Answer:
Option A: (5,0)
Step-by-step explanation:
Given
[tex]y \leq \frac{2}{5}x-2[/tex]
Required
Select an ordered pair
Option A: (5,0)
This means
[tex]x = 5[/tex] [tex]y = 0[/tex]
Substitute these values in [tex]y \leq \frac{2}{5}x-2[/tex]
[tex]0 \leq \frac{2}{5} * 5 - 2[/tex]
[tex]0 \leq 2 - 2[/tex]
[tex]0 \leq 0[/tex]
This is a true statement.
Option B: (0,5)
This means
[tex]x = 0[/tex] [tex]y = 5[/tex]
Substitute these values in [tex]y \leq \frac{2}{5}x-2[/tex]
[tex]5 \leq \frac{2}{5}* 0 -2[/tex]
[tex]5 \leq 0 -2[/tex]
[tex]5 \leq -2[/tex]
This is a false statement.
Option C: (-2,5)
This means
[tex]x=-2[/tex] [tex]y = 5[/tex]
Substitute these values in [tex]y \leq \frac{2}{5}x-2[/tex]
[tex]5 \leq \frac{2}{5}* -2 -2[/tex]
[tex]5 \leq \frac{-4}{5} -2[/tex]
[tex]5 \leq \frac{-4-10}{5}[/tex]
[tex]5 \leq \frac{-14}{5}[/tex]
[tex]5 \leq -2.8[/tex]
This is a false statement.
Option D: (-5,2)
This means
[tex]x=-5[/tex] [tex]y = 2[/tex]
Substitute these values in [tex]y \leq \frac{2}{5}x-2[/tex]
[tex]2 \leq \frac{2}{5}* -5 -2[/tex]
[tex]2 \leq -2 -2[/tex]
[tex]2 \leq -4[/tex]
This is a false statement.
Only option A represents a true statement,
Hence, option A is a solution to the inequality
