Answer:
x=2
Step-by-step explanation:
x+(2x)^2=18
Answer:
Absolute value is a number's distance from 0, so when comparing quantities, such as positive and negative, the greater absolute value is of that number.
For ex:
|-11| > |6| , because |-11| = 11, |6| = 6, and 11 > 6.
So, |-11| > |6|
![g(x) = 2(x-2)^2-5 \text{ is equivalent to } 2x^2-8x+3](https://tex.z-dn.net/?f=g%28x%29%20%3D%202%28x-2%29%5E2-5%20%5Ctext%7B%20is%20equivalent%20to%20%7D%202x%5E2-8x%2B3)
<em><u>Solution:</u></em>
Given expression is:
![f(x) = 2x^2-8x+3](https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%5E2-8x%2B3)
We have to find the equivalent expression
![\mathrm{Write}\:2x^2-8x+3\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2](https://tex.z-dn.net/?f=%5Cmathrm%7BWrite%7D%5C%3A2x%5E2-8x%2B3%5C%3A%5Cmathrm%7Bin%5C%3Athe%5C%3Aform%3A%5C%3A%5C%3A%7Dx%5E2%2B2ax%2Ba%5E2)
![f(x) = 2x^2-8x+3](https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%5E2-8x%2B3)
![\mathrm{Factor\:out\:}2](https://tex.z-dn.net/?f=%5Cmathrm%7BFactor%5C%3Aout%5C%3A%7D2)
![2\left(x^2-4x+\frac{3}{2}\right)](https://tex.z-dn.net/?f=2%5Cleft%28x%5E2-4x%2B%5Cfrac%7B3%7D%7B2%7D%5Cright%29)
![\mathrm{Add\:and\:subtract}\:\left(-2\right)^2\:](https://tex.z-dn.net/?f=%5Cmathrm%7BAdd%5C%3Aand%5C%3Asubtract%7D%5C%3A%5Cleft%28-2%5Cright%29%5E2%5C%3A)
![2\left(x^2-4x+\frac{3}{2}+\left(-2\right)^2-\left(-2\right)^2\right)](https://tex.z-dn.net/?f=2%5Cleft%28x%5E2-4x%2B%5Cfrac%7B3%7D%7B2%7D%2B%5Cleft%28-2%5Cright%29%5E2-%5Cleft%28-2%5Cright%29%5E2%5Cright%29)
Simplify the above equation
![2(x^2-4x + \frac{3}{2} + 4 -4)\\\\2(x^2-4x +4 + \frac{3}{2} - 4)\\\\2(x^2-4x +4 -\frac{5}{2}) ------- eqn 1](https://tex.z-dn.net/?f=2%28x%5E2-4x%20%2B%20%5Cfrac%7B3%7D%7B2%7D%20%2B%204%20-4%29%5C%5C%5C%5C2%28x%5E2-4x%20%2B4%20%2B%20%5Cfrac%7B3%7D%7B2%7D%20-%204%29%5C%5C%5C%5C2%28x%5E2-4x%20%2B4%20-%5Cfrac%7B5%7D%7B2%7D%29%20-------%20eqn%201)
Using the algebraic identity,
![x^2+2ax+a^2=\left(x+a\right)^2](https://tex.z-dn.net/?f=x%5E2%2B2ax%2Ba%5E2%3D%5Cleft%28x%2Ba%5Cright%29%5E2)
Therefore,
![x^2-4x+4=\left(x-2\right)^2](https://tex.z-dn.net/?f=x%5E2-4x%2B4%3D%5Cleft%28x-2%5Cright%29%5E2)
Substitute the above in eqn 1
![2((x-2)^2-\frac{5}{2})](https://tex.z-dn.net/?f=2%28%28x-2%29%5E2-%5Cfrac%7B5%7D%7B2%7D%29)
Simplify the above equation by multiplying 2 with terms inside the bracket
![2(x-2)^2 -5](https://tex.z-dn.net/?f=2%28x-2%29%5E2%20-5)
Thus the equivalent expression is ![g(x) = 2(x-2)^2-5](https://tex.z-dn.net/?f=g%28x%29%20%3D%202%28x-2%29%5E2-5)
Area of a circle formula: area = pi x r^2
R is the radius which is half the diameter.
Area of the clock = pi x 6^2
Area = 36 pi. Square inches ( exact area)
Or using 3.14 for pi = 113.04 square inches
Since the margin of error is 5%, the minimum of supporters will be less than the maximum of disapprovers.
So the third option will be correct. You cannot make certain conclusions based on this survey.