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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 :

Answer:

  • the number of days = 3 days
  • the nonviable answer = -4 days

Step-by-step explanation:

We can find the number of days when the two students earn the same profit using the system of equations. Since their profits will be the same, then P(x) = Q(x).

[tex]P(x)=Q(x)[/tex]

[tex]-x^2+5x+12=6x[/tex]

[tex]x^2+x-12=0[/tex]

[tex](x+4)(x-3)=0[/tex]

[tex]x=-4\ or\ 3[/tex]

Since the number of days cannot be negative, hence:

  • the number of days = 3 days
  • the nonviable answer = -4 days

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