Sure, let's solve these problems step-by-step:
### Part a:
Jack rode his bike 10 miles in 30 minutes.
1. Convert the time from minutes to hours:
[tex]\[
30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours}
\][/tex]
2. Calculate the speed in miles per hour (mph) using the formula:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
Substituting the values:
[tex]\[
\text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mph}
\][/tex]
So, Jack's speed is 20 mph.
### Part b:
Chris placed a ladder 4 feet from the base of a 12-foot wall. We need to determine the length of the ladder.
Here, we can use the Pythagorean theorem because the ladder, the wall, and the ground form a right triangle. Let [tex]\( L \)[/tex] be the length of the ladder:
1. According to the Pythagorean theorem:
[tex]\[
L^2 = \text{base}^2 + \text{height}^2
\][/tex]
Substituting the values:
[tex]\[
L^2 = 4^2 + 12^2 = 16 + 144 = 160
\][/tex]
2. Solving for [tex]\( L \)[/tex] by taking the square root of both sides:
[tex]\[
L = \sqrt{160} \approx 12.65 \text{ feet}
\][/tex]
So, the ladder is approximately 12.65 feet long.
### Part c:
A TV's size is determined by the diagonal measurement of its screen. We need to find the size of a TV with dimensions 18 inches by 24 inches.
Again, we can use the Pythagorean theorem. Let [tex]\( D \)[/tex] be the diagonal size of the TV:
1. According to the Pythagorean theorem:
[tex]\[
D^2 = \text{width}^2 + \text{height}^2
\][/tex]
Substituting the values:
[tex]\[
D^2 = 18^2 + 24^2 = 324 + 576 = 900
\][/tex]
2. Solving for [tex]\( D \)[/tex] by taking the square root of both sides:
[tex]\[
D = \sqrt{900} = 30 \text{ inches}
\][/tex]
So, the size of the TV is 30 inches.
### Summary
- Jack's speed is 20 mph.
- The ladder is approximately 12.65 feet long.
- The TV size is 30 inches.
