--Answer--
Any proposed solution of a rational equation that makes a denominator equal to the numerator is rejected.
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Answer:
y=0
Step-by-step explanation:
Rewrite Evaluate Powers:
3![3^{2y-1}+3^{-1}+2*3^{y}*3^{-1}=1](https://tex.z-dn.net/?f=3%5E%7B2y-1%7D%2B3%5E%7B-1%7D%2B2%2A3%5E%7By%7D%2A3%5E%7B-1%7D%3D1)
Calculate:
![(3^{y})^{2}*\frac{1}{3} +2*3^{y}*\frac{1}{3}=1](https://tex.z-dn.net/?f=%283%5E%7By%7D%29%5E%7B2%7D%2A%5Cfrac%7B1%7D%7B3%7D%20%2B2%2A3%5E%7By%7D%2A%5Cfrac%7B1%7D%7B3%7D%3D1)
Solve using substitution:
![t=3^{y}](https://tex.z-dn.net/?f=t%3D3%5E%7By%7D)
Solve the equation for t:
t=-3
t=1
Substitute back to t=3^y
3^y=-3
3^y=1
y∉R
![3^{y}=1](https://tex.z-dn.net/?f=3%5E%7By%7D%3D1)
y=0
To group an expression, means that the factors of the expression are to be separated in (), [] or {}.
An expression with a value of 80 is: ![2^2 \times ( [2 + 2] \times [3 + 2] )](https://tex.z-dn.net/?f=2%5E2%20%5Ctimes%20%28%20%5B2%20%2B%202%5D%20%5Ctimes%20%5B3%20%2B%202%5D%20%29)
The number is given as:
![80](https://tex.z-dn.net/?f=80)
Factorize
![80 = 2 \times 40](https://tex.z-dn.net/?f=80%20%3D%202%20%5Ctimes%2040)
Factorize 40
![80 = 2 \times 2 \times 20](https://tex.z-dn.net/?f=80%20%3D%202%20%5Ctimes%202%20%5Ctimes%2020)
Express
as an exponent
![80 = 2^2 \times 20](https://tex.z-dn.net/?f=80%20%3D%202%5E2%20%5Ctimes%2020)
Express 20 as 4 x 5
![80 = 2^2 \times ( 4 \times 5)](https://tex.z-dn.net/?f=80%20%3D%202%5E2%20%5Ctimes%20%28%204%20%5Ctimes%205%29)
Express 5 as 3 + 2
![80 = 2^2 \times ( 4 \times [3 + 2] )](https://tex.z-dn.net/?f=80%20%3D%202%5E2%20%5Ctimes%20%28%204%20%5Ctimes%20%5B3%20%2B%202%5D%20%29)
Express 4 as 2 + 2
![80 = 2^2 \times ( [2 + 2] \times [3 + 2] )](https://tex.z-dn.net/?f=80%20%3D%202%5E2%20%5Ctimes%20%28%20%5B2%20%2B%202%5D%20%5Ctimes%20%5B3%20%2B%202%5D%20%29)
Hence, the above expression has a numerical value of 80
Read more about numerical expressions at:
brainly.com/question/24787226
The breadth of rectangle is 14 cm
The perimeter of rectangle is 65 cm
<em><u>Solution:</u></em>
Given that,
Area of rectangle = 259 square centimeter
Length of rectangle = 18.5 cm
<em><u>The area of rectangle is given by formula:</u></em>
![Area\ of\ rectangle = length \times breadth](https://tex.z-dn.net/?f=Area%5C%20of%5C%20rectangle%20%3D%20length%20%5Ctimes%20breadth)
<h3><u>Find the breadth:</u></h3>
Substitute the given values in above formula:
![259 = 18.5 \times breadth\\\\breadth = \frac{259}{18.5}\\\\breadth = 14](https://tex.z-dn.net/?f=259%20%3D%2018.5%20%5Ctimes%20breadth%5C%5C%5C%5Cbreadth%20%3D%20%5Cfrac%7B259%7D%7B18.5%7D%5C%5C%5C%5Cbreadth%20%3D%2014)
Thus breadth is 14 cm
<h3><u>Find the perimeter:</u></h3>
The perimeter of rectangle is given by formula:
![Perimeter = 2(length + breadth)](https://tex.z-dn.net/?f=Perimeter%20%3D%202%28length%20%2B%20breadth%29)
Substitute the given values in above formula:
![perimeter = 2(18.5+14)\\\\perimeter = 2(32.5)\\\\perimeter = 65](https://tex.z-dn.net/?f=perimeter%20%3D%202%2818.5%2B14%29%5C%5C%5C%5Cperimeter%20%3D%202%2832.5%29%5C%5C%5C%5Cperimeter%20%3D%2065)
Thus perimeter of rectangle is 65 cm
No he would get back $4.56. Start with $20 -13.59-1.85=4.56