Answer:
The solutions are ![x=-3,\:x=3](https://tex.z-dn.net/?f=x%3D-3%2C%5C%3Ax%3D3)
Step-by-step explanation:
To factor this cubic polynomial
you must:
- Group the polynomial into two sections
![x^3+3x^2-9x-27=\left(x^3+3x^2\right)+\left(-9x-27\right)](https://tex.z-dn.net/?f=x%5E3%2B3x%5E2-9x-27%3D%5Cleft%28x%5E3%2B3x%5E2%5Cright%29%2B%5Cleft%28-9x-27%5Cright%29)
- Factor out -9 from
![(-9x-27)](https://tex.z-dn.net/?f=%28-9x-27%29)
![(-9x-27)=-9\left(x+3\right)](https://tex.z-dn.net/?f=%28-9x-27%29%3D-9%5Cleft%28x%2B3%5Cright%29)
- Factor out
from ![(x^3+3x^2)](https://tex.z-dn.net/?f=%28x%5E3%2B3x%5E2%29)
![(x^3+3x^2)=x^2\left(x+3\right)](https://tex.z-dn.net/?f=%28x%5E3%2B3x%5E2%29%3Dx%5E2%5Cleft%28x%2B3%5Cright%29)
![x^3+3x^2-9x-27=-9\left(x+3\right)+x^2\left(x+3\right)](https://tex.z-dn.net/?f=x%5E3%2B3x%5E2-9x-27%3D-9%5Cleft%28x%2B3%5Cright%29%2Bx%5E2%5Cleft%28x%2B3%5Cright%29)
- Factor out common term
![x+3](https://tex.z-dn.net/?f=x%2B3)
![-9\left(x+3\right)+x^2\left(x+3\right)=\left(x+3\right)\left(x^2-9\right)](https://tex.z-dn.net/?f=-9%5Cleft%28x%2B3%5Cright%29%2Bx%5E2%5Cleft%28x%2B3%5Cright%29%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-9%5Cright%29)
![x^3+3x^2-9x-27=\left(x+3\right)\left(x^2-9\right)](https://tex.z-dn.net/?f=x%5E3%2B3x%5E2-9x-27%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%5E2-9%5Cright%29)
- Factor
![x^2-9](https://tex.z-dn.net/?f=x%5E2-9)
![x^2-9=\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E2-9%3D%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
![x^3+3x^2-9x-27= \left(x+3\right)\left(x+3\right)\left(x-3\right)](https://tex.z-dn.net/?f=x%5E3%2B3x%5E2-9x-27%3D%20%5Cleft%28x%2B3%5Cright%29%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-3%5Cright%29)
![x^3+3x^2-9x-27=\left(x+3\right)^2\left(x-3\right)=0](https://tex.z-dn.net/?f=x%5E3%2B3x%5E2-9x-27%3D%5Cleft%28x%2B3%5Cright%29%5E2%5Cleft%28x-3%5Cright%29%3D0)
- Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0
![x+3=0, \quad{x=-3}\\x-3=0, \quad{x=3}](https://tex.z-dn.net/?f=x%2B3%3D0%2C%20%5Cquad%7Bx%3D-3%7D%5C%5Cx-3%3D0%2C%20%5Cquad%7Bx%3D3%7D)
The solutions are
![x=-3,\:x=3](https://tex.z-dn.net/?f=x%3D-3%2C%5C%3Ax%3D3)
Hello!
To find what percent of states begin w/ a W, all you need to do is divide 44 by 50
44/50
Once you've done so, you'll get 0.88, which you can convert to 88%
I hope this helps!
<span>With a boys to girls ratio of 8:7, this means 8/15 of the campers are boys and 7/15 of the campers are girls.
We are told that there are 195 total campers.
To find # of boys: 195 (the total # of campers) x 8/15 (fraction of the campers that are boys) = 104 boys
To find # of girls: 195 (total # of campers) x 7/15 (fraction of the campers that are girls) = 91 girls
Note: If you do not know how to multiply by fractions, let me know, I have another trick that takes more time but doesn't require the use of fractions.
</span>
If you would like to solve 15a^9b^4 / <span>5a^5b, you can calculate this using the following steps:
</span>15a^9b^4 / <span>5a^5b = 3a^(9-5)b^(4-1) = 3a^4b^3
</span>
The correct result would be <span>D. 3a^4b^3.</span>
(16 ounces = 1 pound)
130 ounces = 8.125 pounds
130 ounces is greater than 8 pounds.
HOPE THIS HELPED
:)