Answer:
Hence, the distance between (7,8) and (-8,0) is:
17
Step-by-step explanation: (a,b)=(7,8) and (c,d)=(-8,0)
Hope this helps!!!!!!
Answer:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
Step-by-step explanation:
The given system of linear equations is:
![(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28cos%5Ctheta%29x%2B%28sin%5Ctheta%29y%3D1%5C%5C%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
We have to solve the equations for the values of
.
Let us use elimination method in which we eliminate one of the variables from the two variables.
For this, let us multiply the first equation by
and second equation by ![cos\theta](https://tex.z-dn.net/?f=cos%5Ctheta)
Now, the equations become:
![(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)](https://tex.z-dn.net/?f=%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5Ctheta.sin%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5E2%5Ctheta%29y%3Dsin%5Ctheta%20.......%20%281%29%5C%5C%5C%5C%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5Ctheta.cos%5Ctheta%29y%3D0%5C%5C%5CRightarrow%20%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5E2%5Ctheta%29y%3D0%20.....%20%282%29)
Now, let us add (1) and (2):
![(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta](https://tex.z-dn.net/?f=%28sin%5E2%5Ctheta%29y%2B%28cos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28sin%5E2%5Ctheta%2Bcos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%281%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20y%20%3D%20sin%5Ctheta)
Using the equation:
![(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
Putting value of
:
![\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta](https://tex.z-dn.net/?f=%5CRightarrow%20%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29sin%5Ctheta%3D0%5C%5C%5CRightarrow%20%28sin%5Ctheta%29x%3D%28cos%5Ctheta%29sin%5Ctheta%5C%5C%5CRightarrow%20x%20%3D%20cos%5Ctheta)
So, the answer to the system of linear equations is:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
0.6 is 6 tenths. 6/10 is the fraction form but you have to simplify so it becomes 3/5.
Answer: Hello, The mean is is 17 and the median is 20
Step-by-step explanation: The mean is a type of average. It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. ... That is the mean. The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
Answer:
y = 5x - 3
Step-by-step explanation:
5 times the input indicates multiplication, and the 3 less indicates subtraction.