Answer:
21
Step-by-step explanation:
In order to form a chord you need to:
- Select one point. You have 7 choices
- Select a another point. You have just 6 choices because you have to dicard the point alredy chosen
- Connect the two points with a chorde
Since we have 7 choices for the first point and 6 for the second one, one might think that there are a total of 7*6 = 42 choices.
However the correct answer is 21, because you have to take into the account that selecting the point A first and selecting the point B on second step is the same than selecting the point B first and then the point A, because the chord is the same.
Therefore we are counting each chord twice, and we have to divide the result by 2, obtaining 7*6 / 2 = 21.
You can also calculate the amount by using the combiatorial number. The total amount of possibilities to select k elements from a set of n, with n higher than or equal to k and both positive, without taking into account the order is the combinatorial number of n with k, given by
![{n \choose k} = \frac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=%7Bn%20%5Cchoose%20k%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D%20)
In this case, in order to form a chord we need to select 2 points of the seven we are given, ignoring order, thus the total amount of possibilities is
![{7 \choose 2} = \frac{7!}{2!5!} = \frac{7*6*5*4*3*2*1}{2*1*5*4*3*2*1} = \frac{7*6}{2} = 21](https://tex.z-dn.net/?f=%20%7B7%20%5Cchoose%202%7D%20%3D%20%5Cfrac%7B7%21%7D%7B2%215%21%7D%20%3D%20%5Cfrac%7B7%2A6%2A5%2A4%2A3%2A2%2A1%7D%7B2%2A1%2A5%2A4%2A3%2A2%2A1%7D%20%3D%20%5Cfrac%7B7%2A6%7D%7B2%7D%20%3D%2021%20)
As we calculated before.
Well 7x8=56 so that means 7 x 8 = 5 6 so they are the total same and equal to each other because it's an equation even of you space out e v e r y t h i n g...
Answer:
1. Center: (-4,3) Radius: 4
2. C
3. C (x^2 + (y+4)^2 = 16)
4. 50 miles
Step-by-step explanation:
1. Look up how to read equations of circles
2.Soh Cah Toa
3. equations of circles again
4. Pythagorean Theorem