2/2, 4/4, 5/5, 7/7, or any fraction with the same numerator and denominator will be equivalent. All fractions equal 1.
For this case we must solve the following equation:
![12y + 6 = 6 (y + 1)](https://tex.z-dn.net/?f=12y%20%2B%206%20%3D%206%20%28y%20%2B%201%29)
We apply distributive property on the right side of the equation:
![12y + 6 = 6y + 6](https://tex.z-dn.net/?f=12y%20%2B%206%20%3D%206y%20%2B%206)
We subtract 6y on both sides of the equation:
![12y-6y + 6 = 6\\6y + 6 = 6](https://tex.z-dn.net/?f=12y-6y%20%2B%206%20%3D%206%5C%5C6y%20%2B%206%20%3D%206)
We subtract 6 from both sides of the equation:
![6y = 6-6\\6y = 0](https://tex.z-dn.net/?f=6y%20%3D%206-6%5C%5C6y%20%3D%200)
Dividing by 6 on both sides of the equation:
![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
So, the result is ![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
Answer:
![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
Answer:
7.0 < x < 7.6
X is the ideal pH of the swimming pool
Answer:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
![3 + 12 + 48 + 192 + 768](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
Solving (b):
![4 + 32 + 256 + 2048 + 16384](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
Solving (c):
![2 + 6 + 18 + 54 + 162](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
Solving (d):
![3 + 15 + 75 + 375 + 1875](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
Answer:
A: 71°
Explanation:
The interior angles of a triangle must always equal 180°.
We have two of the angles, and if we add them up and subtract it from 180°, we can get the missing angle.
49+60+x=180
Add 49 and 60
109+x=180
Isolate the x, so subtract 109 from 180
x=71°