Larry wants to inscribe an equilateral triangle in a circle using only a compass and straightedge. he will first construct a circle and locate its center. he will then perform the following steps. step 1: set the width of the compass to the diameter of the circle. step 2: plot a point on the circle. place the compass on this point and draw two arcs to cut the circle. these two points of intersection between the arcs and the circle represent two of the vertices. step 3: draw a segment between the two vertices. adjust the width of the compass to the length of the segment. place the compass on one vertex and draw an arc to construct the third vertex. step 4: draw a line from one vertex to the next to form an equilateral triangle. what is the error in larry's construction?

 He set the width of the compass to the diameter of the circle.

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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