select the correct answer from each drop - down menu.\na local movie theater is trying to find the best…

select the correct answer from each drop - down menu.\na local movie theater is trying to find the best price at which to sell popcorn. to reach its goal of making at least $50,000 from popcorn sales this year, the theater decided to hire a consulting firm to analyze its business.\nthe firm determined that the best - case scenario for the theaters revenue generated from popcorn sales, while meeting its revenue goals, is given by this system of inequalities, where $r$ represents the revenue in tens of thousands of dollars and $p$ represents the sale price of popcorn in dollars.\n$rleq - 0.23p^{2}+2.25p$\n$rgeq5$\ncomplete the statements about the systems possible solutions.\nthe point $(4,6)$ is \nthe point $(6,5)$ is

select the correct answer from each drop - down menu.\na local movie theater is trying to find the best price at which to sell popcorn. to reach its goal of making at least $50,000 from popcorn sales this year, the theater decided to hire a consulting firm to analyze its business.\nthe firm determined that the best - case scenario for the theaters revenue generated from popcorn sales, while meeting its revenue goals, is given by this system of inequalities, where $r$ represents the revenue in tens of thousands of dollars and $p$ represents the sale price of popcorn in dollars.\n$rleq - 0.23p^{2}+2.25p$\n$rgeq5$\ncomplete the statements about the systems possible solutions.\nthe point $(4,6)$ is \nthe point $(6,5)$ is

Answer

Answer:

  1. The point $(4,6)$ is not a solution of this system.
  2. The point $(6,5)$ is a solution of this system.

Explanation:

Step1: Analizar la primera desigualdad para el punto $(4,6)$

Dada $r\leq - 0.23p^{2}+2.25p$, sustituimos $p = 4$ y $r = 6$. Calculamos $-0.23\times4^{2}+2.25\times4=-0.23\times16 + 9=-3.68+9 = 5.32$. Como $6>5.32$, no satisface $r\leq - 0.23p^{2}+2.25p$.

Step2: Analizar la segunda desigualdad para el punto $(4,6)$

Dada $r\geq5$, como $6\geq5$, satisface $r\geq5$. Pero como no satisface la primera desigualdad, no es solución.

Step3: Analizar la primera desigualdad para el punto $(6,5)$

Sustituimos $p = 6$ y $r = 5$ en $r\leq - 0.23p^{2}+2.25p$. Calculamos $-0.23\times6^{2}+2.25\times6=-0.23\times36+13.5=-8.28 + 13.5 = 5.22$. Como $5\leq5.22$, satisface $r\leq - 0.23p^{2}+2.25p$.

Step4: Analizar la segunda desigualdad para el punto $(6,5)$

Dada $r\geq5$, como $5\geq5$, satisface $r\geq5$. Entonces es solución.