Segments PX and QY are altitudes of acute triangle PQR, and Z is the midpoint of segment PQ. Prove that triangle XYZ is isosceles. (Please provide a diagram in addition to the actual proof)

Ricky takes out a $31,800 student loan to pay his expenses while he is in college. after graduation, he will begin making payments of $190.66 per month for the next 30 years to pay off the loan. how much more will ricky end up paying for the loan than the original value of $31,800? ricky will end up paying $ more than he borrowed to pay off the loan.

For g(x) = 5x - 3 and h(x) = [tex]\sqrt{x}[/tex], find (g · h)(4)

These tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 9 to x = 10?