Answer:
![715x^4y^9](https://tex.z-dn.net/?f=715x%5E4y%5E9)
Step-by-step explanation:
Given
![(x + y)^{13](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13)
Required
Determine the 10th term
Using binomial expansion, we have:
![(a + b)^n = ^nC_0a^nb^0 + ^nC_1a^{n-1}b^1 + ^nC_2a^{n-2}b^2 +.....+^nC_na^{0}b^n](https://tex.z-dn.net/?f=%28a%20%2B%20b%29%5En%20%3D%20%5EnC_0a%5Enb%5E0%20%2B%20%5EnC_1a%5E%7Bn-1%7Db%5E1%20%2B%20%5EnC_2a%5E%7Bn-2%7Db%5E2%20%2B.....%2B%5EnC_na%5E%7B0%7Db%5En)
For, the 10th term. n = 9
So, we have:
![(a + b)^n = ^nC_{9}a^{n-9}b^{9](https://tex.z-dn.net/?f=%28a%20%2B%20b%29%5En%20%3D%20%5EnC_%7B9%7Da%5E%7Bn-9%7Db%5E%7B9)
![(x + y)^{13} = ^{13}C_{9}x^{13-9}y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5E%7B13%7DC_%7B9%7Dx%5E%7B13-9%7Dy%5E9)
![(x + y)^{13} = ^{13}C_{9}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5E%7B13%7DC_%7B9%7Dx%5E4y%5E9)
Apply combination formula
![(x + y)^{13} = \frac{13!}{(13-9)!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%21%7D%7B%2813-9%29%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13!}{4!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%21%7D%7B4%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%2A9%21%7D%7B4%219%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%7D%7B4%21%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B13%2A12%2A11%2A10%7D%7B4%2A3%2A2%2A1%7Dx%5E4y%5E9)
![(x + y)^{13} = \frac{17160}{24}x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20%5Cfrac%7B17160%7D%7B24%7Dx%5E4y%5E9)
![(x + y)^{13} = 715x^4y^9](https://tex.z-dn.net/?f=%28x%20%2B%20y%29%5E%7B13%7D%20%3D%20715x%5E4y%5E9)
Hence, the 10th term is ![715x^4y^9](https://tex.z-dn.net/?f=715x%5E4y%5E9)
Angle y is the same as 85 degrees
Step-by-step explanation:
length=x
width=x-1
x + x + (x-1) + (x-1) = 54
4x - 2 = 54
4x = 56
x = 14 ft
x = 14 ft
x - 1 = 14 - 1 = 13 ft
x = 14 ft
x - 1 = 14 - 1 = 13 ft
Perimeter= x + x + (x-1) + (x-1)
54 ft = 14 + 14 + (14 - 1) + (14 - 1)
54 ft = 28 + (13 +13)
54 ft = 54 ft
224 students have a sweatshirt.
This is what I got I hope this helps