Triangle xyz is rotated to create the image triangle x'y'z'

How many ordered pairs of positive integers satisfy xy=32?

Ascientist places 24 cells in a petri dish. she knows the cells grow at an exponential rate, doubling in number every hour. how long will it take (in hours) for there to be 1100 cells in the dish? time to 1100 cells: 5.51832530 hours how long will it take to reach 110 cells? time to 110 cells : 2.1963972 hours what is the average rate of change in the number of cells between 9 hours and 11 hours? average rate of change: cells per hour what is the instantaneous rate of change after 7 hours? instantaneous rate of change: cells per hour note: you can earn partial credit on this problem.

Meg constructed triangle poq and then used a compass and straightedge to accurately construct line segment os, as shown in the figure below, which could be the measures of angles pos and angle poq?