Yes it does because the line is straight.
we know that
the volume of a rectangular prism is equal to
![V=L*W*H](https://tex.z-dn.net/?f=%20V%3DL%2AW%2AH%20)
where
L is the length of the box
W is the width of the box
H is is the height of the box
in this problem we have
![V=x^{3\ }+11x^2+20x-32](https://tex.z-dn.net/?f=%20V%3Dx%5E%7B3%5C%20%7D%2B11x%5E2%2B20x-32%20)
![W=x-1](https://tex.z-dn.net/?f=%20W%3Dx-1)
![H=x+8](https://tex.z-dn.net/?f=%20H%3Dx%2B8)
![L=?](https://tex.z-dn.net/?f=%20L%3D%3F)
<u>Find the length of the box</u>
Using a graph tool-------> we will determine the roots of the equation of volume
see the attached figure
the roots are
![x=-8\\x=-4\\ x=1](https://tex.z-dn.net/?f=%20x%3D-8%5C%5Cx%3D-4%5C%5C%20x%3D1)
so
![x^{3\ }+11x^2+20x-32=(x+8)*(x+4)*(x-1)](https://tex.z-dn.net/?f=%20x%5E%7B3%5C%20%7D%2B11x%5E2%2B20x-32%3D%28x%2B8%29%2A%28x%2B4%29%2A%28x-1%29%20)
therefore
<u>the answer is</u>
the length of the box is equal to ![(x+4)](https://tex.z-dn.net/?f=%20%28x%2B4%29%20)
Answer: Choice C
h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5
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Explanation:
When reflecting the function f(x) over the y axis, we replace every x with -x and simplify like so
f(x) = -x^4 - 2x^3 + 3x^2 - 4x + 5
f(-x) = -(-x)^4 - 2(-x)^3 + 3(-x)^2 - 4(-x) + 5
f(-x) = -x^4 + 2x^3 + 3x^2 + 4x + 5
h(x) = -x^4 + 2x^3 + 3x^2 + 4x + 5
Note the sign changes that occur for the terms that have odd exponents (the terms -2x^3 and -4x become +2x^3 and +4x); while the even exponent terms keep the same sign.
The reason why we replace every x with -x is because of the examples mentioned below
-----------
Examples:
The point (1,2) moves to (-1,2) after a y axis reflection
Similarly, (-5,7) moves to (5,7) after a y axis reflection.
As you can see, the y coordinate stays the same but the x coordinate flips in sign from negative to positive or vice versa. This is the direct reason for the replacement of every x with -x.
20 medium and large pumpkins
m ... number of medium pumpkins
l ... number of large pumpkins
20 = m + l
20 = m + (m + 6)
20 = 2 * m + 6
2 * m = 20 - 6
2 * m = 14
m = 7 medium pumpkins
l = 20 - 7 = 13 large pumpkins
Result: Julio bought 13 large pumpkins.