Question

Mia removes the plug 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 −19x + 6, where x is time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty. 10(0)2 − 19(0) + 6 10(x − 6)2 − 1 10(x − 1)2 − 6 (5x − 2)(2x − 3)

Answer 1

Answer:

The correct option is D) (5x − 2)(2x − 3).

Step-by-step explanation:

Consider the provided expression.

$10x^2-19x+6$

Where x is time in minutes.

We need to find the appropriate form of the expression that would reveal the time in minutes when the trough is empty.

When the trough is empty the whole expression becomes equal to 0.

Substitute the whole expression equal to 0 and solve for x that will gives us the required expression.

$10x^2-19x+6=0$

$10x^2-15x-4x+6=0$

$5x(2x-3)-2(2x-3)=0$

$(5x-2)(2x-3)=0$

Now consider the provided option.

By comparison the required expression is D) (5x − 2)(2x − 3).

Hence, the correct option is D) (5x − 2)(2x − 3).