Question

1. which of the following represents the area of a circle with a diameter of 4x - 6? (a) π(16x² + 36) (b) π(16x² - 48x + 36) (c) π(4x² + 9) (d) π(4x² - 12x + 9)

Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter \(d\). Given \(d = 4x-6\), then \(r=\frac{4x - 6}{2}=2x-3\).

Step2: Use the area formula

The area formula of a circle is \(A=\pi r^{2}\). Substitute \(r = 2x - 3\) into the formula:

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Answer:

D. \(\pi(4x^{2}-12x + 9)\)