### Problem StatementThere 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 $x$.

Answered: Image /qna-images/answer/5b089d34-abf9-48bb-8b48-127714d7c880.jpg

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?

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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Question

### 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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