The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: A linear model with ordered pairs at 0, 26 and 2, 34 and 4, 34 and 8, 30 and 10, 0 and 12, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points)

Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer. (3 points)

The answer is below

Step-by-step explanation:

A) From 0 to 2 seconds, the height of the water balloon is increasing from 26 feet to 34 feet (8 ft increase) i.e. at a rate of 4 ft/s (8ft/2 s)

B) From 2 to 4 seconds, the height of the water balloon is held constant at 34 feet, also from 10 to 12 seconds the height is constant at 0 feet

C) From 4 to 8 seconds, the height of the water balloon is decreasing from 34 feet to 30 feet (4 ft decrease within 4 seconds) i.e. at a rate of 1 ft/s (4 ft /4 s).

Also  From 8 to 10 seconds, the height of the water balloon is decreasing from 30 feet to 0 feet (30 ft decrease within 2 seconds) i.e. at a rate of 15 ft/s (30 ft / 2 s).

It is decreasing fastest from 8 to 10 seconds

D) At 10 seconds, the height of the balloon is at 0 feet, this means it is on the ground. It would continue to remain on the ground even at 14 seconds

Step-by-step explenation:

A. The water balloon increase from about 60-75 ft, and time for the x-axis in seconds is 0-2 seconds.

B. 2-4 seconds and the height of the balloon stays the same in 75 ft, which causes the water balloon height the same during its interval which is (2,4). It takes 10-12 seconds the height of the balloon it's the same as the interval which is (10,12). Then it takes from 12-14 seconds so that the height stay the same at 0 ft, so this makes the water balloon to make the height is the same as the interval which is (12,14).

C. The interval (4,6) is the domain when the water balloon height which will decrease faster since the interval is (4,6) so this makes the balloon interval to decrease which will make it (6,8) and (6,10) which of course would have the same slope.

D. I predict that the balloon will reach the height at 16 seconds with 0 feet.Since 10-14 seconds the balloon on the ground which is the balloon height. And well, if the balloon reaches the ground of course it ends at 0 height since it's not moving anywhere.:

the first one, all those points on the line just make a strait line.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right