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.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: