Answer:
There are 7 teams in the league
Step-by-step explanation:
Given that the number of games is given by:
[tex]G(n) = \frac{(n^2-n)}{2}[/tex]
The equation will be used to determine the number of games. As we already know, that 21 games are scheduled which means G(n) is 21 so we have to find n when G(n) is 21
Putting this mathematically
[tex]21 = \frac{n^2-n}{2}[/tex]
Multiplying equation by 2
[tex]2*21 = 2*\frac{n^2-n}{2}\\42 = n^2-n\\n^2-n-42 = 0\\n^2-7n+6n-42 = 0\\n(n-7)+6(n-7) = 0\\(n-7)(n+6)=0\\n-7 = 0 => n=7\\n+6=0 => n=-6[/tex]
As the number of teams cannot be negative, the number of teams in league are 7.
Hence,
There are 7 teams in the league
