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Question 5 of 5

A tank full of water is leaking at a constant rate for 30 minutes. The equation

[tex]\[ y = -9x + 500 \][/tex]

gives the amount of water in the tank, where [tex]\( y \)[/tex] is the number of liters and [tex]\( x \)[/tex] is the number of minutes since the tank began to leak. Which statement is true?

A. There were 500 liters in the tank when the leak started, and it is decreasing by 9 liters per minute.
B. There were 9 liters in the tank when the leak started, and it is decreasing by 500 liters per minute.
C. There were 9 liters in the tank when the leak started, and it is increasing by 500 liters per minute.
D. There were 500 liters in the tank after 30 minutes, and it is decreasing by 9 liters per minute.

Sagot :

GinnyAnswer
To solve this problem, we need to analyze the given equation [tex]\( y = -9x + 500 \)[/tex]. This equation represents the amount of water [tex]\( y \)[/tex] in the tank at any time [tex]\( x \)[/tex] in minutes since the tank began to leak.

Let's examine each term in the equation:

1. Initial Amount of Water:
- When [tex]\( x = 0 \)[/tex] (i.e., at the start, when the leak just began), we substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -9(0) + 500 = 500 \][/tex]
- This tells us that there were 500 liters of water in the tank when the leak began.

2. Rate of Decrease of Water:
- The coefficient of [tex]\( x \)[/tex] in the equation is -9. This means that the amount of water [tex]\( y \)[/tex] is decreasing by 9 liters per minute.

Now, let's verify each of the given options:

- Option A:
"There were 500 liters in the tank when the leak started, and it is decreasing by 9 liters per minute."

Based on our analysis:
- Initial amount of water when [tex]\( x = 0 \)[/tex] is indeed 500 liters.
- The rate of water decrease is 9 liters per minute.

Therefore, Option A is true.

- Option B:
"There were 9 liters in the tank when the leak started, and it is decreasing by 500 liters per minute."

- Based on our analysis, there were 500 liters initially, not 9 liters.
- The rate of water decrease is 9 liters per minute, not 500 liters per minute.

Option B is false.

- Option C:
"There were 9 liters in the tank when the leak started, and it is increasing by 500 liters per minute."

- Based on our analysis, there were 500 liters initially, not 9 liters.
- The water is decreasing, not increasing, and the rate is 9 liters per minute.

Option C is false.

- Option D:
"There were 500 liters in the tank after 30 minutes, and it is decreasing by 9 liters per minute."

- Let's check the water amount after 30 minutes:
[tex]\[ y = -9(30) + 500 = -270 + 500 = 230 \][/tex]
- After 30 minutes, there will be 230 liters in the tank, not 500 liters.

Therefore, Option D is false.

Since Option A is the only true statement, we conclude that the correct answer is:

A. There were 500 liters in the tank when the leak started, and it is decreasing by 9 liters per minute.
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