First to Answer
Answer:
The correct option is the third option. -2 1/4 / -2/3 = 3 3/8
-9/4 / -2/3 = 3 3/8
1/6(12z-18)=2z-3
12/6z-18/6 =2z-3
2z-3=2z-3
there are infinite solutions for this equation or all real numbers
Answer:
First option y=3/5x
Step-by-step explanation:
Because if you look on the graph, at x=5, y=3
in the equation, plug in x=5, you cancel out denominator left with y=3
please hit the heart button :) good luck
Answer:
![7](https://tex.z-dn.net/?f=7)
Step-by-step explanation:
![\frac{7^{-1}}{7^{-2}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B-1%7D%7D%7B7%5E%7B-2%7D%7D)
![7^{-1-(-2)}](https://tex.z-dn.net/?f=7%5E%7B-1-%28-2%29%7D)
![7^{-1+2}](https://tex.z-dn.net/?f=7%5E%7B-1%2B2%7D)
![7^{1}](https://tex.z-dn.net/?f=7%5E%7B1%7D)
![7](https://tex.z-dn.net/?f=7)
I used the following rules:
![a^1=a](https://tex.z-dn.net/?f=a%5E1%3Da)
![a \neq 0](https://tex.z-dn.net/?f=a%20%5Cneq%200)
Answer:
300%
Step-by-step explanation:
Given
![y\ \alpha\ \frac{1}{x^2}](https://tex.z-dn.net/?f=y%5C%20%5Calpha%5C%20%5Cfrac%7B1%7D%7Bx%5E2%7D)
Required
Find the percentage change in y when x decreased by 50%
First, convert to equation
![y\ = \ \frac{k}{x^2}](https://tex.z-dn.net/?f=y%5C%20%3D%20%5C%20%5Cfrac%7Bk%7D%7Bx%5E2%7D)
Where k is the constant of proportionality
When x decreased by 50%
![Y = \frac{k}{(x - 0.5x)^2}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7Bk%7D%7B%28x%20-%200.5x%29%5E2%7D)
![Y = \frac{k}{(0.5x)^2}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7Bk%7D%7B%280.5x%29%5E2%7D)
![Y = \frac{k}{0.25x^2}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7Bk%7D%7B0.25x%5E2%7D)
Expand
![Y = \frac{1}{0.25} * \frac{k}{x^2}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7B1%7D%7B0.25%7D%20%2A%20%5Cfrac%7Bk%7D%7Bx%5E2%7D)
Substitute
for y
![Y = \frac{1}{0.25} * y](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7B1%7D%7B0.25%7D%20%2A%20y)
![Y = 4 * y](https://tex.z-dn.net/?f=Y%20%3D%204%20%2A%20y)
![Y = 4 y](https://tex.z-dn.net/?f=Y%20%3D%204%20y)
The percentage change is then calculated as:
![\%Change = \frac{Y - y}{y} * 100\%](https://tex.z-dn.net/?f=%5C%25Change%20%3D%20%5Cfrac%7BY%20-%20y%7D%7By%7D%20%2A%20100%5C%25)
![\%Change = \frac{4y - y}{y} * 100\%](https://tex.z-dn.net/?f=%5C%25Change%20%3D%20%5Cfrac%7B4y%20-%20y%7D%7By%7D%20%2A%20100%5C%25)
![\%Change = \frac{3y}{y} * 100\%](https://tex.z-dn.net/?f=%5C%25Change%20%3D%20%5Cfrac%7B3y%7D%7By%7D%20%2A%20100%5C%25)
![\%Change = 3 * 100\%](https://tex.z-dn.net/?f=%5C%25Change%20%3D%203%20%2A%20100%5C%25)
![\%Change = 300\%](https://tex.z-dn.net/?f=%5C%25Change%20%3D%20300%5C%25)
<em>The percentage in y is 300%</em>