Ten hours after a runner and cyclist leave the house at the same time and head in the same direction, the cyclist is 150 miles ahead of the runner. If the cyclist's speed is seven mph more than twice the speed the speed of runner, find the speed of the runner and the cyclist.

Speed of runner:
mph

Speed of cyclist:
mph

Step-by-step explanation:

Let the speed of runner be r and speed of cyclist be c

We have following equations based on the given

Simplifying first equation

Comparing this with second equation

And finding the value of c

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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step-by-step explanation: