In a chess match, a win counts as 1 point, a draw counts as 0.5 point, and a loss counts as 0 points. after 21 games between the two players, the winner was 8 points ahead of the loser. how many points did the winner have? pls

14.5

Step-by-step explanation:

First, let's confirm that total points = total number of games played.

Suppose, if any one of the player wins all the games, then,

total points = 21(1) + 0 = 21 = total number of games

Suppose, all the games end in draw. Then,

21(0.5) + 21(0.5) = 21(0.5 + 0.5) = 21(1) = 21 = total number of games

Suppose, if one player wins in 10 games and the remaining 11 games end in draw, then,

10(1) + 11(0.5 + 0.5) = 10 + 11 = 21 = total number of games

So, in all cases, total points = total number of games played

Now, let x be the points that the loser has.

So, the winner's points should be x + 8.

Total number of games played = 21

Since, total points = total number of games played,

x + (x + 8) = 21

2x + 8 = 21

2x = 21 - 8 = 13

x = 6.5

Winner's points = x + 8 = 6.5 + 8 = 14.5.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.