The flag of a country contains an isoceles triangle. (recall that an isoceles triangle contains two angles with the same measure) if the measure of the third angle is 15 degrees more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (recall that the sum if the measure of the angles of a triangle is 180 degrees)

angles: 33, 33, 114

Step-by-step explanation:

An isosceles triangle has 2 angles with the same measure x

the third angle = 15+3x

the 3 angles of a triangle = 180

x+ x + 3x+15 = 180

combine like terms

5x + 15 = 180

subtract 15 from each side

5x+15-15 = 180 - 15

5x = 165

divide by 5

5x/5 = 165/5

x = 33

two angles measure 33

the third angle = 3x+15

                        = 3*33 + 15 = 99+15 = 114

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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