Question

The volume of a box, a rectangular prism, is represented by the function f(x) = x3 + 7x2 + 4x – 12. The length of the box is (x + 6), and the width is (x + 2). Which expression represents the height of the box?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The expression represents the height of the box will be,h=(x-3).

What is volume?

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Given data;

l= (x + 6)

w=(x + 2).

The volume of the rectangle having length l, width w, and height h is;

V=lwh

f(x)=V= x³ + 7x² + 4x – 12

lwh=x³ + 7x² + 4x – 12

Substitute the given value;

$\rm (x+5)(x-1)(h)=x^3+x^2-17x+15 \\\\ (x^2+4x-5)(h)=x^3+x^2-17x+15 \\\\\ x^2+4x-5)(h)=(x2+4x-5)(x-3) \\\\ h=(x-3)$

Hence, the expression represents the height of the box will be,h=(x-3).

To learn more about the volume, refer to brainly.com/question/1578538

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