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Find the area of the pentagon whose vertices are: \((-5,-5),(5,-5),(8,6),(-8,6),\) and (0,12.5)

Solve the following linear programming problems. Hauling hazardous waste: A waste disposal company is contracted to haul away some hazardous waste material. A full container of liquid waste weighs 800 lb and has a volume of \(20 \mathrm{ft}^{3} . \mathrm{A}\) full container of solid waste weighs 600 lb and has a volume of \(30 \mathrm{ft}^{3} .\) The trucks used can carry at most 10 tons \((20,000\) lb) and have a carrying volume of \(800 \mathrm{ft}^{3} .\) If the trucking company makes \(\$ 300\) for disposing of liquid waste and \(\$ 400\) for disposing of solid waste, what is the maximum revenue per truck that can be generated?

Mozart wrote some of vocal music's most memorable arias in his operas, including Tamino's Aria, Papageno 's Aria, the Champagne Aria, and the Catalogue Aria. The total playing time of all four arias is 14.3 min. Papageno's Aria is 3 min shorter than the Catalogue Aria. The Champagne Aria is 2.7 min shorter than Tamino's Aria. The combined time of Tamino's Aria and Papageno 's Aria is five times that of the Champagne Aria. Find the playing time of all four arias.

Market research has indicated that by \(2010,\) sales of MP3 portables will mushroom into a 70 billion dollar market. With a market this large, competition is often fierce- -with suppliers fighting to earn and hold market shares. For \(x\) million MP3 players sold, supply is modeled by \(y=10.5 x+25,\) where \(y\) is the current market price (in dollars). The related demand equation might be \(y=-5.20 x+140 .\) (a) How many million MP3 players will be supplied at a market price of 88 dollars ? What will the demand be at this price? Is supply less than demand? (b) How many million MP3 players will be supplied at a market price of 114 dollars ? What will the demand be at this price? Is demand less than supply? (c) To the nearest cent, at what price does the market reach equilibrium? How many units are being supplied/demanded?

As part of an algebra field trip, Jason takes his class to the airport to use their moving walkways for a demonstration. The class measures the longest walkway, which turns out to be \(256 \mathrm{ft}\) long. Using a stop watch, Jason shows it takes him just 32 sec to complete the walk going in the same direction as the walkway. Walking in a direction opposite the walkway, it takes him \(320 \mathrm{sec}-10\) times as long! The next day in class, Jason hands out a two-question quiz: (1) What was the speed of the walkway in feet per second? (2) What is my (Jason's) normal walking speed? Create the answer key for this quiz.