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A(x)=(2+2x)^(2)
Roxane wants to add a border around a square picture. The function models 
A, the new area of the picture in square inches if it has a border 
x inches wide. Which of the following statements is the best interpretation of the ordered pair 
(0.5,9) ?
Choose 1 answer:
(A) When a 0.5 -inch border is added around the picture, the new side length of the picture is 9 inches.
(B) When a 0.5 -inch border is added around the picture, the new perimeter of the picture is 9 inches.
(C) When a 0.5 -inch border is added around the picture, the new area of the picture is 9 times the original area.
(D) When a 0.5 -inch border is added around the picture, the new area of the picture is 9 square inches.

A(x)=(2+2x)2 A(x)=(2+2 x)^{2} \newlineRoxane wants to add a border around a square picture. The function models A A , the new area of the picture in square inches if it has a border x x inches wide. Which of the following statements is the best interpretation of the ordered pair (0.5,9) (0.5,9) ?\newlineChoose 11 answer:\newline(A) When a 00.55 -inch border is added around the picture, the new side length of the picture is 99 inches.\newline(B) When a 00.55 -inch border is added around the picture, the new perimeter of the picture is 99 inches.\newline(C) When a 00.55 -inch border is added around the picture, the new area of the picture is 99 times the original area.\newline(D) When a 00.55 -inch border is added around the picture, the new area of the picture is 99 square inches.

Full solution

Q. A(x)=(2+2x)2 A(x)=(2+2 x)^{2} \newlineRoxane wants to add a border around a square picture. The function models A A , the new area of the picture in square inches if it has a border x x inches wide. Which of the following statements is the best interpretation of the ordered pair (0.5,9) (0.5,9) ?\newlineChoose 11 answer:\newline(A) When a 00.55 -inch border is added around the picture, the new side length of the picture is 99 inches.\newline(B) When a 00.55 -inch border is added around the picture, the new perimeter of the picture is 99 inches.\newline(C) When a 00.55 -inch border is added around the picture, the new area of the picture is 99 times the original area.\newline(D) When a 00.55 -inch border is added around the picture, the new area of the picture is 99 square inches.
  1. Plug in x=0.5x=0.5: Plug x=0.5x=0.5 into the function A(x)A(x) to check if the area is indeed 99 square inches.\newlineA(0.5)=(2+2×0.5)2A(0.5) = (2 + 2\times0.5)^2\newlineA(0.5)=(2+1)2A(0.5) = (2 + 1)^2\newlineA(0.5)=32A(0.5) = 3^2\newlineA(0.5)=9A(0.5) = 9
  2. Calculate A(0.5)A(0.5): Since A(0.5)=9A(0.5) = 9, the ordered pair (0.5,9)(0.5,9) means that when a 0.50.5-inch border is added around the picture, the new area of the picture is 99 square inches.

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