A) draw the image of pqr after a 180 about the origin. label the image p'q'r b) then reflect p'q'r across the x-axis. label the image p''q''r.

Solution-

1- When rotating a figure 180 degrees around the origin (As it does not matter whether you move clockwise or counter-clockwise), we apply the rule (x, y) → (-x, -y).

Co-ordinates of the vertices,

P = (1, -1)

Q = (3, -2)

R = (3, -4)

And then calculating the co-ordinates of P', Q', R'

P' = (-1, 1)

Q' = (-3, 2)

R' = (-3, 4)

2- When reflecting a figure across X-axis, we apply the rule (x, y) → (x, -y).

Co-ordinates of the vertices,

P' = (-1, 1)

Q' = (-3, 2)

R' = (-3, 4)

And then calculating the co-ordinates of P'', Q'', R''

P'' = (-1, -1)

Q'' = (-3, -2)

R'' = (-3, -4)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

false

step-by-step explanation: