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Sagot :
Hello!
We have the following system:
[tex]\begin{cases}y\le-x^2+5x{} \\ y>x^2-4{}\end{cases}[/tex]Let's try to solve it by replacing each alternative:
(–1, –1) FALSE
[tex]\begin{cases}-1\le-(-1)^2+5(-1){\rightarrow\boxed{-1\le-6}}\text{ FALSE} \\ -1>(-1)^2-4{{\rightarrow}\boxed{-1>-3}}\text{ TRUE}\end{cases}\text{ }[/tex](0, 2) FALSE
[tex]\begin{cases}2\le-0^2+5(0){{\rightarrow}\boxed{2\le0}\text{FALSE}} \\ 2>0^2-4{{\rightarrow\boxed{2>-4}\text{ TRUE}}}\end{cases}[/tex](2, 5) TRUE
[tex]\begin{cases}5\le-2^2+5(2){{\rightarrow}\boxed{5\le6}\text{ TRUE}} \\ 5>2^2-4{{\rightarrow\boxed{5>0}}}\text{ TRUE}\end{cases}[/tex](4, 1) FALSE
[tex]\begin{cases}1\le-4^2+5({4)}{\rightarrow}\boxed{1\le4}\text{ TRUE} \\ 1>4^2-4{{\rightarrow}\boxed{1>12}\text{ FALSE}}\end{cases}[/tex]Answer:
Alternative C. (2, 5).
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