One hundred deer were released into a wildlife preserve. The population of deer over a certain number of years is shown. Time (years) 0.5 1
1.5 2 2.5 3
3.5 4
Population 100 111 144 193 252 309 352 363 324
The polynomial equation that models these data is P(x) = -24 +462? + 100.
When did the deer population reach its maximum?
O~2.0 years
0 -3.4 years
3.0 years
O-2.4 years

10 * 563.67 = 5636.7

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240