Tree C is the proper tree. The first game has the possibility of a win, a loss, or a tie which the first row represents. The second game could also win, lose or tie, meaning each result would have each possibilty for that game.
Answer:
3 1/3
Step-by-step explanation:
2 1/2 = 5/2
1 1/3 = 4/3
5/2×4/3
5×4/2×3=
20/6=
10/3 = 3 1/3
Answer:
![x^3-9x+2x^2-18\left(x+2\right)\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E3-9x%2B2x%5E2-18%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
Step-by-step explanation:
we are given that ![x^3-9x+2x^2-18](https://tex.z-dn.net/?f=x%5E3-9x%2B2x%5E2-18)
w are sked to step by step factorise the above polynomial
![\left(x^3+2x^2\right)+\left(-9x-18\right)](https://tex.z-dn.net/?f=%5Cleft%28x%5E3%2B2x%5E2%5Cright%29%2B%5Cleft%28-9x-18%5Cright%29)
![-9\mathrm{\:from\:}-9x-18\mathrm{:\quad }-9\left(x+2\right)](https://tex.z-dn.net/?f=-9%5Cmathrm%7B%5C%3Afrom%5C%3A%7D-9x-18%5Cmathrm%7B%3A%5Cquad%20%7D-9%5Cleft%28x%2B2%5Cright%29)
![-9x-9\cdot \:2](https://tex.z-dn.net/?f=-9x-9%5Ccdot%20%5C%3A2)
![-9\left(x+2\right)](https://tex.z-dn.net/?f=-9%5Cleft%28x%2B2%5Cright%29)
![\mathrm{Factor\:out\:}x^2\mathrm{\:from\:}x^3+2x^2\mathrm{:\quad }x^2\left(x+2\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BFactor%5C%3Aout%5C%3A%7Dx%5E2%5Cmathrm%7B%5C%3Afrom%5C%3A%7Dx%5E3%2B2x%5E2%5Cmathrm%7B%3A%5Cquad%20%7Dx%5E2%5Cleft%28x%2B2%5Cright%29)
![-9\left(x+2\right)+x^2\left(x+2\right)](https://tex.z-dn.net/?f=-9%5Cleft%28x%2B2%5Cright%29%2Bx%5E2%5Cleft%28x%2B2%5Cright%29)
![\left(x+2\right)\left(x^2-9\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%5E2-9%5Cright%29)
![x^2-9:\quad \left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E2-9%3A%5Cquad%20%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
![x^2-9](https://tex.z-dn.net/?f=x%5E2-9)
![\mathrm{Rewrite\:}9\mathrm{\:as\:}3^2](https://tex.z-dn.net/?f=%5Cmathrm%7BRewrite%5C%3A%7D9%5Cmathrm%7B%5C%3Aas%5C%3A%7D3%5E2)
![=x^2-3^2](https://tex.z-dn.net/?f=%3Dx%5E2-3%5E2)
![\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3ADifference%5C%3Aof%5C%3ATwo%5C%3ASquares%5C%3AFormula%3A%5C%3A%7Dx%5E2-y%5E2%3D%5Cleft%28x%2By%5Cright%29%5Cleft%28x-y%5Cright%29)
![x^2-3^2=\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E2-3%5E2%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
Hence
![x^3-9x+2x^2-18=\left(x+2\right)\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E3-9x%2B2x%5E2-18%3D%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
a) The jay mistake was he did not factorise ![x^3-9x+2x^2-18x^2-9 furtherb) the complete answer wil be [tex]x^3-9x+2x^2-18\left(x+2\right)\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E3-9x%2B2x%5E2-18x%5E2-9%20further%3C%2Fp%3E%3Cp%3Eb%29%20the%20complete%20answer%20wil%20be%20%3C%2Fp%3E%3Cp%3E%20%5Btex%5Dx%5E3-9x%2B2x%5E2-18%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
Answer:
.26 cents cheaper a roll
Step-by-step explanation:
to find this you would do 3.64/4 to get the price a roll which is .91
and then you would do 20.80/32 to get the price per roll which is .65
then to get the difference you would do .91-.65 to get .26
-28 < 2x - 10 < -10.....add 10 to all sections
-28 + 10 < 2x - 10 + 10 < -10 + 10....simplify
-18 < 2x < 0...divide all sections by 2
-18/2 < 2/2x < 0/2...simplify
-9 < x < 0 <===