Answer:
4
Step-by-step explanation:
You can see, the whole triangle has a height of 12, and a base of 9. The smaller triangle has a base of 3, which is
of 9, and
of 12 is 4.
The new smaller triangle has a height of 4, and a base of 3.
The equation for the function is ![y=x+\frac{1}{2}](https://tex.z-dn.net/?f=y%3Dx%2B%5Cfrac%7B1%7D%7B2%7D)
Explanation:
The equation for the function that passes through the points
and ![\left(\frac{3}{2}, 2\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B3%7D%7B2%7D%2C%202%5Cright%29)
The equation of the line that passes through the points
and
is given by
![y-y_{1}=m\left(x-x_{1}\right)](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%5Cleft%28x-x_%7B1%7D%5Cright%29)
where m is the slope and it can be determined using the formula,
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Substituting the values of x and y in the slope formula, we have,
![m=\left(\frac{2-\frac{3}{2}}{\frac{3}{2}-1}\right)](https://tex.z-dn.net/?f=m%3D%5Cleft%28%5Cfrac%7B2-%5Cfrac%7B3%7D%7B2%7D%7D%7B%5Cfrac%7B3%7D%7B2%7D-1%7D%5Cright%29)
Simplifying, we get,
![\begin{aligned}&m=\frac{\left(\frac{1}{2}\right)}{\left(\frac{1}{2}\right)}\\&m=1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26m%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%7D%7B%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%7D%5C%5C%26m%3D1%5Cend%7Baligned%7D)
Thus, the slope is m=1.
Substituting the values in the equation
, we have,
![y-\frac{3}{2} =1(x-1)](https://tex.z-dn.net/?f=y-%5Cfrac%7B3%7D%7B2%7D%20%3D1%28x-1%29)
Multiplying the terms within the bracket,
![y-\frac{3}{2} =x-1](https://tex.z-dn.net/?f=y-%5Cfrac%7B3%7D%7B2%7D%20%3Dx-1)
Adding
on both sides of the equation,
![y=x+\frac{1}{2}](https://tex.z-dn.net/?f=y%3Dx%2B%5Cfrac%7B1%7D%7B2%7D)
Thus, the equation for the function is ![y=x+\frac{1}{2}](https://tex.z-dn.net/?f=y%3Dx%2B%5Cfrac%7B1%7D%7B2%7D)
(0,3) and (9,0)
x y x y
hope this helps
Answer:
You got it, I have been busy and I am glad to see someone feeling the same way as me!