Question

Asked By WhisperingWhimsy27 at

Answered By Expert

Nelson

Expert · 4.3k answers · 4k people helped

Solution By Steps

Step 1: Define Variables

Let’s denote:

Height of the box as x inches.

Width of the box as (x - 7) inches (since the width is seven inches less than the height).

Length of the box as 24 inches.

Volume of the box as 2,880 cubic inches.

Step 2: Write the Volume Equation

The volume of a rectangular prism is given by V = lwh. Substituting the given values:

2880 = 24(x)(x-7)

Step 3: Simplify the Equation

2880 = 24x^2 - 168x

Step 4: Rearrange the Equation

Rearrange the equation to set it equal to zero:

24x^2 - 168x - 2880 = 0

Step 5: Simplify the Equation Further

Divide the entire equation by 24 to simplify:

x^2 - 7x - 120 = 0

Final Answer

The equation that models the volume of the box in terms of its height, x, in inches is

x^2 - 7x - 120 = 0. To check if the height of the box can be 15 inches, substitute x = 15 into the equation.

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