E MTH1120 A ALEKS - Marquita Davis - Know X b Answered: a person's eye level X X If a p PVVROTURTtuFljpdgJ2gz8nsHUvStcj_d129IDiThHbAQq9fdE-_2HQIMXZoGOhZ99QCrgDyNjCNO16Syg5SmqEP vledge Check Question 3 ers of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along one of the sides has length x (in meters). Side along house ction that gives the area A (x) of the garden (in square meters) in

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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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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**Initial Knowledge Check**

**Question 3**

Tom has 280 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. 

As shown below, one of the sides has length \( x \) (in meters).

[Diagram of a rectangular garden with a shaded area labeled "Side along house" and one side labeled \( x \).]

---

(a) Find a function that gives the area \( A(x) \) of the garden (in square meters) in terms of \( x \).

\[ A(x) = \square \]

(b) What side length \( x \) gives the maximum area that the garden can have?

Side length \( x = \square \) meters

(c) What is the maximum area that the garden can have?

Maximum area: \(\square\) square meters

---

**Diagram Explanation:** 

The diagram illustrates a rectangular garden next to a house. The fencing encloses three sides: two perpendicular to the house and one parallel. The side labeled \( x \) runs parallel to the house and forms one of these sides. The area of the garden depends on the values of \( x \) and the other dimensions determined using the total fencing available.
Transcribed Image Text:**Initial Knowledge Check** **Question 3** Tom has 280 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing. As shown below, one of the sides has length \( x \) (in meters). [Diagram of a rectangular garden with a shaded area labeled "Side along house" and one side labeled \( x \).] --- (a) Find a function that gives the area \( A(x) \) of the garden (in square meters) in terms of \( x \). \[ A(x) = \square \] (b) What side length \( x \) gives the maximum area that the garden can have? Side length \( x = \square \) meters (c) What is the maximum area that the garden can have? Maximum area: \(\square\) square meters --- **Diagram Explanation:** The diagram illustrates a rectangular garden next to a house. The fencing encloses three sides: two perpendicular to the house and one parallel. The side labeled \( x \) runs parallel to the house and forms one of these sides. The area of the garden depends on the values of \( x \) and the other dimensions determined using the total fencing available.
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