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?

after how many hours does she break even?
y = 80 + 30x=10x2−20
so 10x²-30x-100=0 or x²-3x-10=0
Delta= 3²-4.(1).(-10)=9+40=49
the root of Delta is sqrt49=7
so x= 3-7/2= -2 or x=3+7/2=5
so the number of hours is after x=5 hours

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ApusApus ApusApus · Answer 2 · 2019-03-15T00:22:13-04:00

Answer:

\(x=5\) 5 hours.

Step-by-step explanation:

We have been given an equation \(y=80+30x\), which represents the revenue in dollars for Skylar.

The equation \(y=10x^2-20\) 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:

\(10x^2-20=80+30x\)

Now let is solve for x.

\(10x^2-20-80-30x=80-80+30x-30x\)

\(10x^2-30x-100=0\)

Let us divide our equation by 10.

\(x^2-3x-10=0\)

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

\(x^2-5x+2x-10=0\)

\(x(x-5)+2(x-5)=0\)

\((x+2)(x-5)=0\)

\((x+2)=0\text{ or }(x-5)=0\)

\(x+2-2=0-2\text{ or }x-5+5=0+5\)

\(x=-2\text{ or }x=5\)

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