D. When you substitute for the variables the equation becomes -1-5×6=-31. First, you multiply -5 by 6 to get -30. This makes the equation -1-30=-31. -1-30 is -31 so your equation is now -31=-31.
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)
"4 years less" means something - 4
"3 times her niece's age" means 3x, considering x if her niece's age.
4 less than 3x = 3x - 4
So the answer is that the expression 3x - 4 can be used to represent this problem.
Hope this helps!
Answer: Yes
Step-by-step explanation:
Because they make a rectangle, inasmuch as thir height and weight are the same.
Answer: 102
Step-by-step explanation:
- 17 = (m/6) +-9
+(-) = -
The equation can be written as:
-17 = (m/6) - 9
Opening the parentheses
-17 = -(9m/ 54)
Multiply both sides by 54
(-17 * 54) = - 9m
= - (17*54) = -9m
Divide both sides by -9
- (17*54)/ -9 = m
- divided by - = +
= (17*54) / 9 = m
m = 17 * 6
m = 102