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

select the correct answer from each drop - down menu. a 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. the 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. r ≤ - 0.23p² + 2.25p r ≥ 5 complete the statements about the systems possible solutions. the point (4,6) is of this system. the point (6,5) is of this system. reset next

select the correct answer from each drop - down menu. a 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. the 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. r ≤ - 0.23p² + 2.25p r ≥ 5 complete the statements about the systems possible solutions. the point (4,6) is of this system. the point (6,5) is of this system. reset next

Answer

Explanation:

Step1: Substitute point (4, 6) into inequalities

For $r\leq - 0.23p^{2}+2.25p$, substitute $r = 4$ and $p = 6$. First, calculate $-0.23\times6^{2}+2.25\times6=-0.23\times36 + 13.5=-8.28+13.5 = 5.22$. Since $4\leq5.22$. For $r\geq5$, since $4<5$, the point $(4,6)$ is not a solution.

Step2: Substitute point (6, 5) into inequalities

For $r\leq - 0.23p^{2}+2.25p$, substitute $r = 6$ and $p = 5$. Calculate $-0.23\times5^{2}+2.25\times5=-0.23\times25 + 11.25=-5.75+11.25 = 5.5$. Since $6>5.5$. For $r\geq5$, since $6\geq5$, the point $(6,5)$ is not a solution.

Answer:

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