A special die has a number on each face. The sums of the opposite faces are all equal. Five of the numbers are 5,6,9,11, and 14. What number is on the sixth face?

Step-by-step explanation:

The sum of the opposite faces is 20, because 14 + 6 = 20 and 11 + 9 = 20, so we just need to find the answer to the equation

5 + x = 20

Solving for x, we have

x = 20-5

x = 15.

Therefore, the missing number is 15.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.