Write a proof to show that the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Pj is decorating pupcakes for rocky's birthday party. her color scheme is black, purple, and green. she will use this spinner to determine the color of sprinkles on each pupcake. which model shows the probability of randomly landing on each color?

Aline parallel to a triangle's side splits ab into lengths of x - 5 and x + 2. the other side, ac, is split into lengths of x and x + 12. what is the length of ac? a) 12 b) 24 c) 36 d)

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.