1. in δpqr, pq = pr and m is the midpoint of qr . prove that pm bisects ∠qpr. answer format: δpqm = δ (reason) 2. in δabc, m∠b = m∠c. the angle bisector of ∠b meets ac at point h and the angle bisector of ∠c meets ab at point k. prove that bh = ck. answer format: δbck = δ (reason) 3. in ∆abc the median am is extended to ray am and point p on am is taken so that pm = am. what is the distance from point p to vertices c and b if ab = c and ac = b?

What is the 9th term in the geometric sequence described by this explicit formula? an=-6. (2)(n-1) apex

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.

Find the dimensions of the circle. area = 64π in.² r= in.