Trigonometry is a field of mathematics that studies the relationships that exist between the sides of a triangle and its angles. how much do you know about the properties of triangles? have you worked with them much in the past? these relationships and properties can be used to model many physical properties in the real world. one of these properties is called periodic motion, such as the motion made by a yo-yo going up and down. what kinds of periodic motion are you familiar with? why might scientists and businesses be interested in tracking this type of motion using equations?

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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