Call the number of teams is n

We have: The number of games is n(n+1) games

But each game repeated 2 times 

So the number of the games is \(\dfrac{n\left(n+1\right)}{2}\)

There are 21 games

So \(\dfrac{n\left(n+1\right)}{2}=21\Rightarrow n\left(n+1\right)=42\Rightarrow n=6\)

Just a ruler
Which step is not over.
What is the trick?

 Answer; That is your shadow

We have :

\(x\left\{{}\begin{matrix}x+x\\x-x\\x.x\end{matrix}\right.< =>0\left\{{}\begin{matrix}0+0\\0-0\\0.0\end{matrix}\right.\)

So x =0

x+x=2x
x-x=0
x*x=x²

When you meet high variable  \(x^4,x^5...\) the way for expressing this is change it to factored equations (trans : phương trình tích).

Now change that equation into : \(\left(x+y\right)\left(x-y\right)^2=5\)

So the equation has interger solutions (x;y) = (3;2) , (2;3).

Good luck.

The side of a surface is: \(\sqrt{\left(96:6\right)}\) = \(\sqrt{16}=4\left(cm\right)\)

So the volume of the cube is: \(4.4.4=64\left(cm^3\right)\)

:v oh..... i'm wrong !!! 

Area on one face is :

\(\dfrac{96}{6}=36\left(cm^2\right)\)

The length of an edge is :

\(\sqrt{36}=6\) (cm)

The volume of the cube is :

\(V=6.6.6=6^3=216\left(cm^3\right)\)

Replace d = 200 into \(t=0,45\sqrt{d}\), we have :

\(t=0,45\sqrt{200}=\sqrt{40,5}=6.36396103...\approx6.4\)

So, the rock falls 200 m in 6.4 seconds

With the formula for calculating time is : \(t=0,45.\sqrt{d}\) \(\left\{{}\begin{matrix}t=time\\d=distance\end{matrix}\right.\)

So that , with the distance of 200m , Time to rock falls is :

\(0,45.\sqrt{200}=0,45.10\sqrt{2}=\dfrac{9\sqrt{2}}{2}\approx6,36\) (seconds)

Kaya Renger was wrong because he rounded his answer to the nearest hundredth.

He caught : 12 : (3 - 1) = 6 (fish)

Let x, 7 - x be the 97^th and the 98^th term of the sequence respectively, then 14 - x ; 21 - x ; 35 - 2x are the 100^th, 101^st, 102^nd terms of the sequence respectively. We have :

\(35-2x=69\Leftrightarrow2x=-34\Leftrightarrow x=-17\Leftrightarrow14-x=31\)

So, the answer is 31

Let x, 7 - x be the  97^th and the 98^th term of the sequence respectively, then 14 - x ; 21 - x ; 35 - 2x are the 100^th ,101^st ,102^nd terms of the sequence respectively

We have:

35 - 2x = 69 <=> 2x = -34 <=> x = -17 <=> 14 - x = 31

So the answer is 31

three wear skirts.

three wear skirt

We have the sequence: 3;5;2;-3;-5;-2;3;5;2;...

So to the 198th number of the sequence, the sum of the sequence is still 0. 

We have: 199th number = 3 and 200th number = 5

So the sum of the first 200 terms of the sequence is: \(0+3+5=8\)