1. True or False: When point E (2, -5) is rotated 180° about the origin, and becomes Point E’ (-2, 5).
2. Under a dilation, triangle XYZ where X(6, 3), Y(-2, 4), and Z(10, -2) becomes triangle X’Y’Z’ where X’(12, 6), Y’(-4, 8), and Z’(20, -4). What is the scale factor for this dilation?
-2
2
1/2
-1/2
3. Triangle XYZ where X(7, 2), Y(-3, 8), and Z(-4, 6) is dilated with a scale factor of -4. Where is the dilation located?

Find the gradient of f(x,y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.

Which best describes the construction of a triangle if given the segment lengths of 2 cm, 3 cm, and 5 cm? a) unique triangle b) cannot be determined c) triangle not possible d) more than one triangle