How do I find the center and angle of rotation

9514 1404 393

Step-by-step explanation:

In general, if PQ is rotated to P'Q', the center of rotation (O) will be the point of intersection of the perpendicular bisectors of PP' and QQ'. The angle of rotation will be the angle POP', or QOQ'.

__

The correspondence between preimage vertices ABCD and image vertices can be found by naming the vertices in the same order (clockwise) from one whose correspondence you know.

Here, the correspondence between A and W is given. Vertices clockwise from W are WXYZ, so those are the image points corresponding to ABCD.

__

We note that the midpoints of AW and BX are coincident at the origin. That is, the perpendicular bisectors of these segments are coincident at the origin, so the origin (point O) is the center of rotation. The rotation angle is AOW, an angle that measures 180°.

__

The image point coordinates are the opposites of the preimage point coordinates.

  A(2, 2) ⇒ W(-2, -2)

  B(2, 5) ⇒ X(-2, -5)

  C(5, 5) ⇒ Y(-5, -5)

  D(5, 2) ⇒ Z(-5, -2)

This is another indication that the rotation is 180° about the origin, since that rotation results in the mapping ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

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

~

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.