Answer:
Step-by-step explanation: The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
Answer:
- 120
Step-by-step explanation:
call x is the number you want to find
- (3/4 )x + 3
= (2/3)x - 6![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
- (3/4)x + (7/2) = (2/3)x - (13/2)
- (3/4)x - (2/3)x = - (13 /2) - (7/2)
- (1/12)x = -10
- x = -10 / (1/12) = -120
Answer:
361.09
Step-by-step explanation:
Explanation:
Calculate the standard error of the mean, SE, using this formula, where is the standard deviation and n is the sample size.
For this situation, the sample size is 65, and the standard error of the mean is 44.8. Substitute these values into the formula, and solve for .
So the standard deviation is approximately 361.09.
Answer/Step-by-step Explanation:
4. Midpoint (M) of AB, for A(-2, -3) and B(1, 2) is given as:
![M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29%20)
Let ![A(-2, -3) = (x_1, y_1)](https://tex.z-dn.net/?f=%20A%28-2%2C%20-3%29%20%3D%20%28x_1%2C%20y_1%29%20)
![B(1, 2) = (x_2, y_2)](https://tex.z-dn.net/?f=%20B%281%2C%202%29%20%3D%20%28x_2%2C%20y_2%29%20)
Thus:
![M(\frac{-2 + 1}{2}, \frac{-3 + 2}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7B-2%20%2B%201%7D%7B2%7D%2C%20%5Cfrac%7B-3%20%2B%202%7D%7B2%7D%29%20)
![M(\frac{-1}{2}, \frac{-1}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7B-1%7D%7B2%7D%2C%20%5Cfrac%7B-1%7D%7B2%7D%29%20)
5. Given M(3, 5) as midpoint of CD, and C(-1, -1),
let ![C(-1, -1) = (x_2, y_2)](https://tex.z-dn.net/?f=%20C%28-1%2C%20-1%29%20%3D%20%28x_2%2C%20y_2%29%20)
![D(?, ?) = (x_1, y_1)](https://tex.z-dn.net/?f=%20D%28%3F%2C%20%3F%29%20%3D%20%28x_1%2C%20y_1%29%20)
![M(3, 5) = (\frac{x_1 +(-1)}{2}, \frac{y_1 +(-1)}{2})](https://tex.z-dn.net/?f=%20M%283%2C%205%29%20%3D%20%28%5Cfrac%7Bx_1%20%2B%28-1%29%7D%7B2%7D%2C%20%5Cfrac%7By_1%20%2B%28-1%29%7D%7B2%7D%29%20)
Rewrite the equation to find the coordinates of D
and ![5 = \frac{y_1 - 1}{2}](https://tex.z-dn.net/?f=%205%20%3D%20%5Cfrac%7By_1%20-%201%7D%7B2%7D%20)
Solve for each:
![3 = \frac{x_1 - 1}{2}](https://tex.z-dn.net/?f=%203%20%3D%20%5Cfrac%7Bx_1%20-%201%7D%7B2%7D%20)
![3*2 = \frac{x_1 - 1}{2}*2](https://tex.z-dn.net/?f=%203%2A2%20%3D%20%5Cfrac%7Bx_1%20-%201%7D%7B2%7D%2A2%20)
![6 = x_1 - 1](https://tex.z-dn.net/?f=%206%20%3D%20x_1%20-%201%20)
![6 + 1= x_1 - 1 + 1](https://tex.z-dn.net/?f=%206%20%2B%201%3D%20x_1%20-%201%20%2B%201%20)
![7 = x_1](https://tex.z-dn.net/?f=%207%20%3D%20x_1%20)
![x_1 = 7](https://tex.z-dn.net/?f=%20x_1%20%3D%207%20)
![5 = \frac{y_1 - 1}{2}](https://tex.z-dn.net/?f=%205%20%3D%20%5Cfrac%7By_1%20-%201%7D%7B2%7D%20)
![5*2 = \frac{y_1 - 1}{2}*2](https://tex.z-dn.net/?f=%205%2A2%20%3D%20%5Cfrac%7By_1%20-%201%7D%7B2%7D%2A2%20)
![10 = y_1 - 1](https://tex.z-dn.net/?f=%2010%20%3D%20y_1%20-%201%20)
![10 + 1= y_1 - 1 + 1](https://tex.z-dn.net/?f=%2010%20%2B%201%3D%20y_1%20-%201%20%2B%201%20)
![11 = y_1](https://tex.z-dn.net/?f=%2011%20%3D%20y_1%20)
![y_1 = 11](https://tex.z-dn.net/?f=%20y_1%20%3D%2011%20)
Coordinates of D is (7, 11)