Sally wants to buy her friend a bouquet for his birthday. she wants it to contain both carnations and roses. she has $27.30 to spend. carnations cost $1.42 each and roses cost $2.35 each. which graph below represents the possible combinations of numbers of carnations and roses sally can afford to buy?

The answer to your question is: letter A

Step-by-step explanation:

Data

Total cost = $27.30

carnations = $1.42 = x

roses = $2.35 = y

Equation

               1.42x + 2.35y = 27.30

Solve for y

                    2.35y = -1.42x + 27.30

                           y = -(1.42/2.35) + (27.30/2.35)

                           y = -0.604x + 11.61

Find x and y-intercepts

When x = 0          y = -0.604(0) + 11.61

                            y = 11.61

Point     (0, 11.61)

When y = 0

                        0 = -0-604x + 11.61

                       x = 11.61/ -0.604

                      x = 19.22

Point (19.22, 0)

Look for which graph has these 2 points.

I think is letter A

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).