Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year based on the tax revenue (in thousands of dollars) for the year. Using historical data, Alphaville’s planner produced the model -2x2+ 500x, while Betaville’s planner produced the model x2- 100x + 10,000. What expression gives how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue? If the tax revenue that year in each town is $75,000, how much greater is Alphaville’s budget surplus than Betaville’s that year?

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Abanner is made of a square and a semicircle. the square has side lengths of 24 inches. one side of the square is also the diameter of the semicircle. what is the total area of the banner? use 3.14 for π.

1. a driveway has a 15° grade. if the driveway is 40 meters long, how much does the driveway rise? (nearest tenth of a meter) 2. a person located 4 miles from a rocket launch site sees a rocket at an angle of elevation of 32°. at that moment, how high is the rocket above the ground? (nearest tenth of a mile) 3.an airplane approaches an airport landing strip with an angle of depression of 12°. if the airplane is flying at an altitude of 20,000 feet, find the distance on the ground that the plane will need to land. (nearest 1,000 feet) 4.two buildings are located on opposite sides of the street, 40 meters apart. the angle of elevation from the top of the shorter building to the top of the taller building is 53°. if the taller building is 300 meters tall, what is the height of the shorter building? (nearest meter) 5.george is 187 cm tall. his son, ralph, is 142 cm tall. who casts the longer shadow. george when the sun is 65° above the horizon, or ralph when the sun is 56° above the horizon? how much longer? (nearest centimeter)

Agraph of a trapezoid can have diagonals with slopes that are negative reciprocals and two pairs of adjacent sides that are congruent, true or false, and why