Answer:
x = -7 2/3, y = 1 1/3 and z = 5 1/3.
Step-by-step explanation:
2x+4y+3z=6 ..... 1
x-2y+z=-5 ...... 2
-x-3y-2z=-7 .......3
Add equations 2 and 3 to eliminate x:
-5y - z = -12 .....4
Multiply equation 2 by - 2:
-2x + 4y - 2z = 10
Add this to equation 1:
8y + z = 16 ........ 5
Now add equation 4 to equation 5:
3y = 4
y = 4/3 = 1 1/3.
Now find z by substituting for y in equation 4:
-5(4/3) - z = -12
z = 12 - 20/3
z = 36/3 - 20/3 = 16/3 = 5 1/3.
Finally, we find x by substituting for y and z in equation 1:
2x + 4*4/3 + 3*16/3 = 6
2x = 6 - 16/3 - 16
2x = 18/3 - 16/3 - 48/3 = -46/3
x = 23/3 = 7 2/3.
C
a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment
using the midpoint formula
M = [
(0 + 20 ), (15 + 0)] = (10, 7.5 )
≈0.128 is the correct answer
Answer:
680 games
Step-by-step explanation:
Suppose that 681 tennis players want to play an elimination tournament.
1st round:
One of 681 players, chosen at random, sits out that round and 680 players play. There will be 340 winners plus one player which sits - 341 players for the next round and 340 games
2nd round:
There will be 170 winners plus one player which sits - 171 players for the next round and 170 games
3rd round:
There will be 85 winners plus one player which sits - 86 players for the next round and 85 games
4th round:
There will be 43 winners - 43 players for the next round and 43 games
5th round:
There will be 21 winners plus one player which sits - 22 players for the next round and 21 games
6th round:
There will be 11 winners - 11 players for the next round and 11 games
7th round:
There will be 5 winners plus one player which sits - 6 players for the next round and 5 games
8th round:
There will be 3 winners - 3 players for the next round and 3 games
9th round:
There will be 1 winner plus one player which sits - 2 players for the next round and 1 game
10th round - final:
1 champion and 1 game.
In total,
340 + 170 + 85 + 43 + 21 + 11 + 5 + 3 + 1 + 1 = 680 games
