By definition of the binomial coefficient,
![C(n,k) = \dfrac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=C%28n%2Ck%29%20%3D%20%5Cdfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D)
so we have
![C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)](https://tex.z-dn.net/?f=C%2850%2C3%29%20%2B%20C%2850%2C4%29%20%3D%20%5Cdfrac%7B50%21%7D%7B3%2147%21%7D%20%2B%20%5Cdfrac%7B50%21%7D%7B4%2146%21%7D%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B50%21%7D%7B3%2146%21%7D%20%5Cleft%28%5Cdfrac1%7B47%7D%20%2B%20%5Cdfrac14%5Cright%29%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B50%21%7D%7B3%2146%21%7D%20%5Ctimes%20%5Cdfrac%7B51%7D%7B188%7D%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B51%21%7D%7B3%2146%21%7D%20%5Ctimes%20%5Cdfrac1%7B4%5Ctimes47%7D%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B51%21%7D%7B4%2147%21%7D%20%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B51%21%7D%7B4%21%2851-4%29%21%7D%20%3D%20C%2851%2C4%29)
as required.
Using the distributive property an equivalent expression would be 9z-54
Answer:
ab=bc because b devide ac in two equal sizes
ac=ab+bc
ac=2×ab
ac =2×bc
lets substitute ac and bc there we are given
x+3=2(3x-1)
x+3=6x-2
-5x/-5=-5/-5
x=1
ab=3(1)-1
ab=2
Answer:
100.48 feet
Step-by-step explanation:
The circumfrence of a circle is represented in the equation C=2\pi r^{2}
So we input the values into the equation C=2(3.14)(4)^2 which when entered into a calculator gives you 100.48feet