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Mike repairs televisions. His revenue, in dollars, can be modeled by the equation y = 25 + 30x, where x is the number of hours spent repairing televisions. His overhead cost, in dollars, can be modeled by the equation y=5x^2−10 , where x is the number of hours spent repairing televisions.

After how many hours does he break even?

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

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Respuesta :

[tex]\bf \begin{cases} y=25+30x\impliedby revenue\\\\ y=5x^2-10\impliedby cost \end{cases} \\\\\\ revenue=cost\impliedby \textit{break-even point, neither profit or loss}\qquad thus \\\\\\ 25+30x=5x^2-10\impliedby \textit{solve for "x"}[/tex]

Answer:

h = 7

Step-by-step explanation:

[tex]25 + 30x = 5x^2 - 10\\= 5x^2-30x-35\\= 5(x^2-6x-7)\\= 5((x+1)(x-7))\\\\so...\\x = -1\\x = 7[/tex]

And we want the positive one.

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