Asap (i need to finish this quick) graph complete the sequence of transformations that produces △x'y'z' from △xyz. a clockwise rotation ° about the origin followed by a translation units to the right and 6 units down produces δx'y'z' from δxyz.

A clockwise rotation 90° about the origin followed by a translation

2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° anti-clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° anti-clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180° clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise

∴ Its image is (-y , x)

- If the point (x , y) translated horizontally to the right by h units

∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

∴ Its image is = (x , y - k)

* Now lets solve the problem

- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)

∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)

∴ The image of X is (3 , 5)

∴ The image of Y is (3 , 2)

∴ The image of Z is (1 , 2)

- From the graph

∵ X' = (5 , -1)

∵ Y' = (5 , -4)

∵ Z' = (3 , -4)

- Every x-coordinate add by 2

∴ There is a translation 2 units to the right

- Every y-coordinate subtracted by 6

∴ There is a translation 6 units down

- From all above

* A clockwise rotation 90° about the origin followed by a translation

 2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ

10

step-by-step explanation:

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)