Answer:
5+n
you have to distribute the “+” so you can drop the parenthesis. Then, you have 3+2+n. Add and you end up with 5+n
The count of the equilateral triangle is an illustration of areas
There are 150 small equilateral triangles in the regular hexagon
<h3>How to determine the number of
equilateral triangle </h3>
The side length of the hexagon is given as:
L = 5
The area of the hexagon is calculated as:
![A = \frac{3\sqrt 3}{2}L^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B3%5Csqrt%203%7D%7B2%7DL%5E2)
This gives
![A = \frac{3\sqrt 3}{2}* 5^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B3%5Csqrt%203%7D%7B2%7D%2A%205%5E2)
![A = \frac{75\sqrt 3}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B75%5Csqrt%203%7D%7B2%7D)
The side length of the equilateral triangle is
l = 1
The area of the triangle is calculated as:
![a = \frac{\sqrt 3}{4}l^2](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B4%7Dl%5E2)
So, we have:
![a = \frac{\sqrt 3}{4}*1^2](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B4%7D%2A1%5E2)
![a = \frac{\sqrt 3}{4}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5Csqrt%203%7D%7B4%7D)
The number of equilateral triangles in the regular hexagon is then calculated as:
![n = \frac Aa](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%20Aa)
This gives
![n = \frac{75\sqrt 3}{2} \div \frac{\sqrt 3}4](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B75%5Csqrt%203%7D%7B2%7D%20%5Cdiv%20%5Cfrac%7B%5Csqrt%203%7D4)
So, we have:
![n = \frac{75}{2} \div \frac{1}4](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B75%7D%7B2%7D%20%5Cdiv%20%5Cfrac%7B1%7D4)
Rewrite as:
![n = \frac{75}{2} *\frac{4}1](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B75%7D%7B2%7D%20%2A%5Cfrac%7B4%7D1)
![n = 150](https://tex.z-dn.net/?f=n%20%3D%20150)
Hence, there are 150 small equilateral triangles in the regular hexagon
Read more about areas at:
brainly.com/question/24487155
Answer:
12,376.
Step-by-step explanation:
The order in which they are chosen does not matter so this is a combination NOT a permutation.
That is 17C11
= 17! / (11! 6!)
= (17*16*15*14*13*12) / (6*5*4*3*2*1)
= 12376.