Harry goes to Hogwarts School of Witchcraft and Wizardry. He can travel to school and back in 333 different ways: by the Hogwarts Express, a flying car, or the Knight Bus. He's decided to choose his methods of transportation to and from Hogwarts at random this year.

The triangles are similar. what is the value of x? show your work.

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.

Aball is thrown from a height of 139 feet with an initial downward velocity of 15 ft/s. the ball's height h (in feet) after t seconds is given by the following. h=139-15t-16t^2 how long after the ball is thrown does it hit the ground? round your answer(s) to the nearest hundredth. (if there is more than one answer, use the "or" button.) t =