Skylar repairs microwaves. her revenue, in dollars, can be modeled by the equation y = 80 + 30x, where x is the number of hours spent repairing microwaves. her overhead cost, in dollars, can be modeled by the equation y=10x2−20 , where x is the number of hours spent repairing microwaves. after how many hours does she break even?

5 hours.

Step-by-step explanation:

We have been given an equation , which represents the revenue in dollars for Skylar.

The equation represents Skylar's overhead cost.

Since we know that break even is the point, where total cost equals to total revenues, so to find the break-even we will equate our given both equations as:

Now let is solve for x.

Let us divide our equation by 10.

Let us factor out our quadratic equation by splitting the middle term.

Since the number of hours can not be negative, therefore, the break-even point is 5 hours.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i