From Michelle: Write and equation for the circle with a center, (0,0) and a diameter of 12 Answered by Penny Nom. 





A quadratic equation with imaginary numbers 
20100603 

From Alissa: I am solving a quadratic equation and I got this far;
(x4+i)(x4i)=0
but how do I add the imaginary numbers
i know you multiply x by x and then add 4 + 4 but what do you do with the i's? Answered by Penny Nom. 





A quartic equation 
20100518 

From Austin: Z^410z^2=9 Answered by Penny Nom. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





The equation of a circle 
20100504 

From crystal: find the standard form of the circle with center (2,3) and tangent to the line y=1 Answered by Penny Nom. 





A quadratic equation 
20100503 

From Millie: (3x4)(5xplus2)=0 Answered by Penny Nom. 





Solving a trig equation 
20100421 

From Jason: Please Help! My question is :
Find all of the solutions to sin(x/2)+cosx1=0 Answered by Penny Nom. 





The median 
20100418 

From amper: How could i get the median with this equation f(x)=(x^2+4)3/13 0 Answered by Harley Weston. 





Four less than three times a number is 14 
20100416 

From David: My daughter has two questions that we could use some help with.
First ?
Four less than three times a number is 14
Secound?
The quotient of 15 and w Answered by Penny Nom. 





Polar coordinates 
20100414 

From Lan: Given the rectangular equation (x^2)+2x+(y^2)+y=0, find the polar equation. Answered by Harley Weston. 





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 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. 





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. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





The equation of a circle 
20100218 

From AHMED: find the equation to the circle with centre at the point (1,1) and touching the straight line 5x+12y=7. Answered by Penny Nom. 





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. 





A piece of string 8 inches long is cut in two pieces 
20100202 

From Susan: If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?
Susan Answered by Penny Nom. 





A linear equation with the variable on both sides 
20100116 

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





A pair of simultaneous equations 
20100109 

From Yumiko: Solve the following pair of simultaneous equations.
x^2 4x = y^24
3y=2x  3 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. 





Solving two equations, one with a square root 
20091123 

From kacie: y = square root of x+3
x4y = 7
im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston. 





The equation of a circle 
20091017 

From Renson: A circle passes through (4,2) and (11,5) with center on the line 3y5x+41=0.Determine its equation in standard form. Answered by Penny Nom. 





541.39(1 + i)^15 = 784.09 
20091014 

From Fitore: Hi, I noticed that this question was already posted up, however I was hoping I could solve it without having to use logs. Can you please help me? The equation is:
541.39(1 + i)^15 = 784.09 Answered by Penny Nom. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





Two equations in two unknowns 
20090918 

From Citizen: x+3y=7
x+4y=7 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. 





Quadratic equations 
20090830 

From jovian: how can i find the quadratic equation of the roots 2/5 and 1/3? Answered by Stephen La Rocque. 





The equation of a circle 
20090830 

From tagbo: find the eqn of circle passing through (1 1) and (1 4)and whose radiusis 5/2 Answered by Stephen La Rocque. 





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. 





Factoring 
20090823 

From Bj: Solve for x: 5x^2  35x = 0 Answered by Stephen La Rocque. 





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. 





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. 





A binary equation 
20090707 

From Chinonyerem: Find a bitwise solution (i.e find xi so that each xi E {0,1}) to
32 = x1 + 2x2 + 4x3 + 9x3 + 20x5 Answered by Harley Weston. 





Simultaneous Equations 
20090706 

From Mukulu: Solve the equation simultaneously X/5=(Y+2)/2= (Z1)/4 ……………….eqt 1
3X+4Y+2Z25=0 ………………eqt 2 Answered by Janice Cotcher. 





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. 





3h+10 divided by 2 +9=20 
20090505 

From CJ: what is the solution for the equation 3h+10 divided by 2 +9=20 Answered by Penny Nom. 





4cos^2 (3x) + 3sin (3x) = 1 
20090505 

From Cheryl: Find all solutions of the following equation and show how to do this algebraically.
4cos^2 (3x) + 3sin (3x) = 1 Answered by Harley Weston. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

From Kelly: find a quadratic equation with roots (4i) and (4+i) Answered by Harley Weston. 





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. 





Negative nine minus 7x = negative 5 
20090423 

From gigi: what is negative nine minus 7x = negative 5 Answered by Robert Dawson. 





cos2x = sinx 
20090419 

From stacey: solve the equation cos2x = sinx for 0 < x < 2 pi
giving the answer in terms of pi. Answered by Harley Weston. 





A circle tangent to the Xaxis 
20090329 

From Kiera: Find an equation of the circle that satisfies the stated conditions.
Center C(4,1), tangent to the xaxis Answered by Penny Nom. 





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. 





Solving an equation for b 
20090313 

From ernest: If 2b=96+b+96+1/2b solve for b? Answered by Penny Nom. 





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 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. 





y = p q^t 
20090212 

From Conor: y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0
a) find p and q
b) hence find y when t=4 Answered by Stephen La Rocque. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





Simultaneous equations with an xy term 
20090201 

From angelee: xy+5x2y10=0
2x+y=1 Answered by Penny Nom. 





ax^2 + bx + c = 0 has no real roots and.... 
20090126 

From Alberto: The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:
(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0
Explain the choice. Answered by Robert Dawson and Harley Weston. 





Using y = mx + b 
20090126 

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





Sheep, goats, and hogs 
20090123 

From La: A man buys sheep, goats, and hogs, to the number of 100, for 100 crowns; the sheep cost him 1/2 a crown apiece; the goats cost him 11/3 crowns apiece; and the hogs cost him 31/2 crowns apiece. How many had he of each? Answered by Robert Dawson. 





Solve for x 
20090116 

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





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. 





System of equations  comparison method 
20090102 

From nick: Hi, I am doing a project on system of equations by using comparison method,
but for some reason or another, i can't seem to find any information on the
comparison method at all. So, please would you help me by giving me a website
that you know of that has some information on my method. And, if you know the
answer, can you please tell me why or when do we use system of equations by
using comparison method?
Thank You Answered by Robert Dawson. 





The inverse function for F(x)=x^3+x 
20081218 

From alireza: I want inverse function for F(x)=x^3+x Answered by Robert Dawson. 





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. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





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. 





What is 5x+3y=24? 
20081113 

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





Algebraic equations with fractions 
20081107 

From John: Solve each equation. Check each solution.
1/8+5x/x+2=5/2 10/2y+8  7y+8/y(squared)16 = 8/2y8 Answered by Harley Weston. 





Solve the equation 2x + y = 6 for y. 
20081107 

From fatiuma: Solve the equation 2x + y = 6 for y. Answered by Penny Nom. 





Separating variables 
20081104 

From Terry: by separating variables solve the initial value problem
(x+1)y' + y = 0 y(0) = 1 Answered by Harley Weston. 





A linear system 
20081022 

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





A canal with cross section a semicircle 
20081019 

From Connor: a canal with cross section a semicircle is 10m deep at the centre.
Find an equation for the semicircle and use it to find the depth 4m
from the edge Answered by Penny Nom. 





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 linear equation with fractions 
20081007 

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





Solving an Equation with a Square Root 
20081005 

From Jonathan: the square root of 3x+18 = x
3x+18 are within the square root Answered by Victoria West. 





cos^2x  3cosx = 1 
20080929 

From Danielle: cos2x  3cosx = 1 Answered by Penny Nom. 





Two Step Equation 
20080917 

From calea: i really dont now what twostep equation means? Answered by Janice Cotcher. 





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. 





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 cubic equation 
20080825 

From RAM: The following Cubic Eqn should have three roots  what are they?
x^327=0 Answered by Penny Nom. 





y^2+3yz8z4z=0 
20080817 

From Rae: y^2+3yz8z4z=0 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. 





algebra 
20080731 

From Eric: Would you please solve & explain this equation to me: x^2+2x=x(x+2)?
Thank you Answered by Penny Nom & Stephen La Rocque. 





Width of a Garden Path 
20080730 

From Erin: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? Answered by Janice Cotcher. 





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. 





solving four simultaneous equations 
20080718 

From Muhammad: 2B2C+4E=1
A+B+C+D=0
2B2C2D+E=0
B+C+4D2E=0 Answered by Janice Cotcher. 





CIRCLES 
20080707 

From daryl: Find the equation of the smaller circle that is tangent to the axes and the circle x(squared)+y(squared)=2x+2y1? Answered by Penny. 





Points on a graph 
20080703 

From Rita: Dertermine if the given 3 points are on the graph of the equation.
Equation: y = (x^3)  [2(sqrt{x})]
Points: (0, 0); (1, 1); (1, 1) Answered by Penny Nom. 





A series solution of y' = xy 
20080703 

From sasha: I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks Answered by Harley Weston. 





3y^2  48 = 0 
20080623 

From marquis: 3y^2  48 = 0 Answered by Stephen La Rocque. 





9(d+5)=3(d3)+6d 
20080619 

From davontay: 9(d+5)=3(d3)+6d Answered by Harley Weston. 





A piecewise equation 
20080616 

From John: AT&T charges $39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes.
How can I make a piecewise equation of this problem? Answered by Penny Nom. 





Cows and chickens 
20080616 

From damebochie: I got this problem and want to write a system of equation for it:
Farmer Joe has cows and chickens on his farm. One day he count 76 legs and 24 heads. How many cows and how many chickens are on the farm? write a system of equations and solve.
I don't have any problem to solve it, but I just can;t see how I am going to write this system of equation.
Thank you so much for helping? Answered by Harley Weston. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





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. 





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

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





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

From Tiffany: Find the quadratic equation with roots at (3i) and its complex conjugate. 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 quadratic equation with odd coefficients 
20080415 

From Manashi: If p,q,r be any odd integers, then prove that the roots of the quadratic equation px^2+qx+r=0 can't be rational . Answered by Stephen La Rocque. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





A function satisfying f(x) + 2f(1/x) = x 
20080325 

From Joan: Let f be a function satisfying f(x) + 2f(1/x) =x for all real numbers (x does not equal 0)
a) Find f(1) justify your answer
b) Find f(2) justify your answer Answered by Penny Nom. 





Polar coordinates 
20080305 

From kumi: 2.Sketch the graph of r=(2)/(1sinθ). Make sure you show a complete chart demonstrating how you arrive at your sketch, and sketch the graph neatly and clearly with proper labeling.
b. change the equation above to cartesian coordinates and identify the type of graph.
c.explain which coordinate system gives an easier function to graph and why
d.find a function of the form r=f(θ) for a circle centered at (8,π/2) and with the point (0,0) lying on the circle Answered by Penny Nom. 





Parametric equations 
20080305 

From kumi: I have made a picture of a football pass 45 degrees with 30yds and height of 7ft and 4ft. But I am just stuck there. I have stared at the worksheet for soo long. I have no idea how to solve this, and I don't even know where this is going (I don't understand how parametric equations work). Can you help me with this problem?
1.The quarterback of a football team releases a pass at a height, h, of 7ft above the playing field, and the football is caught by a reciever at a height of 4ft, 30yds directly downfield. The pass is released at an angle of 45 degrees with the horizontal with an initial velocity of vo. The parametric equations for the position of the football at time t are given, in general, by x(t)=(vo cosθ)t and y=h+(vo sinθ)t16t^2.
a. find the initial velocity of the football when it is released
b. write the specific set of parametric equations for the path of the football
c.use a graphing calculator to graph the path of the football and approximate its maximum height
d. find the time the reciever has to position himself after the quarterback releases the football Answered by Harley Weston. 





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. 





Pythagorean equation 
20080227 

From Judy: X^2 + Y^2 = 5^2
Graph all ordered pairs in the coordiante plane that satisfy the Pythagorean equation, x squared plus y squared equals five squared Answered by Stephen La Rocque. 





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. 





Two job offers 
20080210 

From Kelly: Raja has been offered two jobs.
Each of these jobs takes 24 weeks to complete.
One job pays $3440 every 8 weeks. The other job pays $2700 every 6 weeks.
Raja wants to accept the job that pays more per week.
Show how to use equations to help Raja make her choice. Answered by Penny Nom. 





The equation of a circle 
20080205 

From aime: Find the equation of the circle tangent to 3x+4y15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)? Answered by Stephen La Rocque. 





Two equations in x and y 
20080201 

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





18/95 x t =3 3/5 
20080128 

From emily: 18/95 x t =3 3/5 Answered by Penny Nom. 





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. 





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. 





x=sint, y=cos2t 
20080114 

From Art: How do i transform x=sint y=cos2t into a function in terms of x and y Answered by Harley Weston. 





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. 





System of equations 
20071206 

From Jenn: change the equation,xy=4 to form y=mx+b
the solution to the system of equations y=2x and y=x+3 is Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





Find the radius of a circle given the center and a point on the circle 
20071118 

From Raymund: Find the radius if the center is at (0, 5) and one point on the circle is (2,3) Answered by Stephen La Rocque. 





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. 





x^2 + x^3 = n^2 
20071114 

From Rapin: x and n are the whole number and less than 100 , x^2 + x^3 = n^2,
please help to solve this equation. 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. 





The rate of change of the concentration of a solution 
20071030 

From Nicholas: A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the wellmixed salt water solution flow out at the same rate, how much salt is present after 8 minutes?
I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks Answered by Harley Weston. 





a/5= b/7= 8/3 
20071027 

From Kristine: how do you solve for a and b in this equation:
a/5= b/7= 8/3 Answered by Penny Nom. 





4x+8y=32 
20071018 

From Sara: Rewrite the following equation:
4x+8y=32
in function form ("solve for y"). Answered by Penny Nom. 





5x + 9 = 3x + 7 
20071016 

From kristina: hi im kristina and i cannot figure out how 2 do these multistep equations
5x + 9 = 3x + 7 i can on getting the wrong answer according 2 the book Answered by Penny Nom. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Coin jar 
20071007 

From a student: Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and
quarters. The number of dimes is twice the number of nickels and the number
of quarters is three less than the number of nickels. Determine how many nickels,
dimes, and quarters were in the in the jar. Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

From Johan: I need some help in solving this question
x + 2y  3z + 4w = 12
2x + 2y  2z + 3w = 10
0 + y + z + 0 = 1
x  y + z  2w = 4 Answered by Stephen La Rocque. 





Problems solved using quadratic equations 
20071007 

From Lisa: a. Two positive numbers differ by 5. Their product is 234. What are the two numbers?
b. The sum of two numbers is 12. Their product is 30. What are the two numbers?
c.Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
d. The sum of two numbers is 15. Their product is 56. By forming an equation, find the two numbers. Answered by Penny Nom. 





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. 





Two equations in two unknowns 
20070914 

From CAMEILA: NEED T0 SOLVE THIS EQUATION
Y = 2X + 6
Y + 6 = 2x Answered by Stephen La Rocque. 





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. 





Parametric equations 
20070822 

From will: Graph and make a sketch of x = ysquared  6y + 11 in parametric mode (hint: you need to come up with 2 parametric equations).
i have already figured out that the cartesian form of the parametrics will be y = +/ sqroot(x2) + 3, but i do not know how to produce 2 parametric equations from this. Answered by Penny Nom. 





31=6w7 
20070821 

From Shaneka: 31=6w7 Answered by Penny Nom. 





More on the sixth degree equation 
20070821 

From Farzan: Equation 1 :
(R + (6.67*5.98*10^13/((R^2)*2)))^2  (R^2) = (7.27*(10^5)*R)^2
Equation 2 :
(6.67*5.98*10^13/(R^2*2))^2 + 6.67*5.98*10^13/R = (7.27*10^5*R)^2
As you see if we expand the left part of the first equation and simplify, the
equations become same, but these two equations have different answers in my
math software.The first one has 3 amounts for R, but the second one has 6
amounts. Why are the answers different ? Answered by Stephen La Rocque. 





A sixth degree equation 
20070820 

From Farzan: Dear friends
I need to solve this equation with an understandable method for highschool students :
(6.67*5.98*10^13/(R^2*2))^2 + 6.67*5.98*10^13/R = (7.27*10^5*R)^2
please solve this problem if you have time. Answered by Harley Weston. 





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





Identifying a conic from its equation 
20070819 

From Robin: Hi,
Do you have any tips how to identify a conic from its equation? Answered by Leeanne Boehm and Steve La Rocque. 





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. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





Paying off a loan 
20070808 

From Iona: I borrowed $6000. 00 from a friend to pay school fee.
He said I should not pay back any interest but pay $350.00
monthly after graduation.
(1) Make an equation from the above
(2) make a graph
(3) what is the relationship between the months after graduation and the loan?
(4) what is the horizontal and vertical intercept relate to the problem? Answered by Stephen La Rocque. 





Radical equations 
20070803 

From JC: I have to solve this radical equation using the power rule; squaring twice.
radical 2x+3 radical x+1= 1. Answered by Stephen La Rocque. 





Solve y'' + y = 0 
20070728 

From Shihya: How do you solve y’’ + y = 0 Answered by Stephen La Rocque and Harley Weston. 





8(y + 3) + 9(y + 2) = y  3 
20070723 

From jordan: 8(y+3)+9(y+2)=y3 Answered by Penny Nom. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





Algebraic EquationsAx+By=C 
20070702 

From Juan: The general "Standard" form of an equation is Ax+By=C.
ReWrite this equation in slopeintercept (y=mx+b) form. Answered by Harley Weston. 





Simultaneous equations : the Elimination method 
20070621 

From Patricia: I need to find the value of X and Y using the Elimination method.
5/x + 3/y=4
25/x2/y=3 Answered by Stephen La Rocque. 





Solving a literal equation 
20070615 

From Allen: Solve each literal equation for the indicated variable.
D= CS/n (solve for s)
and
A=1/2h (B+b) (solve for b) Answered by Penny Nom. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





15 = 19.2 t (time)  4.9 t squared 
20070611 

From Nicole: 15 = 19.2 t (time)  4.9 t squared Answered by Penny Nom. 





Solving a quadratic equation using the Quadratic Formula 
20070605 

From Stuart: Solve the following quadratic equation:
3xsquared5x4=0 Answered by Stephen La Rocque. 





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. 





System of equations 
20070524 

From Chris: Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom. 





Finding the equation given three roots 
20070521 

From Aydee: 1. find the equation for the roots given: 7,5,2
2. find the equation for the roots given: 5,2+sqrt3,2sqrt3 Answered by Penny Nom and Stephen La Rocque. 





Set up two simultaneous equations 
20070521 

From Admire: The cost of producing windscreen wipers blades at a factory ais partly fixed (due to operating overheads) and partly dependent on the number of blades produced. It costs $300 to produce 1000, and $600 to produce 5000 blades. How much would it cost to produce 24000 blades? 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. 





A tugboat's speed 
20070430 

From Amanda: a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what
constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph. Answered by Stephen La Rocque. 





Finding a parabola's equation by looking at its graph 
20070430 

From Kenzie: The graph shows an arrow going upward crossing at the 2 on the x line
and crossing the 3 on the x line and the vertex on the 6 on the y line. Answered by Stephen La Rocque. 





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. 





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. 





Simultaneous equations 
20070416 

From kyrie: simultaneous equation
4x + 3y = 21
2x * y = 8 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. 





What is the intensity 5m below the surface? 
20070331 

From david: I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Answered by Penny Nom. 





Solve for x and y 
20070327 

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





Graphing a line 
20070323 

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





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. 





x^3 + y^4 = z^5 
20070227 

From Mike: Is there a known solution to the equation: x^3 + y^4 = z^5? This is not for marks. Just a curiosity. Thank you for your time. Answered by Stephen La Rocque. 





Simultaneous equations with envelopes 
20070208 

From Mick: There were 17 envelopes bought, some were brown, some were white. The brown envelopes cost one cent more per envelope than the white ones. The total cost was 80 cents. How much of each type of envelope was bought? Many thanks! Answered by Stephen La Rocque. 





BEDMAS solving for X 
20070207 

From damian: Hi, I am having a problem understanding why when using BEDMAS the text book example of the following question has used bedmas and reduced the calculation to 4/3.
Text book formula: X/200,000 = (X  90,000) / 150,000 X = 4/3 * (X  90,000) X = 360,000
My solution: I always thought that when you do something to one side you do the same to the other. Why would the equation bring the 200,000 / 150,000 down to 4 / 3 I would think it would look something like this. X/200,000 = (X  90,000) / 150,000 X = 200,000*((X  90,000) / 150,000) Answered by Stephen La Rocque. 





Write an equation for this 
20070207 

From BS: How do you write an equation for this: The difference when 7 less than a number is subtracted from twice the number is 12. And also, what is the number? Answered by Penny Nom. 





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. 





Equations with fractions 
20070206 

From Juan and Derek: 3/4x=1/2 3/4+1/5x+1/3=4/5x Answered by Penny Nom. 





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. 





Fencing a field 
20070201 

From Carol: "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at $10/m. The total cost of the fencing is $2200." What is the length of each side fenced with aluminum and steel? Answered by Stephen La Rocque. 





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. 





11^n +22^n = 55^n 
20070129 

From Ankit: 11^n +22^n = 55^n
find the value of n? Answered by Penny Nom. 





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. 





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. 





How do you write the equation y= 4x2 in ax+by=c form? 
20070117 

From Evan: How do you write the equation y= 4x2 in ax+by=c form? Answered by Penny Nom. 





Write an equation to represent a function. 
20070107 

From Noel: x y 3 1 2 0 1 1 0 2 1 3 2 4 3 5
write an equation to represent a function. Answered by Penny Nom. 





A quuadratic equation 
20061222 

From Harold: L=3w4 A=96Square I used the quadratic equation to solve and my answer is still wrong
I convert the square of 1168 to decimal.
here is where i start (3w4) x w=96
could you give me an example Answered by Stephen La Rocque. 





The roots of a quadratic equation 
20061116 

From Lana: If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help. Answered by Penny Nom. 





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. 





The name of an equation 
20061113 

From Lee: I am struggling to find the name of the following equation. I remember watching a TV programme introduced by Arthur C Clarke. The programme focused on an equation that gave a wonderful pattern that went on into infinity. Two maths professors discussed this equation.It was described as 'Gods equation' as it was compared to the shape of trees and other shapes in nature. It was named after the inventor/discoverer. If you have any ideas i would be most grateful. Answered by Penny Nom. 





A system of equations 
20061113 

From Katrina: solve the system of equations using either the substitution or the elimination method. 2x3y= 12 and 4x+6y=15 Answered by Penny Nom. 





(4x5)^2 = 32 
20061111 

From Tracey: (4x5)^2 = 32 Answered by Stephen La Rocque and Penny Nom. 





Simultaneous equations 
20061106 

From An other: e^2yx+2=0 ln(x+3)2y1=0 Answered by Penny Nom. 





Balancing equations 
20061026 

From Della:
With the following equations, how do you know whether you need to apply the multiplication or division rule of equality? 75% t = 18 120% w = 72 Answered by Penny Nom. 





(a^(1/3) – b^(1/3)) ( a^(2/3) + a^(1/3)b^(1/3) + b^(2/3)) 
20061024 

From Julie: (a^{1/3} – b^{1/3}) ( a^{2/3} + a^{1/3}b^{1/3} + b^{2/3}) Answered by Haley Ess. 





Word equations 
20061022 

From Samira: One half of a number is subtracted from the sum of onethird and onequarter of the same number. If the result is 16, find the number. Answered by Stephen La Rocque. 





A matrix equation 
20061014 

From Ngozi: If I have AB = C, where A and C are both 1x6 matrixes and B is a 6x6 matrix, how can I solve for B by dividing C over A? Answered by Chris Fisher. 





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. 





X^1/3X^1/9=60 
20060926 

From Harini: I need the answer for
The value of X in X^1/3X^1/9=60. Answered by Penny Nom. 





Is this unsolvable? 
20060919 

From Al: Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Answered by Penny Nom and Claude Tardif. 





What is the equation? 
20060913 

From A parent: HERE ARE THE COORDINATED (0,3), (1,0), (2,3),(3,6)
WHAT IS THE EQUATION? Answered by Penny Nom. 





How much did I spend on the first trip? 
20060910 

From Alexander: I have $600 to spend.
I take 10 shopping trips.
Each trip I spend $10 more than the last trip.
How much did I spend on the first trip?
Answered by Stephen La Rocque. 





Making and using equations 
20060830 

From Brooke:
write an equation to model the relationship between these variables. Define the variables you use, and refer to your notes for a variety of formats of equations we have studied this year.
week 1: 3 birds infected
week 2: 15 birds infected
week 3: 75 birds infected
week 4: 375 birds infected
Answered by Stephen La Rocque. 





The lower half of a sphere 
20060830 

From Yvette: I am interested in finding out how to represent the lower half of a sphere in the form of z=f(x,y) with r=2 and a centre point (3,1). Answered by Stephen La Rocque and Penny Nom. 





If 5x + 4y = 6 then x + y = ? 
20060818 

From Vijai: If 5x+4y=6
then x+y=? Answered by Stephen La Rocque and Penny Nom. 





x+ 6 / 3 = x+ 6 / x 
20060801 

From Lynne: x+ 6 / 3 = x+ 6 / x
How do I solve this equation? Answered by Penny Nom. 





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. 





[(400/n)5](n+ 4)=400 
20060702 

From Maria and George:
Can somebody solve for n in the following equation please?
[(400/n)5](n+ 4)=400
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. 





Simultaneous Equations 
20060524 

From Angie:
Question: solve the equations
2x3yz=0
3x2y+z=5
x+3y2z=14
for x,y,z
Answered by Stephen La Rocque. 





Solving an equation without using algebra 
20060501 

From Kenneth: How can the following be solved without using algebra?
10 times some number is 3 times the same number plus 14.
Answered by Paul Betts. 





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. 





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. 





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. 





A circle containing two points 
20060313 

From Skye: Write the equation of a circle having area 15pi and containing the points (1, 5) and
(1, 9). Answered by Penny Nom. 





An equation involving logarithms 
20060305 

From Chris: Given that log_{e} y = 0.3log_{e}x+1.2 show that y=3.32 x^{0.3}
Answered by Penny Nom. 





25+36+12=52+m, m= 
20060302 

From Jenny: 25+36+12=52+m, m= Answered by Stephen La Rocque. 





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. 





8  5r / 6 = 3 
20060215 

From Scott: I was trying to help my daughter with the following problem:
8  5r / 6 = 3
Can you give me a quick refresher.
Answered by Stephen La Rocque. 





6^(x+1) = 12^(x3) 
20060205 

From BB: 6^{x+1} =12^{x3} 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. 





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. 





An integer equation 
20051201 

From Henry: 3x = 2y + 7
I know the answer: x=9 and y=10, but what are the algebraic steps to solve the equation? 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. 





3x  5  (4x  8) = 2(2  3x) + 29 
20051106 

From Emma: I do not get how to "solve for x". For example:
3x  5  (4x  8) = 2(2  3x) + 29 Answered by Penny Nom. 





Writing an equation 
20051101 

From Richie: A man's electric bill is $23 less than his gas bill. The two utilities cost him a total of $109. Find the amount of his gas bill. Answered by Penny Nom. 





2x  5x + 6.3 = 14.4 
20051016 

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





Simultaneous equations 
20051013 

From Daniel: 5x + 3y = 22
4x  7y = 20 Answered by Penny Nom. 





3z5+2z=255z 
20051002 

From Davis: 3z5+2z=255z Answered by Penny Nom. 





6x+7=8x13 
20050927 

From A student: show me how to do 6x+7=8x13 Answered by Penny Nom. 





14p  8 = 22 + 20p 
20050927 

From Tiffany: 14p  8 = 22 + 20p Answered by Penny Nom. 





A cone with vertex (1,1,2) 
20050926 

From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. Answered by Penny Nom. 





U'(X)  U(X) = 0; U(0) = 2 
20050923 

From David: Out of interest could you please answer the following questions?
U'(X)  U(X) = 0; U(0) = 2
and
U''(X)  U'(X) = 0; U'(0) = U(0) = 2
Answered by Harley Weston. 





A quadratic 
20050906 

From Ginger: I took a pre alg test today. There was a question on it that I am not sure and is bothering me. Can you tell me the answer?
x square + 13 + 14
Factor this Answered by Penny Nom. 





x = (y^2  b^2)/2b 
20050904 

From Bob: while looking at x=(y^{2}b^{2})/2b on a table I was preparing for a graph, I saw that there is a point where x and y get closer to each other's value. By trial and error I tried to find the point where x=y. I saw a number which looked familiar and I realized it was the square root of 2. and so, if y=b(1+square root of 2) then x=b(1+square root of 2) also, or as x=y.
My question is: How can this result x=y when y=b(1+square root of 2) be algebraically derived from the equation x=(y^{2}b^{2})/2b without pre knowing it is so? Answered by Penny Nom. 





A system of equations 
20050902 

From Gina: How do you interpret the solution of a system of equations by the corresponding graph? Demonstrate your answer by the use of an example. Answered by Penny Nom. 





3A/4 +1=(2A1)/3 
20050821 

From Rachael:
I'm doing a practice test question and the answer I keep turning out is different from the answer on the answer sheet. I think I might be forgetting a step. The problem is:
3A/4 +1=(2A1)/3
The answer is 16. If anyone could explain the steps to me to getting the answer I would be grateful. Whenever I do it I get something completely different.
Answered by Penny Nom. 





Solve for x 
20050720 

From Ed: ^{(x1)}/_{3}  1 = ^{(x + 2)}/_{2} Answered by Penny. 





Discriminant 
20050620 

From A student: If a quadratic has real root, its discriminant b24ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not? Answered by Chris Fisher. 





y = x+2 and y = 2x  1 
20050503 

From Kimberley: Question:
y=x+2
y=2x1 Answered by Penny Nom. 





16x^2+20x12x15 
20050503 

From Tanya: how they got (4x+5)(4x5) from
16x^{2}+20x12x15=4x(4x+5)3(4x+5)=(4x+5)(4x5) Answered by Penny Nom. 





A quadratic equation 
20050427 

From Chris: Solve using the quadratic formula
9x² + 9x  5 = 0
I don't get the same answer as in the text book which is
3+/ ^{√29}/_{36}
Hope you can help....
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. 





tan55.tan65.tan75=tan85 
20050330 

From Jesus: My name is Jesus and I´m a secondary student. I´m trying to verify a trigonometric identity but I don´t know how to do it.please help me!!!!!!!!!.
The identity is : tan55º.tan65º.tan75º=tan85º (the sign (.) indicates multiplication)
Answered by Chris Fisher and Penny Nom. 





A quadratic equation 
20050209 

From Jess: 6x+8=x2 Answered by Claude Tardif. 





By how much is 100 multiplied or divided,... 
20050127 

From Benedict: By how much is 100 multiplied or divided, so that whether the number obtained is divided by 5 or 7, there will be a remainder of 1 and so that at the same time, the first quotient is greater by 4 than the second? Answered by Penny Nom. 





cos 2x = sin x 
20050122 

From Kris: solve the equation
cos 2x = sin x for 0<= x < 360 Answered by Penny Nom. 





2^10 = 1/2^x  1 
20041213 

From Randy: Could you explain to me how the following equation is solved please.
2^10 = 1/2^x  1 Answered by Harley Weston. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 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. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





The integrating factor method 
20040805 

From A student: Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Answered by Harley Weston. 





x^2 = x + 2 
20040726 

From A parent: x2 = x+2
My daughter came home with this equation today and although I know the answer is x=2, i have no way of proving it by showing any working out. Answered by Penny Nom. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} 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. 





Setting up an equation 
20040430 

From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)
and that
xy = 22
Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom. 





x^2/3  7 x^1/3 + 12 = 0 
20040405 

From Jackie: I am having trouble solving this question for x:
1.) x^2/3  7 x^1/3 + 12 = 0 Answered by Penny Nom. 





The substitution method 
20040214 

From Keisha: I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve. 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. 





Diamonds and Pearls 
20031211 

From Lauren: A crown holds a total of 3080 jewels.
It is made up of diamonds and pearls.
There are 10 times as many diamonds as there are pearls.
How many pearls are there? Answered by Penny Nom. 





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. 





4(r2) = r(2+8) 
20031120 

From Angela: I not going to give you the problem that I have, but a problem like it.
4(r2) = r(2+8)
I get mix up trying to solve a problem like this could you help me. So that I will be able to handle the ones on my homework. Answered by Penny Nom. 





Systems of equations 
20031119 

From Scott: I hope that u can help me....I
am a college student taking a class in Pre Calculus.....I have homework
due this Friday and it counts a BIG Percentage on my FINAL grade.....I
am getting mixed up and can not figure out a few problems.....Please help
me.....
Method Of Subsitution
Problem 1. y 8x = 5
x(squared) + y(squared) = 25
Problem 2. y = x(squared)  2x  6
Y = x(squared)  4
Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





Solve for x 
20031027 

From Lonnie: i need help with solving equations and formulas such as 3x+b=6x, for x. I do not understand how you find x. Answered by Penny Nom. 





A parabola 
20031024 

From Delores: Given the vertex (4, 2) y intercept = 6 find if/where the parabola crosses the x axis? Answered by Penny Nom. 





Substitution method 
20030914 

From John:
Hello, my name is john and while I was finishing up my work I stumbled into these problems. a/4b=1 a+b=11 and 6ab=5 4a3b=8 Thanks a lot. I really need some help :) John Answered by Penny Nom. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





Two equations 
20030821 

From Jennifer:
The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours:
3^{2a+1}  283^{a} + 9=0 and 5^{2m}  5^{m}=20 Answered by Penny Nom. 





x+3 = 15x 
20030719 

From Nathan: Without the use of trial and error, is there a way of solving for x where x + 3 = 15x? I know that x = 0.1875, but how do I find whether x + 3 is positive or not if I did not have this information (In other words, how would I solve whether the xvalue was 3 or less, or if it was more than 3)? Answered by Claude Tardif and Penny Nom. 





Setting up a word problem 
20030630 

From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom. 





Sesame Street on Stage 
20030625 

From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





ABCD*4 = DCBA 
20030507 

From Dee:
In the following problem, if the letters A, B, C and D represent some number, what numbers would they represent so that: ABCD*4 = DCBA Answered by Penny Nom. 





The substitution method 
20030414 

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





(n+17)(n+7) = 0 
20030305 

From Janea:
What is the answer to 1. (n+17)(n+7)=0 What is the answer to:2. (y15)(y100)=0 Answered by Penny Nom. 





(x^{y})^{z} = 64 
20030226 

From Melissa: How many ordered triples of positive intergers (xyz) satisfy (x[raised to the y])raised to the z = 64? 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. 





Why quadratic? 
20030121 

From Dan: Why are equations of the form aX^{2} + bX + c =0 call quadratic? The quad indicates 4 but the power is 2. Answered by Penny Nom. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! 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. 





How many trees were planted in March? 
20021020 

From Allison: The number of trees planted by the Alpine Nursery in April was 3 more than twice the number of trees planted in March. If 71 trees were planted in april, write and solve an equation to find how many trees were planted in March. Answered by Penny Nom. 





A functional equation 
20021014 

From Rob: Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n)
b) f(f(n))=3(n) Answered by Claude Tardif. 





A complex quadratic 
20021006 

From Michael: I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Answered by Harley Weston. 





Solving an equation 
20020922 

From Emanuel: how do u solve these problems?:
30/x=7+ 18/2x
3m+1/4 = 2 32m/3 Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





The quadratic formula 
20020911 

From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x^{2}  4x  11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom. 





A solution to an equation 
20020828 

From A student: How do you determine whether a pair of numbers is a solution for an equation? If you could identify the specifics steps I need to take to determine whether it is a solution or not would be appreciated! Thanks i.e. x4=0 Pairs of numbers as possible solutions (4,7) (3,4) (0,4). Answered by Penny Nom. 





Express 5120 as a sum of consecutive numbers 
20020825 

From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm. 





Two equations 
20020726 

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





25m = 100 
20020422 

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





Solve for x 
20020420 

From A student: solve for x. cx 2x+b  =  a c Answered by Peny Nom. 





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. 





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. 





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 rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





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. 





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. 





Undetermined coefficients 
20011122 

From Hoda: The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Answered by Harley Weston. 





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

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





A cubic 
20011110 

From Louise: x^{3} + 9x^{2}  7x  63 Answered by Penny Nom. 





1 minus 5(y) equals negative 2 
20011110 

From Judy: 1 minus 5(y) equals negative 2 Answered by Penny Nom. 





8w15 = 3w10 
20011101 

From A student: 8w15=3w10, w =????? Answered by Paul Betts. 





Why quadratic for a second degree equation? 
20011020 

From Jana: Why do we use the word quadratic to describe second degree equations? Answered by Penny Nom. 





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. 





Investing in a yacht 
20010926 

From Junior: Marvin and his four friends wish to invest in a yacht by sharing equally in the cost. As the date of sale approaches, Marvin realizes that if three more people join the partnership, each partner's share would decrease by $18,000. How much does the yacht cost? Answered by Penny Nom. 





Solving trig equations 
20010922 

From Asad: Can you please explain to me how to solve trig Equations,e.g sin(x)=x^{4}+12/2+cos(x)=x^{6}+9/3= (if this can be solved) Answered by Claude Tardif. 





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. 





5+5+5=550 
20010611 

From Tom: I am in algebra and my teacher gave us an equation that was not true. she told us that we could only use one line segment(it can't bend turn has to be straight) to make the equation true. here is the equation: 5+5+5=550. i have not figured it out but have tried many things and believe it is not mathmatical but cross a # or sign out.also i forgot you can't put a slash mark through the equals sign. 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. 





Graphing equations 
20010501 

From A student: If, for example, 4x^{2}12x+9=0 and 4x^{2}+12x9=0, which I'm assuming it does since you can derive that equation from the first, why do those two equations have different graphs? 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. 





(8 + 5)5 = (y + 4)4 
20010401 

From Kelley: (8 + 5)5 = (y + 4)4 What is the value of y? Answered by Penny Nom. 





Solving an equation 
20010327 

From Jennifer: How would I solve this equation? 1.6 = 2x/(.1x)  the equation in parenthesises is raised to the second power. I know you take the square root of both sides, but there is where I get lost. Answered by Leeanne Boehm. 





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. 





Quadratic equations 
20010311 

From Philip: I am a student in the UK and i am in secondary school and i am doing my GCSE next year. here are my questions: solve the following equations correct to 2 decimal each time. [1] 2xsquared + 5x = 1 [2] 3xsquared(2x+1)=1 [3] xsquared + 7x + 2 = 2x + 4 [4] 5xsquared  3x = xsquared + 4 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. 





What is the value of n? 
20010303 

From Adam: When I add n to 7 and then divide my answer by 4,I get 5. What is the value of n? Answered by Penny Nom. 





Solve for the variable 
20010228 

From Ashley: I've got 2 questions. We (my dad and I) can not figure them out. please help me.  21 = 9  2 (4a + 2) and I am supposed to find out what the variable is.
 2/3 n + 3/8 n = 15/16 (those are fractions). Again, I need to find out what the variable is.
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. 





g(g+5)=0 
20010220 

From Jenna: g(g + 5) = 0 Answered by Penny Nom. 





A quartic equation 
20010215 

From George: Let P(x) = x^{4} + ax^{3} + bx^{2} + cx + d. The graph of y = P(x) is symmetric with respect to the yaxis, has a relative max. at (0,1) and has an absolute min. at (q, 3) a) determine the values for a, b c, and d using these values, write an equation for P(x) b) find all possible values for q. Answered by Harley Weston. 





Linear equations 
20010213 

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





Completing the square 
20010112 

From Jacky Lam: A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square? 8x^{2} + 8x + 4 Answered by Penny Nom. 





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. 





x^5 + y^5 + z^5 = w^5 
20010111 

From Samuel Brown: x^{5} + y^{5} + z^{5} = w^{5} I have no idea whether or not this is possible. Answered by Claude Tardif. 





Solving x  sin(x) = constant 
20001229 

From Keith Roble: If x is in radians, how do you solve for x, where: xsin(x) = constant? Answered by Harley Weston. 





Solving an equation 
20001229 

From Bob: Would you be able to help me solve this math equation.. Solve for b, 2 [b  (q + s)] / q = s 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. 





2step equations 
20001011 

From Jen: i don't get how you find the answer to these equations 140= 4 12e x/2 + 6 = 4 Answered by Penny Nom. 





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. 





A equation with a square root 
20000903 

From Lea: Please help with 2 plus the square root ( and under it has x plus 1) = 6 Thank you Answered by Penny Nom. 





Solving an equation 
20000826 

From Patrick: My question is how would u do a problem like this.......... [2x37] =15?....u have to solve it for absolute value equations....???? Answered by Harley Weston. 





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. 





(mn + m + n)/(m^2 + n^2) = 1 
20000724 

From William: Find all pair of positive integers m and n such that mn + m + n divides m^{2} + n^{2} = 1. Answered by Peny Nom. 





An equation involving x to the x 
20000722 

From Joy Peter: I am joy, a teacher teaching Maths at the secondary level and while solving a sum came to this stage when i got x^{x} (1 + log x) = 0, by which we can conclude that x^{x} = 0 or 1 + log x = 0. If x^{x} = 0, than what should be the value of x? I feel that the value of x should then be 0 (zero) but then how do I explain this to the students as we also know that anything to the power of 0 is 1 but here 0 raised to 0 is 1. If this is not defined then how do I explain this? Answered by Penny Nom. 





n! = 42(n2)! 
20000721 

From Damon Bailey: Solve n! = 42(n2)! Answered by Paul Betts. 





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. 





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. 





4x  [2x (3x  2)] = 13 
20000513 

From Teresa: I need to find the following equation. 4x  [2x (3x  2)] = 13 Answered by Penny Nom. 





Finding a Quadratic Equation given the roots 
20000416 

From A secondary student: How do I find the equation for the quadratic with roots at 2i and its complex conjugate? Answered by Harley Weston. 





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. 





Simultaneous equations 
20000311 

From Laura Molck: My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following. I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!! 1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold? 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. 





Some equations 
20000308 

From Maria: Hi, could you help me with these questions: Find x & solve  72x/3=9
 4x+3/5=2
 62x=14
 1/7x=4/3+1/6
Answered by Penny Nom. 





A mixture problem 
20000306 

From Rebecca Edwards: A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t. 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. 





Can't make an equation! 
20000130 

From Maggie Clarke: An estate is to be distributed among the wife, 3 children and 2 grandchildren. The children will each receive 2x as much as each grandchild, and the wife will receive 4x as much as each child. If the estate amounted to $115,000, how much will each person receive? Answered by Penny Nom. 





Quadratic 
20000126 

From Karen Johnson: What is the reasoning behind the title quadratic equation? 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. 





Solving an equation 
20000117 

From Shelley's Mom:
My daughter has an assignment in math that includes this equation: 6b+5= 10 I've tried to help her with a scale. We've figured that you subtract 5 from each equation so its not 6b = 15. Is this correct and can you help us figure out the next step? Answered by Penny Nom. 





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. 





Derive the quadratic equation 
20000101 

From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom. 





Solving a cubic equation 
19991230 

From Natalia: How can I solve: 2 x^{3}  x^{2} + x  2 = 0 ??? Answered by Penny Nom. 





Solve for v 
19991209 

From Beth: 13/4(v+2)=5 Answered by Penny Nom. 





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. 





How wide is the well? 
19991124 

From Chris Baranski: There is a well and in the well there are 2 sticks one is 2 meters long the other is 3 meters long and they are opposite to each other. They are leaning against the wall of the well. The place where they touch is 1 meter of the bottom of the well. How wide is the well? Answered by Chris Fisher. 





Linear models 
19991109 

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





Multiple step problems 
19991109 

From Maria Rainsdon: I don't understand how to solve these multiple step problems. I wasn't there when my teacher explained it and I am really lost. Here is one of the probs I don't understand: 3m+6=m6. Answered by Penny Nom. 





Equations with fractions 
19991010 

From Lori: I'm a secondary student. How would you figure out a problem such as t2/t =14/3t  1/3. The book gave one example but it is really easy. The work YOU have to do is totally different. You don't have to tell me the answer just how to do such problems like these. Answered by Penny Nom. 





sin x = x/10 
19991007 

From Amandeep Grover: Solve the equation sin x = x/10 Answered by Harley Weston. 





8*(5a)=15 
19990922 

From Shelby: 8*(5a)=15 i cannot get this question!! please help me!! Answered by 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. 





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. 





Question about 3rd degree polynomials 
19990423 

From Patrick Bryan: What is the general solution to the equation with the form: a*x^3 + b*x^2 + c*x + d = 0 I have once seen a solution to this a few years ago, but I do not recall if it was a general solution. What I do know, is that you could simplify this equation to: a*x'^3 + p*x' + q = 0... Answered by Doug Farenick. 





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. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? 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. 





Grade 10 math 
19990408 

From Ron: the type of question i'm having trouble with is 5(2x1)=3(x4) Answered by Penny Nom. 





Quadratic equations 
19990331 

From Ken Niebergall: #1 a^{2}  10a = 2a  36 #2 t(t  5) = 5 (t  5) #3. (x + 4)(x  3) = 8 Thanks. Answered by Jack LeSage and Penny Nom. 





Standard Form 
19990330 

From Pam: How do you put this equation into standard form? y=3.572x+5.409 Would you please put this equation in this form Ax+Dy+C=0 Answered by Penny Nom. 





An airplane problem 
19990308 

From B.M.R.: A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed? Answered by Jack LeSage. 





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. 





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. 





The Left Side of a Parabola. 
19981020 

From Shay: Find the parametrized equation for the left half of the parabola with the equation: Y=x^24x+3 Answered by Chris Fisher. 





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. 





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. 





Grade 9 Algebra 
19980607 

From Tarah Kostenko: I am a grade 9 student and I cannot figure out how to solve these two similar problems. can you please help? 3(y1/2)=1/2 also 2/3(x + 1)=6 I don't come up with the same answers as the book and I can't figure out what I'm doing wrong. Thank you,
Answered by Harley Weston. 





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. 





Find the Numbers. 
19971228 

From Sandy C: The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers. Answered by Penny Nom. 





A problem with arccos. 
19970609 

From Vanessa Chan: Prove: arc cos4/5 + arc cos (5/13) = arc cos (56/65) Answered by Harley Weston. 





The General Equation of a Parabola 
19970528 

From Michelle: My name is Michelle and I am a 10th grade student in algebra 2 w/ analysis. I am doing a report on parabolas and I need to know what the general equation is. I've looked in books and keep finding different ones! I also need to know how they can be used in nature. Thank you so much for your time. I really appreciate it!  Michelle Answered by Harley Weston. 





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. 





Why QUADratic? 
19970319 

From Paula Miller: A student today asked me why a quadratic, with highest power of degree 2, was called a QUADratic. We're awaiting the answer with baited breath! :) Answered by Chris Fisher and Walter Whiteley. 





A Functional Equation. 
19970226 

From Ronald Lui: Find all functions f:S > S statisfying the two conditions: 1)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S 2)f(x)/x is strictly increasing on each of the interval 1 Answered by Saroop Kaul and Chris Fisher. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? Answered by Harley Weston. 





Résolution d'une équation 
20100225 

From sellin: Il faut que j'exprime x en fonction de m dans l'équation suivante et je n'y arrive pas:
3x + 1 = (m1) / 2 * x + (2m + 3) / 5 Answered by Claude Tardif. 





Un système de plusieurs équations et plusieurs inconnues 
20090122 

From Cédrick: J'ai un problème écrit à résoudre estce que vous pouvez m'aider ?
Le premier est le tiers de la somme des deux autres.
La somme du premier et du deuxième est 13.
Le produit du deuxième et du troisième est 56.
Réponse: Le premier nombre est___________________
Le deuxième nombre est _________________
Le troisième nombre est _________________
Answered by PierreLouis Gagnon, Antoine Letarte at Claude Tardif. 





Combien d'éleves fréquentent cette école? 
20080404 

From Jeff: Une ecole compte sept fois plus d'éleve que d'enseignants et enseignantes .De plus , le nombre de membres du personnel non enseignant correspond a la moitié du nombre d'enseignats et enseignantes . Si l'on tient compte de l'ensemble des éleves , du personnel enseignant et du personnel non enseignante , on dénombre 714 personnes . Combien d'éleves fréquentent cette école? Answered by Antoine Letarte. 





Système à deux équations 
20071211 

From Fabrice: un rectangle a 130 m pour périmetre. si on diminue sa longueur de 1 m et on augmente sa largeur de 1 m, l'aire augmentera de 14m².
trouver les deux dimentions du rectangle. (on trouvera, au préalable, la difference des deux dimensions) Answered by Claude Tardif. 





Des mots aux équations 
20061102 

From Julie: La diffÃ©rence de deux nombres, x et y est de 28. Le nombre y correspond aux huit neuviï¿½mes du nombre x. Trouvez ces deux nombres. Answered by Claude Tardif. 





P(x+1)P(x)=x 
20050421 

From Etienne: ~P(x)=a x^{3}+ b
x^{2}+ c
x
~P(x+1)P(x)=x^{2}
question: trouver les trois nombres a,b et c. Answered by Claude Tardif. 





l'équation d'une rotation dans un graphique cartésien 
20011114 

From Ghaith: je d6sir que vous me rafraichissez un peu la mémoire s.v.p. j'aimerai savoir l'équation d'une rotation dans un graphique cartésien merci Answered by Claude Tardif. 





Resolution of the equation f(x)=0 
20000401 

From Naoufal: How can i evalf the equation f(x)=0 with f function . Can you ansear me in french thank you very much Answered by Claude Tardif. 





Les equations 
19991209 

From Enciso Alberto: j'ai les equations suivantes: X1=Rs + A1/(B+W^2) X2=Rs + A2/(B+W^2) X3=Rd + A3/(B+W^2) X4=Rd + A4/(B+W^2) X5=Rg + A5/(B+W^2) X6=Rg + A6/(B+W^2) dont les coefficients Ai (i=1,2,..) et B sont constants (mais on ne conais pas leur valeur) et Rs, Rd, et Rg sont inconnues. Nous pouvons constater que la dependence de ces differentes expessions en fonction de W^2 est identique. Le tracé de l'une de ces expressions en fonction d'une autre est donc une driote. . . . Answered by Claude Tardif. 





ln(x+3)+ln(x+2)=ln(x+11) 
19991124 

From Thibault Portevin: "Résolvez l'équation : ln(x+3)+ln(x+2)=ln(x+11)" Je suis bloqué, pourriezvous m'aider? Answered by Claude Tardif. 





Gravity equation 
19991021 

From JeanMarie Le Ray: J'ai dû traduire un texte avec la formule "gravity equation", que j'ai rendue par "équation de gravité", sans absolument savoir de quoi il s'agit. Quelqu'un saitil si cela est juste et ce qu'est exactement une "gravity equation"? Answered by Claude Tardif. 

