Given: abc is a triangle. prove: bc + ac > ba in triangle abc, we can draw a perpendicular line segment from vertex c to segment ab. the intersection of ab and the perpendicular is called e. we know that be is the shortest distance from b to and that is the shortest distance from a to ce because of the shortest distance theorem. therefore, bc > be and ac > ae. next, add the inequalities: bc + ac > be + ae. then, be + ae = ba because of the . therefore, ba + ac > ba by substitution.

An arrow is shot vertically upward at a rate of 180ft/s. use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. round your answer(s) to the nearest tenth of a second.

You are assembling pieces of an iron gate to complete a fence. the finished gate will look like the one below. in order to assemble the gate it is important to under how the pieces are related. part 1: how are pies 1 and 2 in the archway related? part 2: how are the rectangular sections 5 and 6 in the center of the gate related to each other?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?