Which statement best explains why the value of this expression is equal to −812y? 414x − 812y − 414x a. when x = 0, the first and last terms are 0, so the value of the expression is −812y. b.414 is half of 812, so the two 414's will cancel out 812. c. the sum of a number and its opposite is 1, and the product of any number and 1 is the number itself. d. the sum of a number and its opposite is 0, and the sum of any number and 0 is the number itself.

After applying the composition r0.90 ry to rs what are the coordinates of r' and s'? a. r'(–3, 1),  s'(–3, 5)b. r'(–1, 3),  s'(–5, 3)c. r'(1, 3),  s'(5, 3)d. r'(5, 3),  s'(1, 3)

Segment ab is shown on the graph. which shows how to find the x-coordinate of the point that will divide ab into a 2: 3 ratio using the formula

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.