64 divided by 8 = 8
So you're answer would be 8
Alright, lets get started.
The given function is :
![f(x) = x + 4x^{2} - 36](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20x%20%2B%204x%5E%7B2%7D%20%20-%2036%20)
When we find the domain of any function, we consider the domian is set of input values for which function should remain real and defined.
In this given function , we have not given any points where function seems going undefined.
Hence the domain is : (-∞, +∞) : Answer
Hope it will help :)
Answer:
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.
Based on this the correct system of hypothesis are:
Null hypothesis: ![p \leq 0.3](https://tex.z-dn.net/?f=p%20%5Cleq%200.3)
Alternative hypothesis ![p >0.3](https://tex.z-dn.net/?f=p%20%3E0.3)
Step-by-step explanation:
We have the following info given from the problem:
the random sample of voters selected from the town
represent the proportion of residents favored construction
represent the value desired to test.
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.
Based on this the correct system of hypothesis are:
Null hypothesis: ![p \leq 0.3](https://tex.z-dn.net/?f=p%20%5Cleq%200.3)
Alternative hypothesis ![p >0.3](https://tex.z-dn.net/?f=p%20%3E0.3)
And in order to test this hypothesis we can use a one sample z test for a population proportion and the statistic would be given by:
(1)
And with the data given we have:
option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).
<u>Step-by-step explanation:</u>
We have , The given expression as Three-fourths x = negative 6 , which can be written as
. Now in order to solve this equation in one step , we must notice that coefficient of x must be 1 but it's
, Let's make coefficient of x as 1 by multiplying both side of equations by 4/3:
![\frac{3}{4} (x) = -6](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%28x%29%20%3D%20-6)
⇒ ![\frac{3}{4} (x) = -6](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%28x%29%20%3D%20-6)
⇒ ![\frac{3}{4}(\frac{4}{3} ) (x) = -6(\frac{4}{3} )](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%28%5Cfrac%7B4%7D%7B3%7D%20%29%20%28x%29%20%3D%20-6%28%5Cfrac%7B4%7D%7B3%7D%20%29)
⇒ ![x = -6(\frac{4}{3} )](https://tex.z-dn.net/?f=x%20%3D%20-6%28%5Cfrac%7B4%7D%7B3%7D%20%29)
⇒ ![x = -2(4)](https://tex.z-dn.net/?f=x%20%3D%20-2%284%29)
⇒ ![x = -8](https://tex.z-dn.net/?f=x%20%3D%20-8)
Therefore, x= -8 & correct option to solve the equation Three-fourths x = negative 6 for x in one step is <u>option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).</u>
We can see that the line is horizontal so its slope is 0.