There is a TV screen on the wall in a home theater. The dimensions of the wall (shown in gray) and the screen (shown in blue) are shown below: 10 m 16 m What is the value of z (distance from the edge of the screen to the end of the wall) if the area of the screen is 40 m²?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Problem Statement

There is a TV screen on the wall in a home theater. The dimensions of the wall (shown in gray) and the screen (shown in blue) are shown below:

#### Diagram Description:
- The wall has a rectangular shape.
- The total width of the wall is 16 meters.
- The total height of the wall is 10 meters.
- The TV screen is placed centrally on the wall.
- The distance from each edge of the TV screen to the respective edge of the wall is marked as \(x\).

### Question:
What is the value of \(x\) (the distance from the edge of the screen to the end of the wall) if the area of the screen is 40 m²?

\[
\text{Wall Dimensions:}
\begin{aligned}
  \text{Width} &= 16 \text{ m}\\
  \text{Height} &= 10 \text{ m}
\end{aligned}
\]

\[
\text{Screen Area:}
\begin{aligned}
  \text{Area} &= 40 \text{ m}^2
\end{aligned}
\]

### Solution:

To find the value of \(x\), we will follow these steps:

1. Express the area of the screen in terms of the dimensions of the wall and \(x\).
2. Use the given area of the screen to set up an equation and solve for \(x\).
Transcribed Image Text:### Problem Statement There is a TV screen on the wall in a home theater. The dimensions of the wall (shown in gray) and the screen (shown in blue) are shown below: #### Diagram Description: - The wall has a rectangular shape. - The total width of the wall is 16 meters. - The total height of the wall is 10 meters. - The TV screen is placed centrally on the wall. - The distance from each edge of the TV screen to the respective edge of the wall is marked as \(x\). ### Question: What is the value of \(x\) (the distance from the edge of the screen to the end of the wall) if the area of the screen is 40 m²? \[ \text{Wall Dimensions:} \begin{aligned} \text{Width} &= 16 \text{ m}\\ \text{Height} &= 10 \text{ m} \end{aligned} \] \[ \text{Screen Area:} \begin{aligned} \text{Area} &= 40 \text{ m}^2 \end{aligned} \] ### Solution: To find the value of \(x\), we will follow these steps: 1. Express the area of the screen in terms of the dimensions of the wall and \(x\). 2. Use the given area of the screen to set up an equation and solve for \(x\).
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