Question

A tank full of water is leaking at a constant rate for 15 minutes. The equation is y = -8x + 500, where y is the number of liters and x is the number of minutes that have elapsed since the tank started leaking. Which statement is true?

a) The tank initially had 500 liters of water.
b) The tank was leaking at a rate of 8 liters per minute.
c) The tank will be completely empty after 62.5 minutes.
d) The tank will never be empty.

Answer 1

The tank initially had 500 liters of water, was leaking at a constant rate of 8 liters per minute, and would be empty after 62.5 minutes, according to the given equation y = -8x + 500.

Step-by-step explanation:

The correct answer is: a) The tank initially had 500 liters of water, b) The tank was leaking at a rate of 8 liters per minute, and c) The tank will be empty after 62.5 minutes. The equation provided, y = -8x + 500, describes a linear relationship where 'y' represents the volume of water in liters, and 'x' represents the time in minutes.

a) The y-intercept (500) indicates the initial amount of water in the tank when no time has elapsed (x=0), hence, the tank started with 500 liters. b) The coefficient of 'x' (-8) is the rate of change or the constant rate at which the tank is leaking, which means 8 liters are leaking every minute. c) To find when the tank will be empty, we set y=0 and solve for x, giving us x = 500/8, which simplifies to 62.5 minutes.