Answer:
![Perimeter =58](https://tex.z-dn.net/?f=Perimeter%20%3D58)
Step-by-step explanation:
Given
![AB = 24](https://tex.z-dn.net/?f=AB%20%3D%2024)
See attachment
Required
The perimeter of ABC
First, calculate the lengths of AC and BC.
From the attachment.
![Ax = Az =10](https://tex.z-dn.net/?f=Ax%20%3D%20Az%20%3D10)
![Cx = Cy = 5](https://tex.z-dn.net/?f=Cx%20%3D%20Cy%20%3D%205)
![By =Bz](https://tex.z-dn.net/?f=By%20%3DBz)
So, we have:
![AC = 10 + Cx](https://tex.z-dn.net/?f=AC%20%3D%2010%20%2B%20Cx)
![AC = 10 + 5](https://tex.z-dn.net/?f=AC%20%3D%2010%20%2B%205)
![AC = 15](https://tex.z-dn.net/?f=AC%20%3D%2015)
Also:
![Az + Bz = AB](https://tex.z-dn.net/?f=Az%20%2B%20Bz%20%3D%20AB)
![Az + Bz = 24](https://tex.z-dn.net/?f=Az%20%2B%20Bz%20%3D%2024)
Recall that: ![Ax = Az =10](https://tex.z-dn.net/?f=Ax%20%3D%20Az%20%3D10)
So:
![10 + Bz = 24](https://tex.z-dn.net/?f=10%20%2B%20Bz%20%3D%2024)
![Bz = 24 - 10](https://tex.z-dn.net/?f=Bz%20%3D%2024%20-%2010)
![Bz = 14](https://tex.z-dn.net/?f=Bz%20%3D%2014)
So, we have:
![By = Bz = 14](https://tex.z-dn.net/?f=By%20%3D%20Bz%20%3D%2014)
To calculate BC, we have:
![BC = 5 + By](https://tex.z-dn.net/?f=BC%20%3D%205%20%2B%20By)
![BC=5+14](https://tex.z-dn.net/?f=BC%3D5%2B14)
![BC = 19](https://tex.z-dn.net/?f=BC%20%3D%2019)
The perimeter is then calculated as:
![Perimeter = AB + BC + AC](https://tex.z-dn.net/?f=Perimeter%20%3D%20AB%20%2B%20BC%20%2B%20AC)
![Perimeter = 24 + 19 + 15](https://tex.z-dn.net/?f=Perimeter%20%3D%2024%20%2B%2019%20%2B%2015)
![Perimeter = 58](https://tex.z-dn.net/?f=Perimeter%20%3D%2058)
a: 35c5 or 35 factorial(30!×5!) = 324,362
Answer:
Ramona's answer is correct, Fiona's contains a mistake.
Step-by-step explanation:
We begin with the equation
. Both try to use the exponent law of logarithms, but Fiona makes a mistake in where she puts the exponent. In case you've forgotten, this law says that, given a number a and an exponent n:
![\log{(a^n)}=n\log{(a)}](https://tex.z-dn.net/?f=%5Clog%7B%28a%5En%29%7D%3Dn%5Clog%7B%28a%29%7D)
Fiona's mistake was in putting the exponent above the whole logarithm, instead of inside the argument (the number inside the parentheses). Fiona's step reads
![3x=2\log{(1000)}\\3x=(\log{(1000)})^2](https://tex.z-dn.net/?f=3x%3D2%5Clog%7B%281000%29%7D%5C%5C3x%3D%28%5Clog%7B%281000%29%7D%29%5E2)
When it should read (as Ramona's does):
![3x=2\log{(1000)}\\3x=\log{(1000^2)}](https://tex.z-dn.net/?f=3x%3D2%5Clog%7B%281000%29%7D%5C%5C3x%3D%5Clog%7B%281000%5E2%29%7D)
Answer:
20/30 (2/3)
Step-by-step explanation:
1 5/6 in improper form is 11/6 and 1 2/5 in improper form is 7/5. We need to find an LCM (Least Common Multiple). The LCM in this case is 30. 11/6 times 5 is 55/30 and 7/5 times 6 is 35/30. 55/30 minus 35/30 is 20/30. That could also be simplified to 2/3.