Point a(-7, -2) is rotated 270° counterclockwise and then shifted down 3 units. what are to coordinates of k’?

a. (2,4)

b. (-2, -7)

c. (-2, 4)

d. (7, -5)

C. (-2, 4)

Step-by-step explanation:

First we are going to rotate the point 270°; then we are going to shift it down 3 units.

Remember that the rule to rotate a point 270° counterclockwise about the origin is:

In other words, we just need to switch the coordinates and change the sign of the second coordinate. Let's apply the rule to our point:

Now we know that the coordinates of our point after the rotation are A' = (-2, 7)

The only thing left is shift that point 3 units down; to do it, we just need to subtract 3 from the y-coordinate:

We can conclude that after a rotation of 270° and a translation 3 units down, the coordinates of point K' are (-2, 4).

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

what graph

step-by-step explanation: