Answer:
x=-3
Step-by-step explanation:
Answer:
First Problem:
1/2 * -2 2/5 = 1/2 * -12/5 = -12/10
Simplify -12/10 into -6/5
Step-by-step explanation:
Answer:
The percentage change is 140%
Step-by-step explanation:
Given
---- initial dimension
--- new width
--- new dimension
Required
The percentage increment
The length remains constant because only the width is extended.
The new area is:
![Area =Length * Width](https://tex.z-dn.net/?f=Area%20%3DLength%20%2A%20Width)
![A_2=L * W_2](https://tex.z-dn.net/?f=A_2%3DL%20%2A%20W_2)
Make L the subject
![L = \frac{A_2}{ W_2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7BA_2%7D%7B%20W_2%7D)
Substitute values for A and W
![L = \frac{45m^2}{6m}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B45m%5E2%7D%7B6m%7D)
![L = \frac{45m}{6}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B45m%7D%7B6%7D)
--- this is the length of the garden
Calculate the initial width:
![L= 3W_1](https://tex.z-dn.net/?f=L%3D%203W_1)
Make W1 the subject
![W_1 = \frac{1}{3} * L](https://tex.z-dn.net/?f=W_1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20L)
![W_1 = \frac{1}{3} * 7.5](https://tex.z-dn.net/?f=W_1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%207.5)
![W_1 = 2.5](https://tex.z-dn.net/?f=W_1%20%3D%202.5)
So, the initial area is:
![A_1 = L_1 * W_1](https://tex.z-dn.net/?f=A_1%20%3D%20L_1%20%2A%20W_1)
![A_1 = 2.5 * 7.5](https://tex.z-dn.net/?f=A_1%20%3D%202.5%20%2A%207.5)
![A_1 = 18.75](https://tex.z-dn.net/?f=A_1%20%3D%2018.75)
The percentage change in area is:
![\%A = \frac{A_2 - A_1}{A_1}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7BA_2%20-%20A_1%7D%7BA_1%7D)
![\%A = \frac{45 - 18.75}{18.75}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7B45%20-%2018.75%7D%7B18.75%7D)
![\%A = \frac{26.25}{18.75}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7B26.25%7D%7B18.75%7D)
![\%A = 1.4](https://tex.z-dn.net/?f=%5C%25A%20%3D%201.4)
Express as percentage
![\%A = 1.4*100\%](https://tex.z-dn.net/?f=%5C%25A%20%3D%201.4%2A100%5C%25)
![\%A = 140\%](https://tex.z-dn.net/?f=%5C%25A%20%3D%20140%5C%25)
If the given radius is 5 inches, then the circumference, C is 2pi r, or 2pi(5 inches) = 10pi inches. You MUST include pi in your calculation of C.