Given v=5i + 4j and w=6i-j, find the angle between v and w.

Given: and prove: what is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem

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.

Write the expression as a single natural logarithm. 2 in a - 4 in y