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Alecsey [184]
2 years ago
5

Quick Fix Inc. repairs bikes. Their revenue, in dollars, can be modeled by the equation y = 400 + 220x, where x is the number of

hours spent repairing bikes. Their overhead cost, in dollars, can be modeled by the equation y=20x2+160 , where x is the number of hours spent repairing bikes.
After how many hours does the company break even?

Note: The phrase break even refers to the value where the two functions are equivalent.

Enter your answer in the box.

h
Mathematics
2 answers:
Alex17521 [72]2 years ago
6 0

Answer:

12 hours

Step-by-step explanation:

Sholpan [36]2 years ago
5 0
The break even point is that where the total cost is equal to the total revenue. To determine the number of hours in which Quick Fix Inc. will have a breakeven, we have to equate the two equations and solve for the value of x,
                              400 + 220 x = 20x² + 160
The values of x from the equation are 12 and -1. Since, we do not have a negative for the number of hours, our answer is 12 hours. 
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The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh
konstantin123 [22]

Answer:

33 copies were paperback and 12 were hardcover.

Step-by-step explanation:

Let h represent the number of hardcover copies and p represent the number of paperback copies.

We know that the total number of copies was 45; this gives us the equation

h+p = 45

We know that each hardcover copy is 7 ounces; this gives us the expression 7h.

We also know that each paperback copy is 5 ounces; this gives us the expression 5p.

We know that the total weight was 249 ounces; this gives us the equation

7h+5p = 249

Together we have the system

\left \{ {{h+p=45} \atop {7h+5p=249}} \right.

We will use elimination to solve this.  First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

\left \{ {{5(h+p=45)} \atop {7h+5p=249}} \right. \\\\\left \{ {{5h+5p=225} \atop {7h+5p=249}} \right.

To eliminate p, we will subtract the equations:

\left \{ {{5h+5p=225} \atop {-(7h+5p=249)}} \right. \\\\-2h=-24

Divide both sides by -2:

-2h/-2 = -24/-2

h = 12

There were 12 hardcover copies sold.

Substitute this into our first equation:

12+p=45

Subtract 12 from each side:

12+p-12 = 45-12

p = 33

There were 33 paperback copies sold.

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Step-by-step explanation:

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