Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line through points L and L′ and through M and M′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points N and N′? How do you know?

1. what is the measure of ∠abc? what is the measure of ∠abd?

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of a, h, and k in the general equation.