Answer:
3003
Step-by-step explanation:
This is a combination since the order doesn't matter
15 C 10
The formula
15!
-------
10! (15-10)!
15*14*13*12*11
--------------------
5*4*3*2*1
3003
Answer:
7
Step-by-step explanation:
We are given that
![f_x(-6,7)=-1](https://tex.z-dn.net/?f=f_x%28-6%2C7%29%3D-1)
![f_y(-6,7)=4](https://tex.z-dn.net/?f=f_y%28-6%2C7%29%3D4)
![f(-6,7)=4](https://tex.z-dn.net/?f=f%28-6%2C7%29%3D4)
We have to find the value of f(-5,8),
We know that
![f(x,y)=f(x_0,y_0)+f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Df%28x_0%2Cy_0%29%2Bf_x%28x_0%2Cy_0%29%28x-x_0%29%2Bf_y%28x_0%2Cy_0%29%28y-y_0%29)
We have
![x=-5,y=8](https://tex.z-dn.net/?f=x%3D-5%2Cy%3D8)
![x_0=-6,y_0=7](https://tex.z-dn.net/?f=x_0%3D-6%2Cy_0%3D7)
![f(x,y=f(-6,7)+f_x(-6,7)(x+6)+f_y(-6,7)(y-7)](https://tex.z-dn.net/?f=f%28x%2Cy%3Df%28-6%2C7%29%2Bf_x%28-6%2C7%29%28x%2B6%29%2Bf_y%28-6%2C7%29%28y-7%29)
![f(x,y)=4+(-1)(x+6)+4(y-7)](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D4%2B%28-1%29%28x%2B6%29%2B4%28y-7%29)
![f(x,y)=4-x-6+4y-28=-x+4y-30](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D4-x-6%2B4y-28%3D-x%2B4y-30)
![f(-5,8)=-(-5)+4(8)-30=5+32-30=7](https://tex.z-dn.net/?f=f%28-5%2C8%29%3D-%28-5%29%2B4%288%29-30%3D5%2B32-30%3D7)
When two angles add to 90°, we say they "Complement" each other.
Answer:
c. 14
Step-by-step explanation:
Let the missing y value be y2.
If the data represent a linear function, then:
![\frac{6 - 2}{2 - 1} = \frac{y_2 - 6}{4 - 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%20-%202%7D%7B2%20-%201%7D%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B4%20-%202%7D%20)
![\frac{4}{1} = \frac{y_2 - 6}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B1%7D%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20)
![4 = \frac{y_2 - 6}{2}](https://tex.z-dn.net/?f=%204%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20)
Multiply both sides by 2
![4 \times 2 = \frac{y_2 - 6}{2} \times 2](https://tex.z-dn.net/?f=%204%20%5Ctimes%202%20%3D%20%5Cfrac%7By_2%20-%206%7D%7B2%7D%20%5Ctimes%202%20)
![8 = y_2 - 6](https://tex.z-dn.net/?f=%208%20%3D%20y_2%20-%206%20)
Add 6 to both sides
![8 + 6 = y_2 - 6 + 6](https://tex.z-dn.net/?f=%208%20%2B%206%20%3D%20y_2%20-%206%20%2B%206%20)
![14 = y_2](https://tex.z-dn.net/?f=%2014%20%3D%20y_2%20)
The missing value is 14