Jordan is tracking a recent online purchase. the shipping costs state that the item will be shipped in a 24-inch long box with a volume of 2,880 cubic inches. the width of the box is seven inches less than the height. the volume of a rectangular prism is found using the formula v = l · w · h, where l is the length, w is the width, and h is the height. complete the equation that models the volume of the box in terms of its height, x, in inches. x2 - x = is it possible for the height of the box to be 15 inches?

A. We are given that the length of the box is equal to 24 as indicted in the "24-inch long". From the given, it is also stated that the width of the box is 7 inches less than the height. If the height of the box is x, the width is then x - 7. The equation that would let us solve the problem is,

                            2880 = 24(x)(x - 7)
Simplifying,
                            2880 = 24x² - 168x

B. The value of x from the equation is 15. Thus, the answer is YES. 

The equation that models the volume of the box is: 24x² - 168 = 2,880

It is possible for the height of the box to be 15 inches.

What is the Volume of a Rectangular Prism?

Volume of a Rectangular Prism = length × width × height

Given the following dimension of a box:

Volume = 2,880 cubic inchesLength = 24 inchHeight = xWidth = x - 7

Equation that models the volume of the box, using the formula for the volume of a rectangular prism would be:

(24)(x)(x-7) = 2,880

24x² - 168 = 2,880

To know if 15 is a possible value of x, plug in x = 15 into the equation as follows:

24(15)² - 168(15) = 2,880

2,880 = 2,880 (true)

Therefore, the equation that models the volume of the box is: 24x² - 168 = 2,880

It is possible for the height of the box to be 15 inches.

Learn more about volume of rectangular prism on:

link

You need to show the box plots

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