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.\nr $leq$ $-0.23p^{2}+2.25p$\nr $geq$ 5\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.\nr $leq$ $-0.23p^{2}+2.25p$\nr $geq$ 5\ncomplete the statements about the systems possible solutions.\nthe point $(4,6)$ is \nthe point $(6,5)$ is

Answer

Explanation:

Step1: Check point (4, 6) for first - inequality

Substitute (r = 4) and (p=6) into (r\leq - 0.23p^{2}+2.25p). Calculate (-0.23\times6^{2}+2.25\times6=-0.23\times36 + 13.5=-8.28+13.5 = 5.22). Since (4\leq5.22), the first - inequality holds. Check the second - inequality: (r = 4) and (r\geq5) is false. So, ((4,6)) is not a solution.

Step2: Check point (6, 5) for first - inequality

Substitute (r = 5) and (p = 6) into (r\leq - 0.23p^{2}+2.25p). Calculate (-0.23\times6^{2}+2.25\times6=-8.28 + 13.5=5.22). Since (5\leq5.22), the first - inequality holds. Check the second - inequality: (r = 5) and (r\geq5) is true. So, ((6,5)) is a solution.

Answer:

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