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.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!