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Triangles/343290: I do not know how to set up this problem. Can anyone help me?
Two frames are needed with the same outside perimeter: one frame in the shape of a square and one in the shape of an equilateral triangle. Each side of the triangle is 6 centimeters longer than each side of the square. Find the dimensions of each frame.
1 solutions
Answer 245620 by nerdybill(6948)   on 2010-09-14 22:31:38 (Show Source):
You can put this solution on YOUR website!Two frames are needed with the same outside perimeter: one frame in the shape of a square and one in the shape of an equilateral triangle. Each side of the triangle is 6 centimeters longer than each side of the square. Find the dimensions of each frame.
.
Let x = length of one side of the square (in cm)
then
x+6 = length of one side of the triangle
.
Perimeter of square is 4x
perimeter of triangle is 3(x+6)
.
So:
4x = 3(x+6)
4x = 3x+18
x = 18 centimeters
and
Length of one side of triangle:
x+6 = 18+6 = 24 centimeters
.
Dimensions of square: 18 by 18 by 18 by 18 (centimeters)
Dimensions of triangle: 24 by 24 by 24 (centimeters)
|
Human-and-algebraic-language/342861: Hotels collect 4 percent sale tax on all sales. If the total sales including tax are 1058.30 find the portion that is the tax.
1 solutions
Answer 245420 by nerdybill(6948) on 2010-09-14 11:31:12 (Show Source):
You can put this solution on YOUR website!Hotels collect 4 percent sale tax on all sales. If the total sales including tax are 1058.30 find the portion that is the tax.
.
Let x = hotel bill
then
.04x = tax portion
.
x + .04x = 1058.30
x(1 + .04) = 1058.30
x(1.04) = 1058.30
x = 1017.60
.
tax portion:
.04x = .04(1017.60) = $40.70
|
Rectangles/342879: if a rectangle has width of 5 and diagonal with lenght of 13, what is the area of the rectangle?
1 solutions
Answer 245418 by nerdybill(6948) on 2010-09-14 11:28:00 (Show Source):
You can put this solution on YOUR website!if a rectangle has width of 5 and diagonal with lenght of 13, what is the area of the rectangle?
.
find the length by applying Pythagorean theorem:
Let x = length
then
x^2 + 5^2 = 13^2
x^2 = 13^2 - 5^2
x^2 = 169 - 25
x^2 = 144
x = 12
.
area = 5*12 = 60 square units
|
Trigonometry-basics/341312: let's assume a right triangle ABC. A is the angle theta but we don't know the degree. So a=5 that is the opposite side of theta, b=adjacent side that is unknown, and c=29 representing the hypothenus.
Determine the value of B. Round to two decimal places.
1 solutions
Answer 244433 by nerdybill(6948) on 2010-09-10 09:38:51 (Show Source):
You can put this solution on YOUR website!let's assume a right triangle ABC. A is the angle theta but we don't know the degree. So a=5 that is the opposite side of theta, b=adjacent side that is unknown, and c=29 representing the hypothenus.
Determine the value of B. Round to two decimal places.
.
Since you have a "right triangle", you can apply Pythagorean theorem:
a^2 + b^2 = c^2
5^2 + b^2 = 29^2
b^2 = 29^2 - 5^2
b^2 = 841 - 25
b^2 = 816
b = 28.57
|
Exponential-and-logarithmic-functions/341314: Hello I need a little help with my homework. I started trying to work it out but I am not sure if it is the correct solution. Please help!
Question:
Population growth. The exponential growth rate of the population of United Arab Emirates is 4.4% per year (one of the highest in the world). What is the doubling time?
Sources: Based on data from U.S. Census Bureau; International Data Base 2007
My Answer: I changed 4.4% to .044^2. My result was .001936 or round to 0.002%.
Is this correct? Should I be using the P(t) = P0e^kt? If so how should I go by doing so? Thanks for your help in advance!
1 solutions
Answer 244432 by nerdybill(6948) on 2010-09-10 09:34:29 (Show Source):
You can put this solution on YOUR website!Population growth. The exponential growth rate of the population of United Arab Emirates is 4.4% per year (one of the highest in the world). What is the doubling time?
Sources: Based on data from U.S. Census Bureau; International Data Base 2007
My Answer: I changed 4.4% to .044^2. My result was .001936 or round to 0.002%.
Is this correct? Should I be using the P(t) = P0e^kt? If so how should I go by doing so?
.
Yes, you should be using
P(t) = P0e^kt
.
From the problem you are given:
k = 4.4% = .044
.
Let x = Po (initial population)
then
2x = population doubles
.
So, instead of:
P(t) = P0e^kt
We now have:
2x = xe^(.044t)
.
Now, we solve for t:
2x = xe^(.044t)
dividing both sides by x:
2 = e^(.044t)
take ln of both sides:
ln(2) = .044t
ln(2)/.044 = t
15.75 years = t (doubling time)
|
Systems-of-equations/341349: Trying to help my daughter solve the following..... 7.5 (a - 3) and it says to use the distributive property (?) and expand like terms when possible. I havent done math in forEVER..'dist.prop' and 'like terms' are mysteries to me!
1 solutions
Answer 244426 by nerdybill(6948) on 2010-09-10 09:26:59 (Show Source):
You can put this solution on YOUR website!Given:
7.5 (a - 3)
This says "7.5 times the quantity a minus 3".
.
To "distribute" the 7.5, we multiply each term inside the parenthesis by 7.5.
.
The distributive property simply states that given expression is the same as the following:
7.5 (a - 3)
= 7.5(a) - 7.5(3)
= 7.5a - 22.5
|
test/341139: if sarah can pain a fence in 4 hours and tim can paint the same fence in 8 hours how much would it take them to paint the fence toguether
1 solutions
Answer 244253 by nerdybill(6948) on 2010-09-09 18:43:56 (Show Source):
You can put this solution on YOUR website!if sarah can pain a fence in 4 hours and tim can paint the same fence in 8 hours how much would it take them to paint the fence toguether
.
Let x = time it takes for both to paint fence together
then
x(1/4 + 1/8) = 1
multiplying both sides by 8:
x(2 + 1) = 8
x(3) = 8
x = 8/3 hours
or
x = 2 and 2/3 hours
or
x = 2 hours and 40 minutes
|
Geometry_Word_Problems/341054: The base of a triangle is 2 in.
longer than the height. The area is 12in^2 . Find the
height and the base.
How would I write this equation?
1 solutions
Answer 244223 by nerdybill(6948) on 2010-09-09 16:42:46 (Show Source):
You can put this solution on YOUR website!The base of a triangle is 2 in.
longer than the height. The area is 12in^2 . Find the
height and the base.
.
area for any triangle is:
(1/2)bh
where
b is base
h is height
.
Let h = height
then because "The base of a triangle is 2 in" we have
h+2 = base
.
The formula is:
(1/2)(h+2)h = 12
.
Solving, we start by multiplying both sides by 2 to get:
(h+2)h = 24
h^2 + 2h = 24
h^2 + 2h - 24 = 0
(h+6)(h-4) = 0
.
h = {-6, 4}
we can toss out the negative value leaving:
h = 4 inches (height)
.
Base:
h+2 = 4+2 = 6 inches
|
Travel_Word_Problems/340963: Your word problem on the first page was changed from "A freight train leaves the station traveling (50) miles an hour and a passenger train leaves the station 30 minutes later traveling (70) miles per hour. How long will it take for the passenger train to catch up with the freight train?" to a totally different word problem no matter what tab I clicked. This was not helpful to me. Please show me how to set up a formula to solve this problem.
1 solutions
Answer 244202 by nerdybill(6948) on 2010-09-09 14:18:55 (Show Source):
You can put this solution on YOUR website!A freight train leaves the station traveling (50) miles an hour and a passenger train leaves the station 30 minutes later traveling (70) miles per hour. How long will it take for the passenger train to catch up with the freight train?
.
Apply the distance formula of:
d = rt
where
d is distance (miles)
r is rate or speed
t is time (hours)
.
Realize that 30 minutes = .5 hours
.
Let x = hours traveled by the freight train
then
x - .5 = hours traveled by the passenger train
.
"distance traveled by freight train" = "distance traveled by passenger train"
50x = 70(x-.5)
50x = 70x-35
-20x = -35
x = 1.75 hours
or
x = 1 hour and 45 minutes
|
test/340940: Hi story problems are not favorite and seem to get confused with them. Can you please help me with this one.
Jack usually mows his lawn in 3 hours. Marilyn can mow the same yard in 7 hours, how much time would it take for them to mow the lawn together?
Thanks :o)
1 solutions
Answer 244192 by nerdybill(6948) on 2010-09-09 13:14:57 (Show Source):
You can put this solution on YOUR website!Jack usually mows his lawn in 3 hours. Marilyn can mow the same yard in 7 hours, how much time would it take for them to mow the lawn together?
.
Let x = hous it takes for both to mow lawn
then
x(1/3 + 1/7) = 1
Multiplying both sides by 21:
x(7 + 3) = 21
x(10) = 21
x = 2.1 hours
or
x = 2 hours and 6 minutes
|
Equations/340931: B-9[B-8(4-B)]=608
I'm getting 64.9, I think I'm doing a step wrong?
1 solutions
Answer 244188 by nerdybill(6948) on 2010-09-09 12:56:13 (Show Source):
You can put this solution on YOUR website!You must apply the "order of operations" (PEMDAS):
B-9[B-8(4-B)]=608
Distribute the -8 to terms inside parenthesis:
B-9[B-32+8B]=608
Combining like-terms inside brackets:
B-9[9B-32]=608
Distribute the -9 to terms inside brackets:
B-81B+288=608
Combining like-terms:
-80B+288=608
Subtracting 288 from both sides
-80B=608-288
-80B=320
Dividing both sides by -80
B = -4
|
Triangles/340929: the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.
1 solutions
Answer 244185 by nerdybill(6948) on 2010-09-09 12:51:53 (Show Source):
You can put this solution on YOUR website!the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.
.
Because it is a "right triangle" we can apply Pythagorean theorem:
Let h = height of triangle
then
2h = hypotenuse
.
|
Mixture_Word_Problems/340917: how much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 65% antifreeze?
1 solutions
Answer 244180 by nerdybill(6948) on 2010-09-09 12:31:51 (Show Source):
You can put this solution on YOUR website!how much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 65% antifreeze?
.
Let x = gallons of water added
then
0x + 1(1) = .65(1 + x)
1 = .65(1 + x)
1 = .65 + .65x
.35 = .65x
.35/.65 = x
.54 gallons = x
|
Expressions-with-variables/340910: (x-2)^2 +4 =10
1 solutions
Answer 244172 by nerdybill(6948) on 2010-09-09 11:42:56 (Show Source):
You can put this solution on YOUR website!(x-2)^2 +4 =10
(x-2)(x-2) +4 =10
x^2-2x-2x+4 +4 =10
x^2-4x+8 =10
x^2-4x-2 = 0
Solve by applying the quadratic formula to get:
x = {4.449, -0.449}
.
Details of quadratic to follow:
.
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=24 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 4.44948974278318, -0.449489742783178.
Here's your graph:
 |
|
Proportions/340535: Determine how you could use a 5-unit jar and a 7-unit jar to measure and hold 8 units.
1 solutions
Answer 244022 by nerdybill(6948) on 2010-09-08 17:41:58 (Show Source):
You can put this solution on YOUR website!Determine how you could use a 5-unit jar and a 7-unit jar to measure and hold 8 units.
.
First: fill 5-unit jar and pour contents into 7-unit jar (2-unit empty)
Second: refill 5-unit jar and fill balance of 7-unit jar (now, 5-unit jar has 3-units)
Third: empty 7-unit jar
Fourth: pour the 3-units left in 5-unit jar into 7-unit jar (it now holds 3-units)
Fifth: refill 5-unit jar
.
Contents of both jars now contains 8-units.
|
Numeric_Fractions/340355: This is a question about "Scientific Notation" I couldn't find a tab for it!
Write 0.000036 in scientific notation?
Write 4.78 times 10 to the power of eight in standard notation?
1 solutions
Answer 243862 by nerdybill(6948) on 2010-09-08 10:40:13 (Show Source):
You can put this solution on YOUR website!Write 0.000036 in scientific notation?
that's
3.6 x 10^(-5)
.
Write 4.78 times 10 to the power of eight in standard notation?
478,000,000
|
Quadratic_Equations/340339: Hi,
I need help with:
Evaluate the discriminant b^2 - 4ac. Then use the answer to state how many real-number solutions exist for the equation: y = x^2 + 8x + 16
Thanks!
1 solutions
Answer 243860 by nerdybill(6948) on 2010-09-08 10:34:35 (Show Source):
You can put this solution on YOUR website!This site explains it quite well:
http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php
.
A "quadratic" is in the form of:
y = ax^2 + bx + c
.
Given:
y = x^2 + 8x + 16
we now have:
a is 1
b is 8
c is 16
.
Plug into:
b^2 - 4ac
8^2 - 4(1)(16)
64 - 64
0
.
Since "discriminant" is zero
Conclusion:"ONE real solution"
|
Quadratic_Equations/340338: Hi,
What is y = x^2 + 4x - 1
find the x-intercepts
Thanks!
1 solutions
Answer 243858 by nerdybill(6948) on 2010-09-08 10:30:15 (Show Source):
You can put this solution on YOUR website!What is y = x^2 + 4x - 1
.
To find the x-intercepts, set y=0 and solve for x:
0 = x^2 + 4x - 1
.
Applying the quadratic formula gives you:
x = {0.236, -4.236}
So, your x-intercepts are at:
(0.236,0) and (-4.236,0)
.
Details of quadratic to follow:
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation (in our case  ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=20 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 0.23606797749979, -4.23606797749979.
Here's your graph:
 |
|
Circles/340361: One circle has a radius of 1/2 and another circle has a radius of 1. What is the ratio of the area of the larger circle to the area of the smaller circle?
A. 2:1 B. 3:1 C. 3:2 D. 4:1 E. 5:2
1 solutions
Answer 243851 by nerdybill(6948) on 2010-09-08 10:20:30 (Show Source):
You can put this solution on YOUR website!One circle has a radius of 1/2 and another circle has a radius of 1. What is the ratio of the area of the larger circle to the area of the smaller circle?
A. 2:1 B. 3:1 C. 3:2 D. 4:1 E. 5:2
.
Since area of a circle is (pi)r^2
.
Area with radius of 1/2:
(pi)r^2 =(pi)(1/2)^2 = (1/4)(pi)
.
Area with radius of 1:
(pi)r^2 =(pi)(1)^2 = (pi)
.
Ratio of larger to smaller circle:
(pi):(1/4)(pi)
= (pi)/[(1/4)(pi)]
= 1/(1/4)
= 4
Answer would be D: 4:1
|
Travel_Word_Problems/340285: two planes which are 1860 miles apart travel toward each other. their speeds difer by 70mph. if they pass each other in 3 hours what are their speeds?
1 solutions
Answer 243809 by nerdybill(6948) on 2010-09-08 00:45:40 (Show Source):
You can put this solution on YOUR website! two planes which are 1860 miles apart travel toward each other. their speeds difer by 70mph. if they pass each other in 3 hours what are their speeds?
.
Apply the distance forumla: d=rt
.
Let x = faster plane
then
x-70 = slower plane
.
3x + 3(x-70) = 1860
Dividing both sides by 3:
x + (x-70) = 620
2x-70 = 620
2x = 690
x = 345 mph (faster plane)
.
Slower plane:
x-70 = 345-70 = 275 mph
|
Geometry_Word_Problems/340289: A rectangularwalkway is 18 feet longer than it is wide. If the area of the walkway is 88 squarefeet, find the length and the width.
Is this the correct formula?
(L x W) + 18 = 88
1 solutions
Answer 243808 by nerdybill(6948) on 2010-09-08 00:40:31 (Show Source):
You can put this solution on YOUR website!A rectangular walkway is 18 feet longer than it is wide. If the area of the walkway is 88 squarefeet, find the length and the width.
Is this the correct formula? NO
(L x W) + 18 = 88
.
Let w = width
then from "walkway is 18 feet longer than it is wide" we get:
w+18 = length
.
w(w+18) = 88
w^2+18w = 88
w^2+18w-88 = 0
factoring the left:
(w-4)(w+22) = 0
w = {4, -22}
throw out the negative result, leaving:
w = 4 feet (width)
.
Length:
w+18 = 4+18 = 22 feet (length)
|
Polynomials-and-rational-expressions/340284: OK....need help been trying for the last hour.. still can't get it.
Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
If an object is propelled upward from ground level with an initial velocity of 224 feet per second, its height h in feet t seconds later is given by the equation h = 224t - 16t2. After how many seconds does the object hit the ground?
1 solutions
Answer 243807 by nerdybill(6948) on 2010-09-08 00:36:32 (Show Source):
You can put this solution on YOUR website!Given:
h = 224t - 16t^2
where
h is height in feet
t is time in seconds
.
To determine when the object hit the ground,
set h to zero (because zero is when the object is on the ground) and solve for t:
h = 224t - 16t^2
0 = 224t - 16t^2
0 = 14t - t^2
factoring the right side:
0 = t(14 - t)
setting each term on the right to zero we get:
t = {0, 14}
.
t=0 is when the object just started its flight
So,
t = 14 seconds (solution)
|
Equations/340022: the model M = -0.711+206.6 is used to determine the maximum heart rate of M of and individual who is age A
solve for A
according to this model what is the age of and individual whose maximum heart rate is 155
simpliy all answers
1 solutions
Answer 243680 by nerdybill(6948) on 2010-09-07 18:03:21 (Show Source):
You can put this solution on YOUR website!the model M = -0.711+206.6 is used to determine the maximum heart rate of M of and individual who is age A
solve for A
according to this model what is the age of and individual whose maximum heart rate is 155
.
M = -0.711A + 206.6
Where
M is "max heartrate"
A is age
.
M - 206.6 = -0.711A
(M - 206.6)/(-0.711) = A
(206.6-M)/(0.711) = A
.
Plug in 155 for M:
(206.6-155)/(0.711) = A
(51.6)/(0.711) = A
72.6 years old = A
|
Triangles/339847: The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude?
1 solutions
Answer 243508 by nerdybill(6948) on 2010-09-07 11:38:03 (Show Source):
You can put this solution on YOUR website!The area of triangle T is 625 square inches. If the length of the base b is half the length of the altitude drawn to that base, then what is the length of the altitude?
.
Let x = altitude
then
x/2 = base
.
(1/2)base*height = area
(1/2)(x/2)x = 625
(x/4)x = 625
x^2/4 = 626
x^2 = 2504
x = 50 inches
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