T. J. is hosting a dinner party. T. J. greets the first guest and they shake hands. The second guest arrives and shakes hands with T. J. and the first guest. The third guest arrives and shakes hands with T. J., the first guest, and the second guest. This pattern continues. How many handshakes have taken place after the ninth guest arrives?

Write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).

In the figure below, segment ac is congruent to segment ab: triangle abc with a segment joining vertex a to point d on side bc. side ab is congruent to side ac which statement is used to prove that angle abd is congruent to angle acd? segment ad bisects angle cab. triangle acd is similar to triangle abd. segment ad is congruent to segment ac. angle cab is congruent to angle cba.

Fredrick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin