13x - 21x - 7 = 63
- 8x = 70
x = - 8.75
Answer:
Step-by-step explanation:
Answer:
A. x < 2
Step-by-step explanation:
solution:
=2x<7-3
=2x<4
=x<2
Answer:
[/tex]
Step-by-step explanation:
The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence
![1,1,1,2,3,4,5,6,...](https://tex.z-dn.net/?f=1%2C1%2C1%2C2%2C3%2C4%2C5%2C6%2C...)
the generating function would be
![P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\](https://tex.z-dn.net/?f=P%28x%29%3D1%2Bx%2Bx%5E2%2B2x%5E3%2B3x%5E4%2B4x%5E5%2B5x%5E6%2B...%5C%5C)
we can multiply P(x) by x to get
Note that
![P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)](https://tex.z-dn.net/?f=P%28x%29-xP%28x%29%3D1%2B%282x%5E3-x%5E3%29%2B%283x%5E4-2x%5E4%29%2B%284x%5E5-3x%5E5%29%2B%285x%5E6-4x%5E6%29%2B...%5C%5C%20%20%20%5C%5C%3D1%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2B...%3D1%2Bx%5E3%281%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2B...%29)
which for
can be rewritten as
![(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}](https://tex.z-dn.net/?f=%281-x%29P%28x%29%3D1%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%7D%20%5Cquad%20%5CRightarrow%20%5C%5C%5C%5CP%28x%29%3D%5Cdfrac%7B1%7D%7B%281-x%29%7D%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%5E2%7D)
Answer:
50p
Step-by-step explanation:
you can add them all up together. 27+3+6+14=50!