Question

A plug is removed from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 10x2 − 11x + 3, where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time, in minutes, when the trough is empty. (1 point)

10(0)2 − 11(0) + 3

(5x − 3)(2x − 1)

10(x − 3)2 − 1

10(x − 1)2 − 3

Answer 1

The appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is:

10(x - 3)^2 - 1

This is because the expression 10x^2 - 11x + 3 represents the volume of water in the trough at any given time x, and we are looking for the time when the trough is empty, which is when the volume of water is equal to zero.

Setting the expression equal to zero and solving for x, we get:

10(x - 3)^2 - 1 = 0
10(x - 3)^2 = 1
(x - 3)^2 = 1/10
x - 3 = ±√(1/10)
x = 3 ± √(1/10)

Since we are interested in the positive solution that represents the time it takes for the trough to empty, the answer is:

x = 3 + √(1/10)