Question

1. a circle has a diameter of 13 units. what is the area of the circle to the nearest hundredth of a square unit? a. 40.84 b. 132.73 c. 530.93 d. 2,123.72 problems 10–11: solve each equation. show your thinking. 10. $x - 2\frac{2}{3} = 6\frac{2}{3}$ 11. $\frac{1}{2}x = 12$

Explanation:

Problem 9:

Step1: Find the radius

The diameter \( d = 13 \), so radius \( r=\frac{d}{2}=\frac{13}{2} = 6.5 \).

Step2: Calculate the area

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( r = 6.5 \) into the formula: \( A=\pi\times(6.5)^{2}=\pi\times42.25\approx3.1416\times42.25\approx132.73 \).

Step1: Isolate \( x \)

To solve \( x - 2\frac{2}{3}=6\frac{2}{3} \), add \( 2\frac{2}{3} \) to both sides.

Step2: Add the mixed numbers

\( x=6\frac{2}{3}+2\frac{2}{3} \). Convert mixed numbers to improper fractions: \( 6\frac{2}{3}=\frac{20}{3} \), \( 2\frac{2}{3}=\frac{8}{3} \). Then \( \frac{20}{3}+\frac{8}{3}=\frac{28}{3}=9\frac{1}{3} \) (or as a decimal, approximately \( 9.33 \), but since the problem is about exact fraction addition, the exact value is \( 9\frac{1}{3} \)).

Step1: Isolate \( x \)

To solve \( \frac{1}{2}x = 12 \), multiply both sides by 2.

Step2: Solve for \( x \)

\( x = 12\times2=24 \).

Answer:

B. 132.73

Problem 10: