SOLUTION: A rectangular box is (2x+7) feet wide, (5x+2)feet long and (x-4) feet high. Find the volume. I need to Familiarize,Translate, Carry Out, Check and State To Solve. Not sure what th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A rectangular box is (2x+7) feet wide, (5x+2)feet long and (x-4) feet high. Find the volume. I need to Familiarize,Translate, Carry Out, Check and State To Solve. Not sure what th      Log On


   

Question 180594This question is from textbook
: A rectangular box is (2x+7) feet wide, (5x+2)feet long and (x-4) feet high.
Find the volume. I need to Familiarize,Translate, Carry Out, Check and State To Solve. Not sure what that means. Thank You
Denise This question is from textbook

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure what Familiarize,Translate, Carry Out, Check and State To Solve means either. But let's give it a go
Familiarize - You are given the dimensions of a rectangular box and asked to find the expression that is the volume of that box.
Translate - The volume of a rectangular box with Length L, Width W and Height H is given by L+%2A+W+%2A+H. The dimensions on this box are given to you as W+=+2x%2B7, L=5x%2B2 and H=x-4.
So V+=+LWH
V+=+%285x%2B2%29%282x%2B7%29%28x-4%29
Carry Out - Just grind out the math now
V+=+%285x%2B2%29%282x%2B7%29%28x-4%29
V+=+%2810x%5E2%2B35x+%2B+4x+%2B+14%29%28x-4%29
V+=+%2810x%5E2+%2B+39x+%2B+14%29%28x-4%29
V+=+10x%5E3+%2B+39x%5E2+%2B+14x+-+40x%5E2+-+156x+-+56
V+=+10x%5E3+-x%5E2+-+142x+-+56
To verify, pick a value for x and then solving for V using our equation and then solving again by finding L W and H
Let x = 5 (need to pick a value for x that makes all thee dimensions positive)
So L = 27, W=17 and H = 1. The volume is then 27%2A17%2A1 = 459
Using our equation
V+=+10x%5E3+-x%5E2+-+142x+-+56
V+=+10%2A125+-+25+-+142%2A5+-+56
V+=+1250+-+25+-+710+-+56
V+=+459 so it works