Answer:
80%
Step-by-step explanation:
You multiple .8 by 100 to find percentage, giving you 80%.
The answer to the question is b
Your answer is F.
It says she walks at a rate of 4 miles PER hour. If there is a word “per” that means you are multiplying which gives you 4p.
Lastly, it says she has a goal of walking AT LEAST 18 miles. That means 4p must be same or greater than 18.
Answer:
Ratio of the increase in value to the original value will be 1 : 5
Step-by-step explanation:
This question is incomplete; Here is the complete question.
A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?
Original value of the house = $150000
Value of the house after 5 years = $180000
Appreciation in value of the house after 5 years = $180000 - $150000
= $30000
Now the ratio of the increase in value to the original value = ![\frac{\text{Increased value}}{\text{Original value}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BIncreased%20value%7D%7D%7B%5Ctext%7BOriginal%20value%7D%7D)
= ![\frac{30000}{150000}](https://tex.z-dn.net/?f=%5Cfrac%7B30000%7D%7B150000%7D)
=
or 1 : 5
Therefore, ratio of the increase in value to the original value of the house is 1 : 5
Answer:
j(x) is shifted right by
units
Step-by-step explanation:
Given
![j(x)= 51 cos(x + \frac{\pi}{2})](https://tex.z-dn.net/?f=j%28x%29%3D%2051%20cos%28x%20%2B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29)
![k(x)= 51 cos(x - \frac{3\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%3D%2051%20cos%28x%20-%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
Required
Determine the transformation from j(x) to k(x)
The transformation shows a horizontal shift from j(x) to k(x).
First, we need to determine the unit shifter from j(x) to k(x) as follows;
![j(x)= 51 cos(x + \frac{\pi}{2})](https://tex.z-dn.net/?f=j%28x%29%3D%2051%20cos%28x%20%2B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29)
Express
as ![\frac{5\pi}{4}-\frac{3\pi}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Cpi%7D%7B4%7D-%5Cfrac%7B3%5Cpi%7D%7B4%7D)
So:
becomes
![j(x) = 51cos(x + \frac{5\pi}{4}-\frac{3\pi}{4})](https://tex.z-dn.net/?f=j%28x%29%20%3D%2051cos%28x%20%2B%20%5Cfrac%7B5%5Cpi%7D%7B4%7D-%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
Reorder
![j(x) = 51cos(x -\frac{3\pi}{4}+ \frac{5\pi}{4})](https://tex.z-dn.net/?f=j%28x%29%20%3D%2051cos%28x%20-%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
Comparing this to k(x), we have:
![k(x)= 51 cos(x - \frac{3\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%3D%2051%20cos%28x%20-%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%29)
In other words:
![k(x) = j(x - \frac{5\pi}{4})](https://tex.z-dn.net/?f=k%28x%29%20%3D%20j%28x%20-%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%29)
<em>This implies that j(x) is shifted right by </em>
<em> units</em>