Answer: y=3x-14
Step-by-step explanation:
Given:
The volume of the rectangular prism is
![V=4x^3+5x^2-32x-33](https://tex.z-dn.net/?f=V%3D4x%5E3%2B5x%5E2-32x-33)
Two dimensions are (x+1) and (x+3).
To find:
The missing dimension.
Solution:
We know that, volume of a rectangular prism is
![V=length\times breadth\times height](https://tex.z-dn.net/?f=V%3Dlength%5Ctimes%20breadth%5Ctimes%20height)
It means, volume of a rectangular prism is the product of all dimensions.
We have,
![V=4x^3+5x^2-32x-33](https://tex.z-dn.net/?f=V%3D4x%5E3%2B5x%5E2-32x-33)
Splitting the middle terms, we get
![V=4x^3+4x^2+x^2+x-33x-33](https://tex.z-dn.net/?f=V%3D4x%5E3%2B4x%5E2%2Bx%5E2%2Bx-33x-33)
![V=4x^2(x+1)+x(x+1)-33(x+1)](https://tex.z-dn.net/?f=V%3D4x%5E2%28x%2B1%29%2Bx%28x%2B1%29-33%28x%2B1%29)
![V=(x+1)(4x^2+x-33)](https://tex.z-dn.net/?f=V%3D%28x%2B1%29%284x%5E2%2Bx-33%29)
Splitting the middle term, we get
![V=(x+1)(4x^2+12x-11x-33)](https://tex.z-dn.net/?f=V%3D%28x%2B1%29%284x%5E2%2B12x-11x-33%29)
![V=(x+1)(4x(x+3)-11(x+3))](https://tex.z-dn.net/?f=V%3D%28x%2B1%29%284x%28x%2B3%29-11%28x%2B3%29%29)
![V=(x+1)(x+3)(4x-11)](https://tex.z-dn.net/?f=V%3D%28x%2B1%29%28x%2B3%29%284x-11%29)
So, the three dimensions of the rectangular prism are (x+1), (x+3) and (4x-11).
Therefore, the missing dimension is (4x-11).
<h3>
Answer: D) 1/3</h3>
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Explanation:
Start at (2,-3). Move up 3 and over to the right 6 spots to move to (8,0) which is where point F is located.
We can write the slope as rise/run = 3/6
Go back to (2,-3). Move up 1 and to the right 2 spots to arrive at F ' (4,-2)
Let's now compare the upward movements:
- Initially we moved up 3 units when trying to get to point F
- Now we're only moving up 1 unit when getting to F'
The starting point each time is (2,-3) which is the center of dilation. The jump from 3 to 1 is "times 1/3" and that's our scale factor. Every linear distance in the image is 1/3 times as long compared to the preimage.
We can also get the same scale factor when comparing the horizontal movements as well. The jump from 6 to 2 is also "times 1/3".
Answer:
$88 in total
Step-by-step explanation:
x = number of hours
y = total cost to rent the snowboard.
$25 is already guaranteed
25 + 15.75x = y
since it is 4 hours from 8:30 a.m. to 12:30 a.m. you put 4 into x.
25+15.75(4) = y
88 = y