Question

1. (2 pts) the formula r = \frac{d}{2} can be used to find the radius of a circle, r, given the diameter, d. given r, which equation finds d?

a. d = 2r
b. d = r + 2
c. d = r - 2
d. d = \frac{r}{2}

1. (3 pts) pete earns $8.50 per hour plus tips. on tuesday, he received $16 in tips. how many hours did pete work if he earned a total of $50 on tuesday?

a. 7
b. 6
c. 5
d. 4

1. (3 pts) solve and graph the inequality below on a number line.

8x + 1 < 41

Explanation:

Question 10

Step1: Recall radius - diameter relation

The radius $r$ of a circle is half of the diameter $d$, i.e., $r=\frac{d}{2}$. To find $d$ when $r$ is given, we multiply both sides of the equation by 2.

Step2: Solve for $d$

$d = 2r$

Step1: Set up an equation

Let $h$ be the number of hours Pete worked. His earnings are given by the equation $8.5h+16 = 50$, where $8.5h$ is his earnings from hourly - wage and 16 is his tip earnings.

Step2: Solve for $h$

First, subtract 16 from both sides of the equation: $8.5h=50 - 16=34$. Then divide both sides by 8.5: $h=\frac{34}{8.5}=4$.

Step1: Isolate the variable term

Subtract 1 from both sides of the inequality $8x + 1<41$. We get $8x<41 - 1$, so $8x<40$.

Step2: Solve for $x$

Divide both sides of the inequality $8x<40$ by 8. We have $x < 5$.
To graph on a number line: Draw a number line. Mark a open - circle at 5 (since $x$ is less than 5, not less than or equal to 5) and shade the line to the left of 5.

Answer:

A. $d = 2r$

Question 16