Answer:
![y = 1.67x](https://tex.z-dn.net/?f=y%20%3D%201.67x)
Step-by-step explanation:
Function A:
x || 3 || 6 || 9 || 12 || 15
y || 5 || 10 || 15 || 20 || 25
<em>See attachment for Function B</em>
First, we need to determine the equation of function A using linear interpolation
As follows:
![y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=y%20%3D%20y_1%20%2B%20%28x%20-%20x_1%29%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Take any two corresponding values of x and y to be:
![(x_1,y_1) = (3,5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%283%2C5%29)
![(x_2,y_2) = (15,25)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2815%2C25%29)
The equation becomes:
![y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=y%20%3D%20y_1%20%2B%20%28x%20-%20x_1%29%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![y = 5 + (x - 3)\frac{25 - 5}{15 - 3}](https://tex.z-dn.net/?f=y%20%3D%205%20%2B%20%28x%20-%203%29%5Cfrac%7B25%20-%205%7D%7B15%20-%203%7D)
![y = 5 + (x - 3)\frac{20}{12}](https://tex.z-dn.net/?f=y%20%3D%205%20%2B%20%28x%20-%203%29%5Cfrac%7B20%7D%7B12%7D)
![y = 5 + (x - 3)\frac{5}{3}](https://tex.z-dn.net/?f=y%20%3D%205%20%2B%20%28x%20-%203%29%5Cfrac%7B5%7D%7B3%7D)
Open bracket
![y = 5 + \frac{5x}{3} - \frac{5*3}{3}](https://tex.z-dn.net/?f=y%20%3D%205%20%2B%20%5Cfrac%7B5x%7D%7B3%7D%20-%20%5Cfrac%7B5%2A3%7D%7B3%7D)
![y = 5 + \frac{5x}{3} - 5](https://tex.z-dn.net/?f=y%20%3D%205%20%2B%20%5Cfrac%7B5x%7D%7B3%7D%20-%205)
Collect Like Terms
![y = \frac{5x}{3} - 5 + 5](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5x%7D%7B3%7D%20-%205%20%2B%205)
![y = \frac{5x}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5x%7D%7B3%7D)
![y = 1.67x](https://tex.z-dn.net/?f=y%20%3D%201.67x)
<em>This function is linear and there is no need to check for function B</em>
Number 9 is yes, they are congruent.
number 10 is no, they are not congruent because x=3, so segment xy=3(3)+5 which is 14 and segment yz=9(3)/2 which is 13.5
Answer:
1/3
Step-by-step explanation:
The total number of purple cards are 3 and you are to find the probability of picking a purple card at random so the answer will be 1/3