Answer:
moons: 3
droplets: 5
hearts: 1
squares: 1
nvm dont use this
Step-by-step explanation:
Multiply both sides
8x-96=3x+24
move the terms
8x-3x=24+96
collect like terms
5x=120
solution:
x=24
<h2>
Hello!</h2>
The answer is:
d) ![\frac{(x-1)(11x+1)}{(x-1)(x+2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-1%29%2811x%2B1%29%7D%7B%28x-1%29%28x%2B2%29%7D)
<h2>Why?</h2>
A hole is a point where rational functions lose its continuity, meaning that in that point, there is a discontinuity condition.
We can find the hole of a rational function if there are similar terms on the numerator and the denominator by finding:
First (x-component): The values of x that makes the function equal to 0 in both numerator and denominator.
Second (y-component): Re-evaluating the same term in the other factors of the function to know the y-component.
Finding the x component we have:
![f(1)=\frac{(1-1)(11*1+1)}{(1-1)(1+2)}=\frac{(0)(12)}{(0)(3)}=\frac{0}{0}](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%281-1%29%2811%2A1%2B1%29%7D%7B%281-1%29%281%2B2%29%7D%3D%5Cfrac%7B%280%29%2812%29%7D%7B%280%29%283%29%7D%3D%5Cfrac%7B0%7D%7B0%7D)
So, the x-component is 1,
Then, re-evaluating the function:
![f(1)=\frac{(x-1)(11*1+1)}{(x-1)(1+2)}=\frac{(12)}{(3)}=\frac{12}{3}=4](https://tex.z-dn.net/?f=f%281%29%3D%5Cfrac%7B%28x-1%29%2811%2A1%2B1%29%7D%7B%28x-1%29%281%2B2%29%7D%3D%5Cfrac%7B%2812%29%7D%7B%283%29%7D%3D%5Cfrac%7B12%7D%7B3%7D%3D4)
Therefore, the y-component is 4,
Hence,
The function has a hole at (1,4)
Have a nice day!
Step-by-step explanation:
( y = 4x/5 + 2)
m1.m2 = -1
4/5.m2 = -1
m2 = -5/4
formula = y - y1 = m2 ( x - x1)
y - 3 = -5/4 ( x - 6)
y -3 = -5x /4 + 30/4
y = -5x /4 + 21/2