Find the coordinates of p so that p partitions the segment ab in the ration 3: 4 if a(-9,9) and b(5,-2)

So contrary to what you may believe, 3:4 is not 3/4 here, but rather "3 equal parts to 4 equal parts", which is a total of 7 equal parts. In short, the question is asking you to put point P 3/7 of the way from A to B (or 4/7 of the way from B to A, but we will do the prior.)

So firstly, how far apart is -9 from 5 (the x-coordinates)? That would be 14 units. Multiply 3/7 by 14:

Next, how far apart is 9 from -2 (the y-coordinates)? That would be 11 units. Multiply 3/7 by 11.

Now, since from -9 to 5 you are increasing, add 6 to -9:

-3 is P's x-coordinate.

Next, since from 9 to -2 you are decreasing, subtract 33/7 from 9.

30/7, or 4 2/7 is P's y-coordinate.

Putting it together, P's coordinate is (-3, 30/7).

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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