De=4x+10, ef=2x-1, and df=9x-15, find df

DE and EF are segments of the line DF, so they will add up to DF. This can be represented with this equation:

Combine like terms:

Add 15 to both sides:

Subtract 6x from both sides:

Divide both sides by 3 to get x by itself:

The value of x will be 8.

Plug this value of x into the expression for DF:

DF will equal 57.

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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