Which choice shows the image of triangle QRS after the reflection over the x-axis followed by a rotation of 180° around the origin?

A

Step-by-step explanation:

We see that triangle QRS is located in Quadrant III. (See attachment for labelling of quadrants)

Reflecting it over the x-axis means that we flip it over the x-axis, or we flip it vertically. Doing so, QRS will end up in Quadrant II.

Now, we need to rotate QRS 180 degrees about the origin. The quadrants are all 90 degrees away from each other, which means that if we rotate QRS about the origin 180 degrees, we'll end up two quadrants away from Quadrant II: we'll end in Quadrant IV.

Look at each of the answer choices. The only choice that features Q'R'S' (the image of QRS) in the fourth quadrant is the first choice, or A. So that's the answer.

~ an aesthetics lover

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet