SOLUTION: Melissa plans to ship a computer in a cubic box that measures x inches on a side. She later determines that her shipping cost will be less if she uses a rectangular box that is 3 i

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Question 199760: Melissa plans to ship a computer in a cubic box that measures x inches on a side. She later determines that her shipping cost will be less if she uses a rectangular box that is 3 inches shorter and 5 inches longer than the cubic box. Write an equation V(x) for the volume of the new box and match your result to the correct answer below.
A) V(x)=x^3-15xin^3
B) V(x)=x^3+2x-15in^3
C) V(x)=x^3-2x^2-15xin^3
D) V(x)=x^3+2x^2-15xin^3
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
V%28x%29=length%2Awidth%2Aheight
.
The original box was a cube, so in that case length=width=height. So the volume of the cubic box is:
V%28x%29=x%2Ax%2Ax=x%5E3
.
For the rectangular box, one dimension is 3 inches shorter (say length) and another dimension is 5 inches longer (say width). Nothing is said about the height being different. So for the rectangular box, the area is expressed as:
V%28x%29=%28x-3%29%2A%28x%2B5%29%2Ax
Simplifying...
V%28x%29=%28x%5E2%2B2x-15%29%2Ax
highlight%28V%28x%29=x%5E3%2B2x%5E2-15x%29
.
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Good Luck,
tutor_paul@yahoo.com