Answer:
6.75
Step-by-step explanation:
Answer:
g(x) = x^2 - 7
Step-by-step explanation:
gf(x) = x^2 + 6x + 2
Converting to vertex form:-
g(fx) = (x + 3)^2 - 9 + 2
= (x + 3)^2 - 7.
As you replace the x in g(x) with f(x) in order to get g(f(x) then,
since f(x) = (x + 3), g(x) is x^2 - 7 (answer)
Answer:
y=6*x+101
Step-by-step explanation:
Slope intercept form is y=mx+n, where m is the slope and n is the intercept.
Substituing in that equation the two points we get two different expressions. Now we have to solve a 2x2 system of equations.
I decide to solve it through substraction (literally one expression minus the other). That way we cancel out the n and obtain the value of m.
Now that we have m we plug in the value of m in one of the expressions to obtain the value of n.
To express the final equation we just plug in the values of m and n in the expression y=mx+n!
Answer:
<em>5</em><em> players participated in the tournament.</em>
Step-by-step explanation:
In a small chess tournament, 20 matches were played.
Let us assume that n number of players participated in the tournament
As in each game 2 players play, so the number of ways they can play is,
![=\ ^nC_2](https://tex.z-dn.net/?f=%3D%5C%20%5EnC_2)
As they played 2 games with every other participant in the tournament.
So the total number of games is,
![=\ 2\times ^nC_2](https://tex.z-dn.net/?f=%3D%5C%202%5Ctimes%20%5EnC_2)
But it is given to be 20, so
![\Rightarrow \ 2\times ^nC_2=20](https://tex.z-dn.net/?f=%5CRightarrow%20%5C%202%5Ctimes%20%5EnC_2%3D20)
![\Rightarrow \ ^nC_2=10](https://tex.z-dn.net/?f=%5CRightarrow%20%5C%20%5EnC_2%3D10)
![\Rightarrow \dfrac{n!}{2!(n-2)!}=10](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7D%3D10)
![\Rightarrow \dfrac{n(n-1)}{2}=10](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Bn%28n-1%29%7D%7B2%7D%3D10)
![\Rightarrow {n(n-1)=20](https://tex.z-dn.net/?f=%5CRightarrow%20%7Bn%28n-1%29%3D20)
As
, so we get n=5.
Therefore, 5 players participated in the tournament.
Answer:
y+0
As y=0 represent x-axis whose slope is 0 and intersects y-axis at the origin.