The denominator must be the same, so just think of the LEAST COMMON MULTIPLE, The LCM here is 8, because you can multiply 4 by 2 to get 8.
so when you multiply, you multiply both on the top and on the bottom, so this would be:
3 x 2 / 4 x 2 = 6 / 8
Now you can add or subtract: 6/8 - 1/8 = 5/8
Answer:
Triangle 1: x = 80 degrees, acute
Triangle 2: x = 10 degrees, right
Step-by-step explanation:
Triangle 1:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:
![60 + 40 +x = 180](https://tex.z-dn.net/?f=60%20%2B%2040%20%2Bx%20%3D%20180)
Solve for x:
![100 + x = 180\\x = 80](https://tex.z-dn.net/?f=100%20%2B%20x%20%3D%20180%5C%5Cx%20%3D%2080)
So, x = 80 degrees
Because all the angles are less than 90 degrees, this is an acute triangle.
Triangle 2:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation (with the right angle given):
![3x + 60 + 90 = 180](https://tex.z-dn.net/?f=3x%20%2B%2060%20%2B%2090%20%3D%20180)
Solve for x:
![3x + 150 = 180\\3x = 30\\x = 10](https://tex.z-dn.net/?f=3x%20%2B%20150%20%3D%20180%5C%5C3x%20%3D%2030%5C%5Cx%20%3D%2010)
So, x = 10 degrees
Because there is an angle measuring 90 degrees, this is a right triangle.
Answer: ![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
Step-by-step explanation:
In the geometric sequence we can see each time we are dividing by 5. That is the same as multiplying by
so that is the common ratio.
Answer:
![h(x)=\dfrac{x}{2}+5](https://tex.z-dn.net/?f=h%28x%29%3D%5Cdfrac%7Bx%7D%7B2%7D%2B5)
Step-by-step explanation:
You are given the function
. To find the inverse function
do such steps:
1. Rewrite the function f(x) as
![y=2x-10](https://tex.z-dn.net/?f=y%3D2x-10)
2. Express x in terms of y:
![y+10=2x\\ \\x=\dfrac{y}{2}+5](https://tex.z-dn.net/?f=y%2B10%3D2x%5C%5C%20%5C%5Cx%3D%5Cdfrac%7By%7D%7B2%7D%2B5)
3. Change x into y and y into x:
![y=\dfrac{x}{2}+5](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bx%7D%7B2%7D%2B5)
Now, the inverse function is
![f^{-1}(x)=\dfrac{x}{2}+5](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cdfrac%7Bx%7D%7B2%7D%2B5)