🎁BACK-TO-SCHOOL DEAL. Subscribe Now to get 40% OFF at only 8.49 USD/month, only valid until Sep 30th, 2024

Question

Select the correct answer from each drop-down menu. 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 = lwh, 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?

Asked By WhisperingWhimsy27 at

Answered By Expert

Nelson

Expert · 4.3k answers · 4k people helped

Sign in to see the answer

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.

🧑‍🏫 More Questions

Question $5 / 13$ What value would be returned based on the formula in Cell A49? \begin{tabular}{|l|l|} \hline 43 & npab \\ \hline 44 & npce \\ \hline 45 & npfo \\ \hline 46 & npbb \\ \hline 47 & norp \\ \hline 48 & \\ \hline 49 & $=$ COUNTIF(A43:A47,"NP*") \\ \hline \end{tabular} Report Problem

Find the angle between 0° and 360° that is coterminal with 375°.

Which of the following is true? Select all that apply. True Fale Al queries have an explicit location True Fale The explicit location is found inside the query. Trum! Falose The explict location always tells you where users are located when they type the query. Thes False The explicit location makes the query easier to understand and interpret.

an area code of 212 what is his npi number

is the wager by david grann a good or bad recommendation for a book about jennifer harman by jackie alyson