Identify the transformation that carries the figure onto itself.
a) reflect across the line y = 7 and rotate 270° clockwise about (−7, 8)
b) reflect across the line x = 7 and rotate 270° clockwise about (−7, 8)
c) reflect across the line y = −7 and rotate 540° clockwise about (−7, 8)
d) reflect across the line x = −7 and rotate 540° clockwise about (−7, 8)

The correct option is D.

Step-by-step explanation:

The vertices of given figure are (-9,8), (-7,7), (-5,8), (-7,9).

1. If figure reflect across the line y = 7, then

The vertices of image are (-9,6), (-7,7), (-5,6), (-7,5).

Then rotate 270° clockwise about (−7, 8).

The vertices of image are (-5,6), (-6,8), (-5,10), (-4,8). These are not the vertices of given figure, theretofore option A is incorrect.

2. If figure reflect across the line x = 7, then

The vertices of image are (23,8), (21,7), (19,8), (21,9).

Then rotate 270° clockwise about (−7, 8).

The vertices of image are (-7,38), (-6,36), (-7,34), (-8,36). These are not the vertices of given figure, theretofore option B is incorrect.

3. If figure reflect across the line y = -7, then

The vertices of image are (-9,-22), (-7,-21), (-5,-22), (-7,-23).

Then rotate 540° clockwise about (−7, 8).

The vertices of image are (-5,38), (-7,37), (-9, 38), (-7.39). These are not the vertices of given figure, theretofore option C is incorrect.

4. If figure reflect across the line x = -7, then

The vertices of image are (-5,8), (-7,7), (-9,8), (-7,9).

Then rotate 540° clockwise about (−7, 8).

The vertices of image are (-9,8), (-7,9), (-5,8), (-7,7). These are the vertices of given figure, theretofore option D is correct.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

i think it's ф or x=6,-6

step-by-step explanation:

-x^2=-36

x^2=-36

ф

or

if you mean by : -(x^2)=-36

it'll be: x^2=36

x=6,x=-6

hope it'll ! have a good day!

you for asking!