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a zookeeper is monitoring the population of penguins. the group needs two times more males than females to thrive, and the zoo only has room for 10 female penguins. let x = the number of female penguins and y = the number of male penguins. write the constraints to represent a thriving population of penguins at the zoo.
0 < x ≤ 10 and 0 < y ≤ 20
x > 0 and y > 0
0 < x ≤ 10 and y > 20
x > 0 and y < 10

The constraint which represent a thriving population of penguins at the zoo is:

            0 < x ≤ 10   and   0 < y ≤ 20.

Let x = the number of female penguins and y = the number of male penguins.

Now, it is given that:

The group needs two times more males than females to thrive, and the zoo only has room for 10 female penguins.

This means that:

   0 < x ≤ 10

( Because there are no room for more than 10 penguins )

Also,

   y= 2x

Since,

   x>0

This means that: 2x>0

i.e. y>0

and x ≤ 10

i.e. 2x ≤ 20

i.e.  y ≤ 20

Hence, the constraints which represent a thriving population of penguins at the zoo is:

                 0 < x ≤ 10 and 0 < y ≤ 20.

x = 2y +10

x = -2y + 5

Step-by-step explanation: