I think that the answer is 16
Answer:
K(8, 4)
Step-by-step explanation:
Given:
M(2, 1), P(12, 6)
MK:KP = 3:2
Required:
Coordinates of K
SOLUTION:
Coordinates of K can be determined using the formula below:
![x = \frac{mx_2 + nx_1}{m + n}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7Bmx_2%20%2B%20nx_1%7D%7Bm%20%2B%20n%7D%20)
![y = \frac{my_2 + ny_1}{m + n}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7Bmy_2%20%2B%20ny_1%7D%7Bm%20%2B%20n%7D%20)
Where,
![M(2, 1) = (x_1, y_1)](https://tex.z-dn.net/?f=%20M%282%2C%201%29%20%3D%20%28x_1%2C%20y_1%29%20)
![P(12, 6) = (x_2, y_2)](https://tex.z-dn.net/?f=%20P%2812%2C%206%29%20%3D%20%28x_2%2C%20y_2%29%20)
![m = 3, n = 2](https://tex.z-dn.net/?f=%20m%20%3D%203%2C%20n%20%3D%202%20)
Plug in the necessary values to find the coordinates of K:
![x = \frac{mx_2 + nx_1}{m + n}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7Bmx_2%20%2B%20nx_1%7D%7Bm%20%2B%20n%7D%20)
![x = \frac{3(12) + 2(2)}{3 + 2}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B3%2812%29%20%2B%202%282%29%7D%7B3%20%2B%202%7D%20)
![x = \frac{36 + 4}{5}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B36%20%2B%204%7D%7B5%7D%20)
![x = \frac{40}{5}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B40%7D%7B5%7D%20)
![x = 8](https://tex.z-dn.net/?f=%20x%20%3D%208%20)
![y = \frac{my_2 + ny_1}{m + n}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7Bmy_2%20%2B%20ny_1%7D%7Bm%20%2B%20n%7D%20)
![y = \frac{3(6) + 2(1)}{3 + 2}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B3%286%29%20%2B%202%281%29%7D%7B3%20%2B%202%7D%20)
![y = \frac{18 + 2}{5}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B18%20%2B%202%7D%7B5%7D%20)
![y = \frac{20}{5}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B20%7D%7B5%7D%20)
![y = 4](https://tex.z-dn.net/?f=%20y%20%3D%204%20)
The coordinates of K = (8, 4)
I would say no but i don't know how to do your problem by how your describing it sorry :(
Answer:
the "negative solution" is -3
Step-by-step explanation:
Represent the number by n.
Then n^2 - 24 = 5n
We rewrite this in standard quadratic form:
n^2 - 5n - 24 = 0
This factors as follows; (n + 3)(n - 8) = 0
The roots are n = -3 and n = 8. Thus, the "negative solution" is -3