Question

1. refer to the figures.

equation

x =

9)
a circle with a radius of 5 cm is shown.
make sure that you use the correct units in your answers.
(a) find the exact circumference of the circle. write your answer in terms of π.

(b) using a calculator, approximate the circumference of the circle.
to do the approximation, use the π button on the calculator, and round your answer to the nearest hun

Explanation:

Step1: For the first figure (angle - related)

Since the two angles \((x + 15)^{\circ}\) and \(50^{\circ}\) are equal (assuming they are vertical angles or congruent angles), the equation is \(x+15 = 50\).
Subtract 15 from both sides: \(x=50 - 15\).

Step2: For the second figure (angle - related)

Since the sum of \((17 + 2x)^{\circ}\) and \((6x+3)^{\circ}\) is \(180^{\circ}\) (they are supplementary angles), the equation is \((17 + 2x)+(6x + 3)=180\).
Combine like terms: \(8x+20 = 180\).
Subtract 20 from both sides: \(8x=180 - 20=160\).
Divide both sides by 8: \(x = 20\).

Step3: For the circle (circumference - related)

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 5\) cm.
For part (a), substitute \(r = 5\) into the formula: \(C=2\pi\times5 = 10\pi\) cm.
For part (b), using \(\pi\approx3.14159\), \(C = 10\pi\approx10\times3.14159 = 31.4159\approx31.42\) cm.

Answer:

• First figure: Equation \(x + 15=50\), \(x = 35\)
• Second figure: Equation \((17 + 2x)+(6x + 3)=180\), \(x = 20\)
• 9(a): \(10\pi\) cm
• 9(b): \(31.42\) cm