







Finding the area of a regular polygon 
20070504 

From Dana: We are trying to figure the square footage of a tetradecagon....sort of a round house with 14 sides that are 8 ft' in length. It has a height of 9 ft. How do we figure the square footage of this? Answered by Stephen La Rocque. 





A tube through a board at 45 degrees 
20190615 

From Guy: I need to insert a tube 5/8" diameter into a board at a 45 degree angle. What size hole must I drill for the tube to fit snugly? Answered by Harley Weston. 





Pennies, nickels, dimes, and quarters 
20190509 

From william: Ann has 177 coins (pennies, nickels, dimes, and quarters)
Her total value is $19.90
She has the same number of nickels as dimes.
She has the same number of quarters as dimes.
How many of each does she have? Answered by Penny Nom. 





Double the number of pennies each week 
20190228 

From Donald: If I save a penny a week,double it every week,How many weeks will it take to reach 1,000,000 dollars Answered by Penny Nom. 





An open top box 
20181212 

From Kirklan: Jeremy wants to construct an open box from an18inch square piece of aluminum. He plans to cut equal squares, with sides of x inches, from each corner and then fold each side up to form the box. If Jeremy wants the volume of the box to be 432 cubic inches, what should the minimum length of the sides of the squares cut from each corner be? Find the volume, V, of the box as a function of x. Given: V = length × width × height. Answered by Penny Nom. 





A square and a triangle 
20181203 

From Livvy: a square with a perimeter of 48 and a triangle with a perimeter of 38. when they are joined they make a pentagon. please find the perimeter
how can you find the perimeter of this. could you please help me? Answered by Penny Nom. 





Monthly Pension 
20180528 

From Kenneth:
Hello:
I have a question regarding how the units cancel in the following:
A company uses the following calculation to determine the monthly payment for its employees as they retire:
1.1% * average 5 years highest salary * years of service
If an employee worked 33 years and his average 5 year salary is $30,705.17, what is his monthly payment?
I used the following to determine his monthly payment, but I am not sure how the units cancel especially the years.
1.1% * $30,705.17 * 33 years divided by 12 months/year
I determined his payment as $928.83 per month, but the year units do not cancel unless the 1.1% is per year.
Is the correct calculation 1.1%/year * $30,705.17 * 33 years divided by 12 months/year so that the units cancel properly?
The $\$30,705.17$ is an average for 5 years of working. It is not $30,705.17 per year.
I thank you for your assistance. Answered by Penny Nom. 





Two regular pentagons 
20180319 

From Kip: The ratio of the corresponding apothems of two similar regular pentagons is 5:7 What is the ratio of their areas? Answered by Penny Nom. 





A penny is thrown from the top of a building 
20180316 

From Zoraida: A penny is thrown from the top of a 26.7meter building and hits the ground 3.39 seconds after it was thrown. The penny reached its maximum height above the ground 0.89 seconds after it was thrown.
a. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.
b. What is the maximum height of the penny above the ground? 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. 





When are the hands of a clock perpendicular? 
20180111 

From Nazrul: How many times in a day are the hands of a clock perpendicular to each other? How can I find the times? Please help me. Answered by Penny Nom. 





Needing the area of an irregular Pentagon 
20171206 

From Dale: I'm needing to find the square footage of an irregular pentagon.
I've seen the other questions similar to this one, but without a great deal of difficulty can't get you the angle degrees, or the length between opposing angles.
I'm hoping that a different bit of information can help. So here goes:
The longest side is 67ft long.
One of its legs is 39ft long, and the other is 18ft long.
The leg off of the other end of the 39ft leg is 35ft long.
The leg off of the other end of the 18ft is 49ft long, and meets the other end of the 35ft side.
The information that I DO have, which I'm hoping makes the difference, is that the 39ft and the 18ft sides are parallel.
Also, while the angles at each end of the 67ft side are not right angles, they are fairly close to it,
approximately 80 degrees at the 39 ft side corner, and 100 degrees at the 18ft side corner.
Dale. Answered by Harley Weston. 





Parallel and Perpendicular lines 
20170717 

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





A suspension bridge 
20160818 

From sai: The main cable of a suspension bridge has the shape of a parabola. The cables are strung from the top of two towers, 61 metres apart, each 15.25 metres high above the roadway. The cable is 1.5 metres above the roadway at the point that is directly between the towers.
h(x)=a(x30.5)^2+1.5
where a is the constant and its value to be determined.
a) determine the value of the constant a by using that the fact that height of the suspension cable, h(x) is 15.25 metres at each tower. Hence, write the updated model equation. Answered by Penny Nom. 





An open ball is an open set? 
20160623 

From Aqeel: Theorem: The open ball is an open set? Answered by Harley Weston. 





A barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom. 





Dimes and pennies 
20160426 

From Renae: Charity has 42 more pennies than dimes. Hope has 7 times as many pennies than dimes. Hope and Charity have the same number of dimes. Together they have $5.46. How many dimes and pennies do each have? Answered by Penny Nom. 





Pizza delivery 
20160403 

From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.
Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)
I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it!
It would be gladly appreciated if you could help! Answered by Penny Nom. 





Perpendicular lines 
20160214 

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





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





The area of a pentagon 
20141104 

From Gracie: i really need help with this problem in my math book, will you help?
"Derrick drew regular pentagon with side lengths of 8 centimeters.
He divided the pentagon into 5 identical triangles, and measured the
height of one of the triangles to be 5.5 centimeters. Find the area of
the pentagon."
this really makes no sense to me. Can you help me with anything
to make it easier?
THANKS!!!!! Answered by Penny Nom. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





A parabolic suspension bridge 
20140311 

From jeffrey: the towers of a parabolic suspension bridges 200 meter long are 40 meter high and the lowest point of the cable is 10 meter above the roadway.Find the vertical distance from the roadway to the cable at 50 meter from the center. Answered by Penny Nom. 





A circle which is tangent to two perpendicular lines 
20140309 

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





A contest with 31 people 
20130906 

From Kevin: There is a contest with 31 people and only one winner each week.
We play for 17 weeks.
What are the odds of winning at least one week?
The chances of winning each week are independent from previous weeks. Answered by Robert Dawson. 





Two perpendicular lines 
20130815 

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





Drawing a pentagon 
20130506 

From jacob: hello. i am trying to draw a template for a project. but i don't have a
protractor. i'm trying to draw a normal pentagon with 2cm sides. what
i'm trying to figure out is the distance in centimeters from point a, to c,
in a straight line. this is needed so that i can measure and create the
shape without a protractor, and keep the angles and sides correct.
if you can help me with the measurement, or help me another way,
any help would be greatly appreciated. thank you. Answered by Penny Nom. 





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

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





A 5 pointed star in a circle 
20120805 

From wiljohn: find the area of a 5 pointed star in the circle with a radius of 12.517 Answered by Chris Fisher. 





John's electronic store 
20120725 

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





Drawing an isosceles triangle 
20120510 

From Nazrul: How can I draw an isosceles triangle whose each angle adjacent to the base is twice the vertex angle? Answered by Chris Fisher. 





The period T of a pendulum 
20120327 

From Ashley: The period T of a pendulum is given in terms of its length, l, by T=2pi sqrt(l/g) where g is the acceleration due to gravity(a constant)
a. find dT/dl
b. what is the sign of dT/dl
c. what does the sign of dT/dl tell you about the period of the pendulums? Answered by Penny Nom. 





A suspension bridge 
20111130 

From jennifer: suspension bridges like the golden gate bridge, are used to span large distances.
when the main curved cables are attached to the deck by vertical cables they will end
up in the shape of parabola. assume that we need to build a bridge that spans
2,400 feet. the two towers 165feet tall each where placed at 400feet from either
side. the lowest point of the center of the bridge at 10feet. vertical suspension cables
where placed at 25foot interval. how many feet of cable are needed to connect
the deck to the main cables between the two towers? show all working. Answered by Penny Nom. 





The interior angles of a pentagon 
20110310 

From Daima: I need help!
The interior angle of a pentagon i s5 ( I hope ) or 540 degrees.
The interior angle of a pentagon is what? Explain to me please.
Daima Answered by Penny Nom. 





Two perpendicular chords 
20100911 

From edwin: two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. I do not a have clue on how to do it so can you please help me with it Answered by Robert Dawson. 





Differentiable on an interval 
20100812 

From Dave: Hi
I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help. Answered by Robert Dawson. 





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 capilano suspension bridge 
20100603 

From nida: the capilano suspension bridge in north vancouver is the world's highest footbridge of its kind. the bridge is 140m long . from the ends of the bridge the angles of depression of a point on the river under the bridge are 41 degrees and 48 degrees. how high is the bridge above the river to the nearest metre Answered by Penny Nom. 





Two adjacent rectangular dog pens 
20100301 

From Janet: Clint is constructing two adjacent
rectangular dog pens. Each pen will be three times as long
as it is wide, and the pens will share a common long side.
If Clint has 65 ft of fencing, what are the dimensions of
each pen? Answered by Penny Nom. 





A regular pentagon 
20091214 

From Jamie: A regular pentagon is inscribed in a circle of radius 4.5 cm.
Determine its perimeter and area to one decimal place!
Thank YOU ! :) Answered by Penny Nom. 





Two adjacent pig pens 
20091204 

From alysia: A pig farmer wants to build two adjacent pens using 96 feet of fencing. He wants rectangular pens that share the short side and the overall length is to be six more than twice the width. What should be the dimensions of the overall pen? Answered by Penny Nom. 





Two similar pentagons 
20091116 

From louis: The lengths of five sides of a pentagon are 1,3,5,7,and 12 units. If the length of the longest side of a similar polygon is 18 units, find the perimeter of the larger pentagon. I think I figured it out Not sure though. Answered by Penny Nom. 





Pennies and dimes 
20091111 

From Rachel: Kesha had only pennies and dimes in her change purse. When she counted out her change she had 64 cents/ of she had 6 times as many pennies as she did dimes, how many pennies did she have? Write equation and solve it.
Can someone help me with this? Answered by Penny Nom. 





The extended real numbers 
20091102 

From Justin: Hello there, I was wondering is the set of extended real numbers a closed set or an open set?
Justin Answered by Robert Dawson. 





Is it a rectangle? 
20091029 

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





Two non zero vectors 
20091027 

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





Pennies, nickels and dimes 
20090922 

From Kiadadh: Show 12 ways to come up with 28 cents using only pennies, nickles and dimes Answered by Robert Dawson. 





Toss a coin and roll a die 
20090921 

From Celeste: Can you please tell me how to set up this problem to find the answer. I know they are independent from there I don't know.
a coin and a regular sixsided die are tossed together once. What is the probability that the coin shows a head or the die has a 5 on the upward face? Answered by Penny Nom. 





An area problem 
20090830 

From Amber: Area of hexagon ABCDEF with the vertices (3,0) (7,0) (9,2) (7,4) (3,4) (1,0) Answered by Harley Weston. 





A pentagon inscribed in a circle 
20090729 

From Faisal: O is the center of the circle. Sides AB and AE are equal. Angle B = 95,
angle C = 130, angle D = 138. Find angles A and E.
Diagram is attached.
Best,
Faisal Answered by Chris Fisher. 





Buying pens and staplers 
20090722 

From Ellen: one more math question,
six pens and four staplers cost $7.10. four pens and seven staplers cost $9.50
find the cost of one pen and one stapler. Answered by Penny Nom. 





Finding the Line Joining Perpendicular Feet 
20090716 

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





The product of gradients between 2 perpendiculars lines 
20090611 

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





Probability of Two Independent Events 
20090607 

From Sharon: A basketball player is given 2 freeshots, if the probability of making 1 of the 2 shots is 3/4 what is the probability of making 2 of the 2 shots or both shots? Answered by Janice Cotcher. 





Perpendicular lines 
20090507 

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





15 pigs in 4 pens 
20090422 

From Melissa: A farmer has 15 pigs. He wants to put them all into 4 pens, have an
odd number of pigs in each pen, and have no pigs left over. Also, he
isn't thinking about having any for dinner, as they are his pets.
How does he do it? Answered by Robert Dawson. 





A perpendicular line in standard form 
20090421 

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





The interior angles of a pentagon 
20090420 

From Mary: If four interior angles of a fivesided figure pentagon measure 100 degrees each, what will the fifth angle measure? Answered by Harley Weston. 





Parallel and perpendicular lines 
20090408 

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





The perimeter of a pentagon 
20090407 

From Malysa: A pentagon has an area of 1400 cm squared. Determine its perimeter. Answered by Harley Weston. 





Dependent & Independent Events 
20090306 

From maci: what is the probablility of drawing at random 2 blue marbles in a row
if there is 3 red,4 green,2 yellow,and 5 blue marbles? Answered by Janice Cotcher. 





Symmetries of a polyhedron 
20090302 

From Vincent: I want to ask is there a formula to find out the number of axes of rotation & plane
of reflection of a 3D figure, like pentagon, pyramid? Answered by Chris Fisher. 





Augmented matrix: independent, dependent, or inconsistent? 
20090223 

From Anna: Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.
x + y + z = 11
x  y + 3z = 5
2x + 2y + 2z = 15 Answered by Harley Weston. 





Time in a Swing 
20090222 

From Barb: I looked at the questions concerning a pendulum as I know I need to use this formula but I am stiil not able to figure this problem out. Can you help?
If a child is on a swing with a 10 foot chain, then how long des it take to complete one cycle of the swing?
I know I am suppose to use the formula 8T^2 = pi^2 L but I do not understand how to do this.
Thanks Answered by Janice Cotcher. 





A line is perpendicular to another line 
20090116 

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





A kennel with 3 individual pens 
20090106 

From Jean: An animal clinic wants to construct a kennel with 3 individual pens, each with a gate 4 feet wide and an area of 90 square feet. The fencing does not include the gates.
Write a function to express the fencing as a function of x.
Find the dimensions for each pen, to the nearest tenth of a foot that would produce the required area of 90 square feet but would use the least fencing. What is the minimum fencing to the nearest tenth? Answered by Harley Weston. 





What is so important about quadratics? 
20081129 

From zoe: what is so important about quadratics? Answered by Harley Weston. 





A word problem about a regular pentagon 
20081116 

From Sandra: If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm. Answered by Chris Fisher and Penny Nom. 





Purchasing pens and pencils 
20081107 

From Maggie: A mechanical pencil costs 50 cents and a pen costs 25 cents. If I spend 5.00 on 17 pens and pencils, how many of each does that buy? Answered by Penny Nom. 





Perpendicular lines 
20081016 

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





Bags of pennies 
20081011 

From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West. 





Lines that pass through a point 
20080930 

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





Perpendicular 
20080908 

From amanda: hi my name is amanda medjuck i am in grade 7. we are learning basic geometry terms and have to
define words BUT I DONT KNOW WHAT A PERPENDICULAR LINE IS PLEASE HELP ME!!! Answered by Penny Nom. 





Parallel and perpendicular lines 
20080906 

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





Cost of pencil is rising every year since 7 years ago 
20080806 

From Mari: Cost of pencil is rising every year since 7 years ago. If the cost of
pencil last year was 60 cents which is the sum of the cost from the
last two previous years, what is the cost of the pencil now, the cost
seven years ago. Answered by Penny Nom. 





A fivesided coin 
20080629 

From carla: A new fivesided coin is to be made in the shape of figure 8.6
The point A on the circumference of the coin is the centre of arc CD, which has a radius of 2cm
Similarly B is the centre of arc DE, and so on.
Find the area of one face of the coin. Answered by Harley Weston. 





A jar of pennies 
20080618 

From Ryan: if you are given a jar of pennies and you had to find the weight of one penny
without opening the jar.when you graph it, You have to y= the mass of the container and x= number of coins
you use the slope to find the weight of the penny how would u go about doing that? Answered by Stephen La Rocque. 





A line which is perpendicular to another line 
20080618 

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





Double one penny for 30 days 
20080611 

From kerwin: one penny doubled for 30 days what is the answer? Answered by Penny Nom. 





The area of a regular pentagon 
20080602 

From Jenna: I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given. Answered by Penny Nom. 





The angles of an irregular pentagon 
20080520 

From victoria: The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle? Answered by Penny Nom. 





An open box 
20080423 

From Le: Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. Answered by Harley Weston. 





The area of an irregular pentagon 
20080402 

From shane: i Need to find out what this adds up to i have a diagram of a pentagon and all the shides are different how do i do this if the sides are 5100,7200,7200,7400,7400 Answered by Harley Weston. 





A fish tank in the shape of an irregular pentagon 
20080329 

From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)
there will 3 right angles A, B, E
my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher. 





A pentagon inscribed in a circle 
20080319 

From Elaine: My question as written on my homework is: Given a pentagon inscribed in a circle of radius r, determine a) the angle between any two sides of the pentagaon b) the perimeter of the pentagaon c) the area of the pentagon. I know this kind of counts as three questions, so if you can only answer one, that's okay. Any help will be much appreciated. Thanks! Answered by Stephen La Rocque. 





Two perpendicular lines 
20080307 

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





A three dimensional object 
20080304 

From Briana: what is the 3d term for pentagon? like a circle is a shhere? Answered by Penny Nom. 





Two regular pentagons 
20080227 

From Shirley: Regular pentagon QRSTU has a side length of 12 centimeters and an area of
248 square centimeters. Regular pentagon VWXYZ has a perimeter of 140
centimeters.
I need to find its area. Answered by Stephen La Rocque. 





A square and an equilateral triangle 
20080210 

From Emily: A square pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen. Answered by Stephen La Rocque. 





A dependent variable 
20080130 

From lavada: i need the definition to dependent variable Answered by Stephen La Rocque. 





How many houses must they paint? 
20071212 

From Natalie: The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds.
If they work for four months of the summer and their expenses are 152
pounds per a month, how many houses must they paint for each of them
to have one thousand pounds at the end of the summer? Answered by Penny Nom. 





A triangle and a pentagon 
20071208 

From Olivia: A regular pentagon has an area of 800 square centimetres. What is the area of the triangle extended from one side of the pentagon? Answered by Stephen La Rocque. 





Proving a quadrilateral is a rhombus 
20071203 

From Jeanie: How do you prove that a quadrilateral is a rhombus because the diagonals
of the quadrilateral are perpendicular and bisect each other using the 2column
proof method? Answered by Stephen La Rocque. 





Chris has twice as many $1 bills as pennies 
20071102 

From vicky: Chris has twice as many $1 bills as pennies, twice as many dimes as he has $10 bills, and twice as many pennies as he has dimes. How much money does he have? Answered by Penny Nom. 





Convert a diameter of a pencil into centimeters 
20071102 

From Kaitlyn: I need to convert a diameter of a pencil into centimeters, but how many
diameters are in a centimetres? Thanks =) Answered by Penny Nom. 





The area of a regular pentagon 
20071101 

From sarah: i'm trying to find the area of a regular pentagon with 200m sides, ive split it into 5 triangles so i dont know either sizes of the lengths and i need to find the height!
how? Answered by Penny Nom. 





Parabolic suspension bridge 
20071009 

From Jessica: A suspesion bridge with weight uniformly distributed along its length has twin towers
that extend 75 meters abouve the road surfce and are 400 meters apart.The cables are
parabolic in shape and are suspended from the tops of the towers. The cables touch the road
surface at the center of the bridge. Find the height of the cables at a point
100 meters from the center. (Assume that the road is level.) Answered by Stephen La Rocque. 





Doubling every day 
20071007 

From Jerrie: Patti saved pennies for 10 days. The first day she saved 1 cent. Every day after that she saved twice as much as the day before. How much money did Patti save altogether? Answered by Stephen La Rocque. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





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

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





Perpendicular lines 
20070906 

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





Area and perimeter 
20070816 

From sheryl: a 50*70 horse pen is 240 feet and 3500 square feet
a 60*60 horse pen is 240 feet and 3600 square feet
why is there a 100 square feet difference? Answered by Penny Nom. 





How many pennies will a half gallon bottle hold? 
20070811 

From Harold: How many pennies will a half gallon bottle hold Answered by Penny Nom. 





All five angles of a pentagon ABCDE are equal 
20070804 

From Jerry: All five angles of a pentagon ABCDE are equal. The diagonals AC, AD and BD have the same length. Prove that all five sides of the pentagon are equal in length. Answered by Penny Nom. 





Find the area of a regular pentagon inscribed in a circle 
20070803 

From Tracy: Can you please help me with finding the area of a regular pentagon inscribed in a circle using the Pythagorean theorem. The radius of the circle is 5 cm and each side AB = BC = CD = DE = EA = 6 cm. Answered by Stephen La Rocque, Leeanne Boehm and Chris Fisher. 





Equation of a perpendicular line 
20070728 

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





Area of a star in a regular pentagon with side length 10cm 
20070724 

From Chetna: A regular pentagon with side 10 cm has a star drawn within (the vertices match).
What is the area of the star? Answered by Stephen La Rocque. 





Area of a pentagonal lot 
20070509 

From Mimi: I would like to know the square footage of a pentagon with the
following measurements:
Property is .43 of an Acre
Front: 57.11'
NW: 105.78'
S: 120'
SE: 145'
E: 102.86'
I don't want you to try to show me how to work thru the problem since
I will never comprehend it. For some reason, I am unable to perform these
kinds of equations. I will greatly appreciate your help. Answered by Penny Nom. 





Finding out if two line equations are parallel or perpendicular 
20070428 

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





The area of an irregular pentagon 
20070414 

From Steven: I have been given a coursework in which i have to investigate various shapes to find the one that would give the largest area with 1000m perimeter.
I'm stuck in a part where i have to calculate the area of a irregular pentagon. i don't know where to start from. I can make up the length of all the sides (5 sides), so long they add up to 1000, but i'm not quite sure what to do after that. Answered by Penny Nom. 





Reducing the over all size of a irregular pentagon 
20070411 

From Gilbert: I'm having trouble figuring out how to reduce the over all size of a irregular pentagon.
The pentagon I'm trying to reduce has 2 right angles adjacent to each other.
Basically the shape of a house. I have width, length of the legs and the height of the peak.
But cannot figure out how to get the size of a reduced version that keeps the same proportion
and angles.
Thanks
Gilbert Answered by Penny Nom. 





An irregular pentagon 
20070411 

From reg: Hi, i have been given an irregular pentagon in which i have to work out the area.
I have been told to make three triangles and then work out the area of these triangles and then add them up.
I require your help because i have the length of two sides of one of the triangle  how do i work out the other side?
I have not been provided with any angles  can i make the angles up? Answered by Penny Nom. 





Slopes of perpendicular lines 
20070327 

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





The area of an irregular pentagon 
20070326 

From grace: hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much. Answered by Penny Nom. 





A line that is perpendicular to another line 
20070316 

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





The period of a simple pendulum 
20070310 

From Melissa: The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa Answered by Penny Nom. 





A truncated cone 
20070310 

From Russell: Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom.
Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service.
Russell Answered by Penny Nom. 





An irregular pentagon 
20070308 

From kelly: If I have a pentagon with 2 sides of length 5 and one with a length of 2, what are the lengths of other 2 sides? Answered by Stephen La Rocque. 





The net for a pentagonal pyramid 
20070305 

From MaKayla: How many bases does the net for a pentagonal pyramid have? Answered by Penny Nom. 





A pentagon inscribed in a circle 
20070222 

From Amanda: Find the formula for calculating the length of the side of a pentagon given the radius of the circle that encloses it. Once you find the formula, find the length of the side of a pentagon which is enclosed in a circle 12 cm in diameter. So I need to know the formula, and the length of the side of the pentagon. Thank you!! Answered by Penny Nom. 





The area for a pentagon 
20070209 

From nicole: how do you find the area for a pentagon Answered by Stephen La Rocque. 





Splitting a 5 acre piece of property 
20070125 

From John: I have a 5 acre piece of property that I wish to split into 5 individual 1 acre parcels. The 5 acre parcel 1s 660 feet in length and 330 feet in width. The first two parcels are 264'x165', but I am asking for help getting the perimeters of the last 3 lots, one of which is a irregular pentagon. All of the one acre parcels must have an area of 43,560 square feet each. Answered by Penny Nom. 





A regular pentagonal pyramid 
20070125 

From Vickifazio: a regular pentagonal pyramid has a base perimeter of 1,085 ft. How long is one side of the base? Answered by Stephen La Rocque. 





A line perpendicular to another line 
20070113 

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





21 pigs and only 4 pig pens 
20070111 

From Emma: i was given this pig pen problem. if there are 21 pigs and only 4 pig pens how can you distribute the pigs into the pens and have an odd number of pigs in each pen. it doesn't seem possible to me. i need help! Answered by Haley Ess. 





How do the perimeters of the two pentagons compare? 
20070102 

From Robert: If the area of one pentagon is eightyone times the area of another pentagon, how do the perimeters of the two pentagons compare? Answered by Penny Nom. 





Parallel and perpendicular lines 
20061207 

From Valeria: I m having trouble with parallel and perpendicular lines a problem i need help with is y=6 find the slope if al line parallel to the graph of each equation Answered by Stephen La Rocque. 





Bill has four more dimes than nickels ... 
20061105 

From Allison: bill has four more dimes than nickels, and seven fewer nickels than pennies.he has a total of $3.35. how many of each kind of coin has he? Answered by Karen McIver. 





The area of regular pentagon inscribed in a circle 
20061012 

From Admire: i need help on how to find area of regular pentagon inscribed in a circle of radius 8cm Answered by Stephen La Rocque and Penny Nom. 





Family of lines 
20060929 

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





The velocity of a pendulum, part II 
20060907 

From Erin: We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says....
"estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain." Answered by Harley Weston. 





$10.00 worth of pennies 
20060830 

From Amelia: IF YOU MADE A LINE WITH $10.00 WORTH OF PENNIES, HOW LONG WOULD THE LINE BE? Answered by Stephen La Rocque and Penny Nom. 





Building an octagonshaped deck 
20060711 

From Maurice: I'm a landscaper and one of my customers wants me to build her an octagon shaped deck in the back yard that has a measurement of 16 by 16. I'm not sure of the way to measure for materials required. It will be built with 2 by 6 lumber with a half inch spacing between the 2 by 6. Answered by Stephen La Rocque. 





The area of a pentagon 
20060511 

From Jessica: i have to find the area of a pentagon ABCDE whose vertices are A (2,5), B (2,2),C(2,4), D(5,2) and E(4,2) Answered by Stephen La Rocque. 





A fence around a pen 
20060330 

From Daryl: I hope you can help me out with the attached problem, It has been driving me crazy. Answered by Stephen La Rocque and Penny Nom. 





The area of a pentagon 
20060201 

From Edward: I am working on finding the Sq. ft of a pentagon. I saw another question like it but I am lost. I have a pentagon that is 6ft on every side what is the Sq Footage of that pentagon? Answered by Penny Nom. 





An array of pennies by year 
20051229 

From Sheila: What is an array? How do you create an array using 100 pennies by years? Answered by Penny Nom. 





Josh and John were both exposed to the flu 
20051216 

From Dudley: Josh and John were both exposed to the flu. John has a 25% chance of getting it, while Josh has a 75% chance of getting it. What are the chances that at least one of them has the flu?
Answered by Penny Nom. 





Can we take the derivative of independent variable 
20051018 

From Mussawar: why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why. Answered by Walter Whiteley. 





Open dots and closed dots 
20050929 

From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny. 





The area of a pentagon 
20050824 

From Susan: I need to calculate the square footage of a regular pentagon (all angles are equal). Each side is 16 feet long. Answered by Penny Nom. 





An irregular pentagon 
20050223 

From Tony: Please help me with confirming the area in square footage of the irregular pentagon
My Name is Tony and I am working on understanding the square footage as calculated in the drawing. I also believe this is a secondary level question.
I saw the example http://mathcentral.uregina.ca/QQ/database/QQ.09.03/dana2.html and would appreciate how you worked through the problem, but couldn't find the calculations so that I could adapt them to my sizes. Answered by Penny Nom. 





The area of a pentagon 
20040606 

From Dana: HELLO, I NEED HELP IN DETERMINING THE SIZE OF A PENTAGON.
one side is 280',from both ends of the 280 'section,we have 300' lengths,from one of these 300' sections we have a 118' length,which goes over to a length of 228',will this be enough info. or should i provide more. thanks Answered by Penny Nom. 





Sum of the angles in a pentagon 
20040311 

From Ashish: What is the sum of all the measures of the angles of a Pentagon Answered by Penny Nom. 





Arrays of pennies 
20040117 

From Kathleen: How do I create an array of 100 pennies? Answered by Penny Nom. 





Lines 
20031114 

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





An array of pennies 
20030523 

From Saundra: If you have 100 pennies and you are suppose to make an array do you arrange the pennies by date? Answered by Penny Nom. 





Profit for a dance studio 
20030428 

From Craig: A dance studio charges $80 per student for a series of 2 hour lessons. The studio's costs are $30 per hour for the instructor, $15 per lesson for the room rental, and $3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class. Answered by Penny Nom. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





Collinear Points 
20030113 

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





Constructions of polygons 
20030103 

From Garrett: Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon? Answered by Chris Fisher. 





Construct a pentagon 
20021212 

From Mary: We were wondering what the instructions/formula, stepbystep, is to make a pentagon. Answered by Chris Fisher and Penny Nom. 





Probability 
20020816 

From Chris:
There are two possible outcomes for a random event, A and B. The probability of A being the outcome is 63%, and B 37%. What is the likelihood that B will be chosen twice, consecutively? Three times, ten? Answered by Andrei Volodin. 





Pigs in pens 
20020710 

From Shannon: A farmer has 21 pigs and 4 pens, he must put an odd number of pigs in each pen, how does he do it? Answered by Penny Nom and Chris Fisher. 





Normal lines 
20011211 

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





A polygon with five sides 
20011003 

From A student: I was asked a question in 5th grade today that goes: i am a polygon with five sides and 2 right angles what do i look like and what is my name Answered by Penny Nom. 





Intersection of perpendicular cylindrical surfaces 
20010731 

From Charlie: Please consider two right circular cylinders, perpendicular one to the other, and of unlike radii in a 3 dimensional Cartesian space with mutually perpendicular x,y,z axes. If one cylinder is centered on the y axis with radius ra, and the other on the z axis with radius rb, then the expression for the first surface would be x^{2} + z^{2} = ra^{2}, y = any number. Likewise, the second cylinder's surface would be x^{2} + y^{2} = rb^{2}, z = any number. It is my intent to define the curve at the intersection of these two cylindrical surfaces. From sketching the conditions it appears that this intersection resembles an ellipse folded about its minor axis. Answered by Chris Fisher. 





Marginal Propensity to Consume 
20010509 

From Esther: The derivative of the national consumption function C = f(y) is called the ____________________. Answered by Judi McDonald. 





Area of a regular polygon 
20010501 

From Carl: What is the formula for finding the area of a regular Hexagon and a regular Pentagon Answered by Penny Nom. 





A lemon and a recall 
20010425 

From Katie: A Man has two cars, a recall and a lemon. The probability that the recall starts is 10%. The proabability that the lemon will start is 5%. What is the proabability that both cars will start? Answered by Andrei Volodin. 





Hexominos 
20010405 

From Tom: What is a hexomino and how many different shapes are possible? Answered by Harley Weston. 





A suspension bridge 
20010324 

From Janna: The cables of a suspension bridge hang in a curve which approximates a parabola. The road bed passed through the vertex. If the supporting towers are 720m apart and 60m high, find: a) an equation of the parabola (it's y = ^{1}/_{2160}x^{2}) b)the height of the cables at a point 30m from the vertex. I substituted 30 in for the x value and got 0.42 and the answer is 42. What did I do wrong? Answered by Denis Hanson and Claude Tardif. 





Kinds of lines 
20010209 

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





An irregular polygon 
20010209 

From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher. 





A dollar, quarter, dime, nickle and penny 
20010107 

From Sarah: Arnold has a dollar coin, one dime, one quarter, one nickel, and a penny. The number of different sums of money that can be formed using three coins is... Answered by Penny Nom. 





Is this a right triangle? 
20001208 

From Alicia: How would you setup and answer a problem like these one? Triangle ABC has vertices A(2,2), B(1,2), and C (1,2). Use slopes to determine if the triangle is a right triangle. Answered by Penny Nom. 





Bridges and parabolas 
20001118 

From Lauren: My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Answered by Harley Weston. 





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. 





Independent tests 
20001007 

From A student: If the falsepositive rate of each test in a battery of tests is 0.05, how many independent tests can be included in the battery if we want the probability of obtaining at least one falsepositive result to be at most 0.2? Answered by Harley Weston. 





Velocity of a pendulum 
20000828 

From Mekca: A pendulum hangs from the ceiling. as the pendulum swings, its distance,d cm, form one wall of the room depends on the number of seconds,t, since it was set in motion. assume that the equation for d as a function of t is: d=80+30cos3.14/3t, t>0. estimate the instantaneous rate of change of d at t=5 by finding the average rates for t=5 to 5.1, t=5 to 5.01, and t=5 to 5.001. Answered by Harley Weston. 





Parallel and perpendicular lines 
20000508 

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





An expected value 
20000424 

From Carl Pride: Suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent. sample: What is the expected number of students who will pass?? Answered by Harley Weston. 





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. 





Angles in Polygons 
19990121 

From Jen:
 How do u find the interior angles of a pentagon when you are given 4 of the angles and you need to find the fifth?
 If you are given the measure of each exterior angle of a regular polygon, how do you figure out how many sides the polygon has?
 i need all information on polygons and how to find their angles!!!
Answered by Jack LeSage. 





Concurrent Lines in a Triangle 
19980810 

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





Pentominoes 
19961114 

From Sam Maraldo: What is a pentominoe? I need to understand the concept and how/why it is used? Answered by Penny Nom. 





A tangent to a circle is perpendicular to the radius at the point of contact. 
19961022 

From Rita Leung: I wonder if there is any proof for this theorem  A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please? Answered by Chris Fisher and Harley Weston. 





A coin problem 
19960416 

From Julie Hebert and Simon Hamel: How many weighings would you need to find out which pile is fraudulent? Answered by Penny Nom. 





pente nulle 
20070831 

From stephanie: si la pente dune droite est nulle alors cette droite est quoi ??? Answered by Claude Tardif. 

