Problem

Interpret \(A(x)=(x+3)(x+7)\) for \(x\ge~0\) as a rectangle-area model. State both dimensions with units, evaluate their areas at \(x=0\) and \(x=5\), and check the results against the displayed answer diagram.

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The dimensions are x meters by 10 meters. At x = 0 they are 0 and 10 meters, so area is 0 square meters; at x = 5 they are 5 and 10 meters, so area is 50 square meters.

The dimensions are (x + 3) meters by (x + 7) meters. At x = 0, the area is zero because x = 0; at x = 5 the area is 5 square meters.

The dimensions are (x + 3) meters by (x + 7) meters. At x = 0 they are 3 and 7 meters, so area is 21 square meters; at x = 5 they are 8 and 12 meters, so area is 96 square meters.

The dimensions are (x + 3) square meters by (x + 7) square meters. At x = 0 they are 3 and 7 square meters, so area is 21 fourth-power meters; at x = 5 area is 96 fourth-power meters.

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Interpret \(A(x)=(x+3)(x+7)\) for \(x\ge~0\) as a rectangle-area model. State both dimensions with units, evaluate their areas at \(x=0\) and \(x=5\), and check the results against the displayed answer diagram.

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