50 POINTS Quadrilateral PQRS is mapped onto its image using which of the following sets of transformations?

reflection across x = -2; clockwise rotation of 90° about the origin
reflection across x = 2; clockwise rotation of 90° about the origin
reflection across y-axis; counter-clockwise rotation of 90° about the origin
reflection across y-axis; clockwise rotation of 90° about the origin

Reflection across = -2; clockwise rotation

Step-by-step explanation: To get this answer, you first must work out the other answers. If you reclect across the x-axis and rotate 90 degrees clockwise, you'll find the shape to be in almost the exact same place it was before.

The third choice is illogical, because if you reflect over the y-axis, the shape is nowhere near where you need it to be, and rotating it 90 degrees counterclockwise is gonna bring it back to where you started.

The fourth option is the same as the third yet this time the clockwise rotation will bring you down to the negative y's, which is the opposite of where you need to be.

Therefore, that is why the first option is the better one to choose. Reflecting the shape over x = -2 is going to give you the correct orientation you needed for the 90 degree rotation.

I hope this helps!

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: