Judy began her proof of the converse of the Pythagorean theorem by drawing triangle ABC with side lengths in inches of 5, 12, and 13. She then showed that 5^2 + 12^2=13^2 as follows. 5^2+12^2=13^2
25+144=169
169=169

Next, she drew triangle DEF, with two of the sides forming a 90° angle. If she has done her proof correctly so far, which of these is a length of one of the sides forming the 90° angle? Select two that apply.

A.3 in
B.4 in
C.5 in
D.12 in
E.13 in

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.

The first few steps in solving the quadratic equation 9x2 + 49x = 22 ? 5x by completing the square are shown. 9x2 + 49x = 22 ? 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103

Factor the polynomial expression x6 – x3 – 20