hello
Step-by-step explanation:
Let the initial point of the vector be (x,y). Then the magnitude of the vector v can be written as:
![|v|= \sqrt{ (-1-x)^{2} + (5-y)^{2} }](https://tex.z-dn.net/?f=%7Cv%7C%3D%20%5Csqrt%7B%20%28-1-x%29%5E%7B2%7D%20%2B%20%285-y%29%5E%7B2%7D%20%7D%20)
The magnitude of vecor v is given to be 10. So we can write:
![10= \sqrt{ (-1-x)^{2} + (5-y)^{2} } \\ \\ 100=(-1-x)^{2} + (5-y)^{2}](https://tex.z-dn.net/?f=10%3D%20%5Csqrt%7B%20%28-1-x%29%5E%7B2%7D%20%2B%20%285-y%29%5E%7B2%7D%20%7D%20%5C%5C%20%5C%5C%20100%3D%28-1-x%29%5E%7B2%7D%20%2B%20%285-y%29%5E%7B2%7D)
Now from the given options, we have to check which one satisfies the above equation. That point will be the initial point of the vector.
The point in option d, satisfies the equation.
Thus, the answer to this question is option D
Answer:
See below:
Step-by-step explanation:
So we know that there is a
feet long board and that it is split into 6 pieces.
With that information, we can split it by doing the following:
1. ![\frac{3}{4} *\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%2A%5Cfrac%7B1%7D%7B6%7D)
We can do this because we have a board that is 0.75 feet long and we multiply it by one sixth because we want to divide a fraction and to do that we have to flip the fraction.
After doing that, we get our answer of ![\frac{3}{24}=\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B24%7D%3D%5Cfrac%7B1%7D%7B8%7D)
This means that each piece is
feet long.
Cheers!
Answer:
a) ![2^{3}](https://tex.z-dn.net/?f=2%5E%7B3%7D)
b) ![2^{5}](https://tex.z-dn.net/?f=2%5E%7B5%7D)
c) ![2^{8}](https://tex.z-dn.net/?f=2%5E%7B8%7D)
d) ![\frac{5}{2^{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%5E%7B3%7D%20%7D)
e) ![2^{4} + 2^{3}](https://tex.z-dn.net/?f=2%5E%7B4%7D%20%2B%202%5E%7B3%7D)
Step-by-step explanation:
a) 8 = 2 x 2 x 2
b) 32 = 2 x 2 x 2 x 2 x 2
c) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
d) 5 x 2^3 / 64 = 5 x 8 / 64
= 40/64
= 5/8
= ![\frac{5}{2^{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%5E%7B3%7D%20%7D)
e) 16 - (-2)^3 = 16 - (-8)
= 16 + 8
= ![2^{4} + 2^{3}](https://tex.z-dn.net/?f=2%5E%7B4%7D%20%2B%202%5E%7B3%7D)
Answer:
n squared - 10n + 24
Step-by-step explanation: