The transformation of triangle abc is an example of what?
a) a dilation of 2.
b) translation of (0, 8)
c) translation of (0, -8)
d) a reflection across the y-axis

The correct option is C.

Step-by-step explanation:

From the given figure it is clear that the vertices of triangle ABC are A(1,1),  B(5,3) and C(2,6).

The vertices of triangle A'B'C' are A'(1,-7), B'(5,-5) and C'(2,-2).

The relation between preimage and image is defined by the rule

It is the rule of translation. It means the figure ABC translate 8 units down.

The transformation of triangle ABC is an example of translation of (0, -8).

Therefore the correct option is C.

the answer is the third / last answer

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .