From the table below, determine whether the data shows an exponential function. explain why or why not.

Option a. No; the domain values are at regular intervals and the range values have a common sum 1.

Step-by-step explanation:

x1=3, x2=1, x3=-1, x4=-3

y1=1, y2=2, y3=3, y4=4

x1-x2=3-1→x1-x2=2

y2-y1=2-1→y2-y1=1

x2-x3=1-(-1)=1+1→x2-x3=2

y3-y2=3-2→y3-y2=1

x3-x4=-1-(-3)=-1+3→x3-x4=2

y4-y3=4-3→y4-y3=1

The data doesn't show an exponential function, because the domain values are at regular intervals and the range values have a common sum 1.

x> 6

step-by-step explanation:

8x+8> 7x+14

8x-7x> 14-8

x> 6

(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