The coordinates of the vertices of △pqr are p(−3,4), q(−3,1), and r(−1,1). the coordinates of the vertices of △p′q′r′ are p′(−6,−5), q′(−6,−1), and r′(−4,−1)

which statement correctly describes the relationship between △pqr
and △p′q′r′ ?

a.) △pqr is congruent to △p′q′r′ because you can map △pqr to △p′q′r′
using a reflection across the x-axis followed by a translation 3 units to the left, which is a sequence of rigid motions.
b.) △pqr is congruent to △p′q′r′ because you can map △pqr to △p′q′r′
using a translation 3 units to the left followed by a reflection across the x-axis, which is a sequence of rigid motions.
c.) △pqr is not congruent to △p′q′r′ because there is no sequence of rigid motions that maps △pqr to △p′q′r′
.
d.) △pqr is congruent to △p′q′r′ because you can map △pqr to △p′q′r′ using a reflection across the x-axis followed by a translation 1 unit down, which is a sequence of rigid motions.

The correct option is D, i.e., ΔPQR is not congruent to ΔP'Q'R' because there is no sequence of rigid motions that maps ΔPQR to ΔP'Q'R'.

Explanation:

It is given that the coordinates of the vertices of △PQR are P(−3,4), Q(−3,1), and R(−1,1). The coordinates of the vertices of △P′Q′R′ are P′(−6,−5), Q′(−6,−1), and R′(−4,−1).

Plot these points on a coordinate plane and draw the triangles ΔPQR to ΔP'Q'R'.

According to the definition of congruent two triangles are congruent if their sides and interior angles of first triangle are same as the second triangle.

From the graph it is noticed that the side PQ and P'Q' are not equal. Similarly PR and P'R' are not equal.

Therefore, the ΔPQR is not congruent to ΔP'Q'R' because there is no sequence of rigid motions that maps ΔPQR to ΔP'Q'R' and the correct option is D.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0