Find the coordinate of T' after a 90° counterclockwise rotation of the triangle about the origin and then a translation of 3 units up and 4 units to the left

 c. (0, 5)

Step-by-step explanation:

T = (2, -4)

90° rotation counterclockwise means (x, y) = (-y, x)

new T = (4, 2)

3 units up means add 3 to the y-coordinate

newer T = (4, 5)

4 units left means subtract 4 from the x-coordinate

T' = (0, 5)

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 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.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

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

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.