The correct answer is:
5 hours.
Explanation:
To find the break-even point, we set the two functions equal to each other:
20+30h = 10h²-80
Since this is a quadratic equation, we want it set equal to 0 to solve. First we will subtract 20 from each side:
20+30h-20 = 10h²-80-20
30h = 10h²-100
Subtract 30h from each side:
30h-30h = 10h²-100-30h
0 = 10h²-30h-100
We will use the quadratic formula to solve this:
[tex] x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} [/tex]
Instead of x, we have h. Our values for a, b and c are:
a = 10
b = -30
c = -100
This gives us:
[tex] h=\frac{--30\pm \sqrt{(-30)^2-4(10)(-100)}}{2(10)}
\\
\\=\frac{30\pm \sqrt{900--4000}}{20}
\\
\\=\frac{30\pm \sqrt{900+4000}}{20}
\\
\\=\frac{30\pm \sqrt{4900}}{20}
\\
\\=\frac{30\pm 70}{20}=\frac{30-70}{20}\text{ or }\frac{30+70}{20}
\\
\\=\frac{-40}{20}\text{ or }\frac{100}{20}=-2\text{ or }5 [/tex]
Since a negative number of time makes no sense, we use h = 5.
It took Mary 5 hours for her to break even when repairing the microwave.
Break even is the point at which the revenue is equal to the cost. Revenue is the amount of money made from selling goods and cost is the money spent on production.
Hence:
h = -2 or h = 5
It took Mary 5 hours for her to break even when repairing the microwave.
Find out more on break even at: https://brainly.com/question/9212451
