To prove the Pythagorean Theorem, Justin began with a right triangle and drew an altitude from the vertex opposite the hypotenuse to the hypotenuse. This resulted in the original triangle being divided into two smaller triangles. Which of these facts will allow Justin to finish his proof?
A One of the smaller triangles is congruent to the original triangle, and one is not.
B
Both of the smaller triangles are congruent to the original triangle.
One of the smaller triangles is similar to the original triangle, and one is not.
D
Both of the smaller triangles are similar to the original triangle.

The product of two negative rational numbers is always zero sometimes zero never zero

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.

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =