There are 64 volleyball teams entering a single-elimination tournament. in the first round of each play, each team plays one other team, so 32 games will be played in all. the 32 remaining teams will advance to the second round, which will have 16 games in all, and so on. this continues until there is one team remaining. there are no tie games, and games are played into over times if needed. how many rounds of play are needed before a winner is determined?

Per round there are a certain amount of teams which cuts the amount of games in half. For Example, in the first round there are 64 teams which cuts the amount of games in half to 32 games. This will keep occurring until there are only 2 teams left with one game (This declares the winner).

First round:

64 teams

32 games

Second round:

32 teams

16 games

Third round:

16 teams

8 games

Fourth Round:

8 teams

4 games

Fifth Round:

4 teams

2 games

Sixth Round:

2 teams

1 game

Thus, a winner will be determined in the sixth round of the tournament.

Best of Luck!

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1