Point A has coordinates (3,4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, what are the coordinates of the image?

The coordinates of the image of point A are (-1, -6)

Step-by-step explanation:

Let us revise the rule of translation to the left, down, and reflection across the x-axis

∵ The coordinates of point A are (3, 4)

∵ It is translated 4 units left

∴ h = 4

→ By using the 1st rule above

∴ Its image is (3 - 4, 4)

∴ Its image is (-1, 4)

∵ Its is reflected across the x-axis

→ By using the 3rd rule above change the sign of its y-coordinate

∴ The new image is (-1, -4)

∵ It is translated 2 units down

∴ k = 2

→ By using the 2nd rule above

∴ The final image is (-1, -4 - 2)

∴ The final image is (-1, -6)

∴ The coordinates of the image of point A are (-1, -6).

250

step-by-step explanation:

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.