![\bf \begin{cases} f(x)=2x-1\\ g(x)=x^2+3x-1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)+g(x)\implies (2x-1)+(x^2+3x-1)\implies 2x+3x-1-1+x^2 \\\\\\ x^2+5x-2 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Af%28x%29%3D2x-1%5C%5C%0Ag%28x%29%3Dx%5E2%2B3x-1%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Af%28x%29%2Bg%28x%29%5Cimplies%20%282x-1%29%2B%28x%5E2%2B3x-1%29%5Cimplies%202x%2B3x-1-1%2Bx%5E2%0A%5C%5C%5C%5C%5C%5C%0Ax%5E2%2B5x-2%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill)
![\bf f(x)-g(x)\implies (2x-1)-(x^2+3x-1)\implies 2x-1-x^2-3x+1 \\\\\\ -x^2-x \\\\[-0.35em] ~\dotfill\\\\ f(x)\cdot g(x)\implies (2x-1)\cdot (x^2+3x-1) \\\\\\ \stackrel{2x(x^2+3x-1)}{2x^3+6x^2-2x}~~+~~\stackrel{-1(x^2+3x-1)}{(-x^2-3x+1)}\implies 2x^3+5x^2-5x+1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{2x-1}{x^2+3x-1}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29-g%28x%29%5Cimplies%20%282x-1%29-%28x%5E2%2B3x-1%29%5Cimplies%202x-1-x%5E2-3x%2B1%0A%5C%5C%5C%5C%5C%5C%0A-x%5E2-x%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0Af%28x%29%5Ccdot%20g%28x%29%5Cimplies%20%282x-1%29%5Ccdot%20%28x%5E2%2B3x-1%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7B2x%28x%5E2%2B3x-1%29%7D%7B2x%5E3%2B6x%5E2-2x%7D~~%2B~~%5Cstackrel%7B-1%28x%5E2%2B3x-1%29%7D%7B%28-x%5E2-3x%2B1%29%7D%5Cimplies%202x%5E3%2B5x%5E2-5x%2B1%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0A%5Ccfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%5Cimplies%20%5Ccfrac%7B2x-1%7D%7Bx%5E2%2B3x-1%7D)
the division doesn't simplify any further.
First you need to find the rate. This problem is based on the formula d = rt
d = distance
r = rate
t = time.
The question is asking how many miles will it travel in 8 hours so to find this out we need to find the rate when the car travels 240 miles in 4 hours. We use this information and plug it into the model d = rt
d = 240
r = don't know yet
t = 4 hr
d = rt
240 = 4r
240 / 4 = 4r / 4
60 = r
r = 60
So the car is going at a rate of 60 miles per hour. Now that we know this we can solve for how many miles the car will travel in 8 hours.
d = rt
d = r * t
d = 60 * 8
d = 480
So the car will travel 480 miles in 8 hours
Another way to think about this is that you know the car traveled 240 miles in 4 hours and the question is wanting to know how far the car will travel in 8 hours, which would be double the 4 hours so 240 + 240 = 480
Answer: 136 square feet
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Explanation:
The front face is a triangle with base 6 and height 4.
The area is 0.5*base*height = 0.5*6*4 = 12 square feet
The back face is also 12 square feet since the front and back faces are identical triangles.
So far we have 12+12 = 24 square feet of surface area.
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The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.
To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.
This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.
So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.
Just work this problem out backwards. First write out an equation.
(x+4)•3=30
Now solve :
(x+4)•3=30
3x+12=30
-12 -12
3x=18
/3 /3
x=6
Your answer is 6!
Hoped I helped!
The volume of a cylinder is r^2
dh
enter values, then you get 3.53, multiply that by the BTU, the answer is 8888 BTU
