Quabbin Reservoir in Massachusetts provides much of Boston’s water. At the start of 2009 the reservoir contained 412 billion gallons of water. (a) If in January 2009 the amount (in billions of gallons) flowing into the reservoir is A and the amount flowing out is B , write an expression for the amount of water in the reservoir at the end of January 2009. (b) If in February 2009 the amount flowing in is 20 billion gallons less than the previous month and the amount flowing out is 12 billion gallons more than the previous month, write an expression for the amount of water in the reservoir at the end of February 2009. (c) Combine like terms to simplify your answer to part (b).

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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