Set 5: Quadratic Equations

Explanation

Answer: A

A rectangle has perimeter 20. Let $x$ be the width. Express the area $A$ as a function of $x$ and find the domain.

$A(x) = 10x - x^2$ , $0 < x < 10$

✓ Correct

$A(x) = 20x - x^2$ , $0 < x < 20$

$A(x) = 10x - x^2$ , $x > 0$

$A(x) = x^2 + 10x$ , $0 < x < 10$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Perimeter $2x + 2 l = 20 \Rightarrow x + l = 10 \Rightarrow l = 10 - x$ . 2. Area $A(x) = x(10 - x) = 10 x - x^2$ . 3. Domain: Width $x > 0$ and Length $10- x > 0 \Rightarrow x < 10$ . So $0< x < 10$ . Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is $A(x) = 10x - x^2$ , $0< x < 10$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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