Find the angle of the rotations for the graphs below. The center of rotation is the origin, and the darker image is the preimage. Your answer will be 90°, 270 degrees, or 180 degrees.

  a. 90°

  b. 180°

  c. 180°

Step-by-step explanation:

For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.

a. The image is in the adjacent clockwise quadrant, so rotation is 90°.

b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.

The mass of one whole pizza is:

256 grams.

Step-by-step explanation:

Take into account the information previously provided:

The two whole pizzas are the same. The first one was cut into four equal pieces. The second was cut into eight equal pieces.

It can be identified by the information and the proportionality that each slice of pizza 1 has twice the mass of the slice of pizza 2, therefore, when it is mentioned that a slice of pizza 1 has 32 grams more than one of pizza 2, it is identified that the original mass of a piece of pizza 2 is 32 grams and the mass of a piece of pizza 1 is:

Pizza slice dough 1 = 32 * 2 = 64 grams.

With this information it can be calculated with pizza 1, where 4 pieces of pizza were obtained, so to calculate the total pizza mass the individual mass is multiplied by 4:

Total pizza weight = 64 grams * 4 = 256 grams.