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, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 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 10 seconds. Use complete sentences to support your answer. (3 points)

See below.

Step-by-step explanation:

So we can picture a graph with the following coordinates:

So the graph should begin at y=60, go up a little, stay there a little, and then start falling downwards.

Part A:

The intervals of the domain where the balloon's height is increasing is right after the release (0,60) until the second second at (2,80). We can see that between these two seconds, the height increased by 20 feet. After that point, the balloon starts falling down and won't rise again. At exactly the second second, however, the balloon is staying still so we won't include the second. Thus, we will use parentheses. Therefore, the interval is:

Part B:

As we can see, the balloon stays the same from the second second up to the third second. At those exact seconds, they are also within the same height, so we include them. Thus:

Part C:

So, we have two intervals where the balloon's height is decreasing. From (3,80) to (4,20) and also from (4,20) to (6,0). Using the slope formula, we can see that the balloon drops at a rate of 60 feet per second. The second interval only drops at a rate of 10 feet per second. We don't know the height of the balloon at x equals 5 seconds, but that doesn't matter since it can be greater than 60 feet per second. Thus, the interval during which the balloon's height is decreasing the fastest is:

Part D:

After and during the sixth, seventh, and eighth seconds, the balloon's height is 0, meaning it's completely on the ground. Without any force such as wind, the balloon would stay there. Therefore, at 10 seconds, the height of the water balloon should still be 0, on the ground.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!