The distance between two points on the plane is given by the formula below
![\begin{gathered} A=(x_1,y_1),B=(x_2,y_2) \\ \Rightarrow d(A,B)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%28x_1%2Cy_1%29%2CB%3D%28x_2%2Cy_2%29%20%5C%5C%20%5CRightarrow%20d%28A%2CB%29%3D%5Csqrt%5B%5D%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D%20%5Cend%7Bgathered%7D)
Therefore, in our case,

Thus,
![\begin{gathered} \Rightarrow d(A,B)=\sqrt[]{(-1-5)^2+(-3-2)^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61} \\ \Rightarrow d(A,B)=\sqrt[]{61} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5CRightarrow%20d%28A%2CB%29%3D%5Csqrt%5B%5D%7B%28-1-5%29%5E2%2B%28-3-2%29%5E2%7D%3D%5Csqrt%5B%5D%7B6%5E2%2B5%5E2%7D%3D%5Csqrt%5B%5D%7B36%2B25%7D%3D%5Csqrt%5B%5D%7B61%7D%20%5C%5C%20%5CRightarrow%20d%28A%2CB%29%3D%5Csqrt%5B%5D%7B61%7D%20%5Cend%7Bgathered%7D)
Therefore, the answer is sqrt(61)
In general,

Remember that

Therefore,
Multiply everything by 2 then combine like terms
Answer:
Y-int: (0,3)
X-int: (4,0)
Equation: y = -3/4x + 3
Step-by-step explanation:
The regression equation of Y on X is given by the following formula:

Where byx is given by the formula:

Where N is the number of values (N=8). We need to find the sum of X values, the sum of Y values, the average of X, the average of Y, the sum of X*Y and the sum of X^2.
The table of values is:
The values we need to know are on the following table:
By replacing the known values in the formula we obtain:

Now, the average of X and Y is the sum divided by N, then:

Replace these values in the formula and find the regression equation as follows:

The answer is a) y=4.6x+28.26
Answer:
Step-by-step explanation:
So here we have a 45-45-90 triangle.
This a special right triangle were the sides across from the 45 degree angles can be considered x, while the hypotenuse is two square roots of x.
Here since we have the sides across from the 45 degree angle we can conclude that 
So if we wanted the hypotenuse we would just plug in this value of x like so:




Therefore the hypotenuse is 18.