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?

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.

Volume of a Rectangular Prism = length × width × height

Given the following dimension of a box:

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

(c, 0) i might be wrong so don't put full faith on my answer

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for