Consider the figure at the right. if ️xyz is translated using the vector (x, y) --> (x-3,y+3) , then rotated 180 degrees about the origin, what will be the x-coordinate of z'?

Given coordinate of Z of the given figure (-1,-1).

First triangle XYZ is being translated by the rule (x,y) --> (x-3, y+3).

On applying that rule, the new coordinates of Z would be

(-1,-1)  >  (-1-3 , -1+3) = (-4, 2).

Now, we need to apply rotation 180 degrees about the origin.

The rule for rotation 180 degrees about the origin is (x,y) --> (-x,-y).

Therefore, final coordinate of Z after rotation 180 degrees about the origin would be

(-4, 2) ---> (4, -2).

answer: 12

step-by-step explanation:

because yes

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.