The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year. x 0 2 4 6 8 10 f(x) 10 15 18 19 18 15 Use the data in the table to create the standard form of the function that models this situation, where a, b, and c are constants.

Think about the data given. Quadratic model with vertex (6, 19) and two points being (0, 10) and (12, 10).

y=a%28x-6%29%5E2%2B19

-

a%28x-6%29%5E2=y-19

a=%28y-19%29%2F%28x-6%29%5E2

from here, any non-vertex point can be used for evaluating "a".

Trying (0,10):

a=%2810-19%29%2F%280-6%29%5E2=-9%2F36=-1%2F4

highlight_green%28y=-%281%2F4%29%28x-6%29%5E2%2B19%29

Do the necessary multiplication in order to find b.

Already seen are a=-1%2F4, and c=19.

Step-by-step explanation:

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.