Question

A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.

white-sided jackrabbits: 5.5x² – 9.2x + 6.9
black-tailed jackrabbits: 5.5x² + 9.9x + 1.3

What polynomial models the total number of white-sided and black-tailed jackrabbits?

11x² + 0.7x + 8.2

11x² – 0.7x + 8.2

11x² – 0.7x – 8.2

–11x² + 0.7x – 8.2

Answer 1

Answer:
`11x^2+0.7x+8.2`

Explanation:

Given: A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.

white-sided jackrabbits:
`5.5x^2-9.2x+6.9`

black-tailed jackrabbits:
`5.5x^2+9.9x+1.3`

The polynomial models the total number of white-sided and black-tailed jackrabbits is given by :-

`5.5x^2-9.2x+6.9+5.5x^2+9.9x+1.3`

Combining like terms we get,

`=5.5x^2+5.5x^2-9.2x+9.9x+6.9+1.3`

`=(5.5+5.5)x^2+(-9.2+9.9)x+8.2\\\\=11x^2+0.7x+8.2`

Hence, the polynomial models the total number of white-sided and black-tailed jackrabbits is
`11x^2+0.7x+8.2`

Answer 2

The answer is 11x² + 0.7x + 8.2

Total number of white-sided and black-tailed jackrabbits is the sum of their polynomials:
5.5x² – 9.2x + 6.9 + 5.5x² + 9.9x + 1.3 = 5.5x² + 5.5x² – 9.2x + 9.9x + 6.9 + 1.3 =
= 11x² + 0.7x + 8.2