This table shows the input and output values for an exponential function f(x) . what is the ratio of outputs for any two inputs that are one value apart? a. 2 b. 4 c. -2 d. -1/2

A

Step-by-step explanation:

We find the ratio by dividing two y-values from 2 consecutive x values (1 unit apart). Notice that in the table, all x-values are 1 unit apart. We can choose any pair of consecutive points.

Let's choose: (2,-4) and (1,-2). We divide -4/-2=+2.

Answer A.

step-by-step explanation: 4 cause 2+2=4

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240