Jacobcon2
Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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) = −x^2 + 7x + 10. The second friend's profit can be determined by the function Q(x) = 4x. 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.

Sagot :

semsee45

Answer:

System of Equations

[tex]\large \begin{cases}P(x)=-x^2+7x+10\\Q(x)= 4x\end{cases}[/tex]

Use the substitution method to solve the given system of equations:

[tex]\large\begin{aligned}P(x) & = Q(x)\\-x^2+7x+10 & = 4x\\-x^2+7x+10 - 4x & = 0\\-x^2+3x+10 & = 0\\x^2-3x-10 & = 0\\x^2-5x+2x-10 & = 0\\x(x-5)+2(x-5) & = 0\\(x+2)(x-5) & = 0\\\implies x+2 & = 0 \implies x=-2\\\implies x-5 & = 0 \implies x=5\end{aligned}[/tex]

As [tex]x[/tex] represents the number of days, then [tex]x\geq 0[/tex]

Therefore:

  • The viable answer is when  [tex]x=5[/tex]   →   5 days
  • The non-viable answer is when  [tex]x=-2[/tex]  (as the number of days cannot be negative)

So the two students will earn the same profit after 5 days.

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.