Help please worth 57 points

Step-by-step explanation:

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

we know that

A dilation is  a Non-Rigid Transformations that change the structure of our original object. For example, it can make our object bigger or smaller using scaling.

The dilation produce similar figures

In this case, it would be lengthening or shortening a line. We can dilate any line to get it to any desired length we want.

A rigid transformation, is a transformation that preserves distance and angles, it does not change the size or shape of the figure. Reflections, translations, rotations, and combinations of these three transformations are rigid transformations.

so

If we have two line segments XY and WZ,  then it is possible to use dilation and rigid transformations to map line segment XY to line segment WZ.

The first segment XY would map to the second segment WZ

therefore

A line segment is always similar to another line segment, because we can always map one into the other using only dilation a and rigid transformations

Always, always.

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.