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(06.04 HC)

Two friends wash cars to make extra money. The profit P(x) of one friend after x days can be represented by the function P(x) = −x2 + 5x + 12. The second friend's profit can be determined by the function Q(x) = 6x. Solve the system of equations. What solution is a viable answer to the question, "After how many days will the two students earn the same profit?" and which solution is a nonviable answer? Show your work and justify your answer.

Respuesta :

varshamittal029

The viable answer, according to the provided profit equations, is that they make the same profit after three days, while the nonviable response is -4 because the number of days must be a positive value.

Given that the profit equation of the first friend is

P(x) = −x² + 5x + 12 ...(1)

and the profit equation of the second friend is

Q(x) = 6x  ...(2)

The system we use to determine when they earn the same profit is provided by:

P(x) = Q(x)

i.e.  −x² + 5x + 12  =  6x  

i.e. x² + x - 12 = 0

i.e. x² + 4x - 3x - 12 = 0

i.e. x(x + 4) - 3(x + 4) = 0

i.e. (x + 4)(x - 3) = 0

i.e. x = 3, -4

Because the number of days must be positive, the viable answer is that they earn the same profit after three days, while the nonviable answer is -4.

Learn more about profit equations here -

https://brainly.com/question/26778029

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