△xyz is mapped to △x'y'z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) . which statement describes the relationship between △xyz and △x'y'z'? △xyz is congruent to △x'y'z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions. △xyz is not congruent to △x'y'z' because the rules do not represent a sequence of rigid motions. △xyz is congruent to △x'y'z' because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions. △xyz is congruent to △x'y'z' because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.

Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .

We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3)  will cause translation.

We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.

So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."

is correct.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2