Use matrices to determine the coordinates of the vertices of the rotated figure. then graph the pre-image and the image of the same coordinate grid. (pictureprovided)

The coordinates of the vertices of the rotated figure are :

U' (1 , -6), V' (-8 , -4), W' (-5 , 7) ⇒ the right answer is figure (d)

Step-by-step explanation:

* Lets study the matrices of the Rotation by 180°  

- When we rotate a point around the origin by 180° clockwise

 or anti-clockwise, we change the sign of the x-coordinate and

 the y-coordinate of the point

- Then matrix of the rotation 180° is

* Now lets solve the problem

- We will multiply the matrix of the rotation  by each point to

 find the image of each point

- The dimension of the matrix of the rotation  is 2×2 and the

 dimension of the matrix of each point is 2×1,  then the

 dimension of the matrix of each image is 2×1

∵ Point U is (-1 , 6)

∴

∴ U' = (1 , -6)

∵ Point V is (8 , 4)

∴

∴ V' = (-8 , -4)

∵ Point W is (5 , -7)

∴

∴ W' = (-5 , 7)

* Now look to the figures to find the right answer

∵ The images of the points are U' (1 , -6), V' (-8 , -4), W' (-5 , 7)

∴ The right answer is figure (d)

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

21

step-by-step explanation: