The total number of animals in a shelter is modeled by f(x) = 2x2 - 45x, where x represents the number of cages at the facility. How many cages are at the facility if it has a total of 243 animals there?
A. 25
B. 27
C. 33
D. 39

B: 27

Step-by-step explanation:

The total number of animals in a shelter is modeled by the function:

Where x is the number of cages at the facility.

We want to determine the number of cages if there are a total of 243 animals at the shelter.

So, we can set our function to 243 and solve for x:

Subtract 243 from both sides:

Solve the quadratic. Factoring and completing the square seems too difficult, so we can use the quadratic formula:

In this case, a = 2, b = -45, and c = -243. Substitute:

Evaluae:

Evaluate:

Therefore, our two solutions are:

Since we cannot have negative or half a cage, we can ignore the second solution.

Therefore, there are a total of 27 cages at the shelter.

Our answer is B.

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !