18
QuizMultiple Choice

Solving Quadratic Equations — Test

Question 18 • Algebraic Reasoning

A contractor is calculating the number of decorative stones for a new rectangular patio. The bids always include a count for the number of stones for the edging, cap e times x , and the number of stones for the center of the patio, cap c times x The various patio sizes have lengths represented by the function f of x and widths represented by g of x x cap e times x is equal to 2 times open paren f plus g close paren of x cap c times x is equal to open paren f times g close paren of x 2 34 62 3 52 133 4 70 260 5 88 435 Which statement describes the combined functions cap e times x and cap c times x ?

Answer
A
Both the number of stones needed for the edge and the number of stones for the center have a constant rate of change.
B
The number of edge stones needed has a constant rate of change, but the number of stones for the center does not.
C
Neither the number of stones needed for the edge nor the number of stones for the center has a constant rate of change.
D
The number of stones for the center has a constant rate of change but the number of edge stones needed does not.

Explanation

A function has a constant rate of change when its outputs change by the same amount for each 1-unit increase in x. The edge counts 34, 52, 70, and 88 increase by 18 each time, while the center counts 62, 133, 260, and 435 increase by 71, 127, and 175. Therefore, the edge count has a constant rate of change, but the center count does not.

AI-written and checked against the verified answer.

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