Answer:
The equation of the graph after translating one unit to the left is;
![y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20-%20%5Cdfrac%7B3%7D%7B2%7D%20%20%5Cright%20%7C%2B3)
Step-by-step explanation:
The given equation is ![y = \left | \dfrac{1}{2}\cdot x - 2 \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%20%7C%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20x%20-%202%20%5Cright%20%7C%2B3)
We note that minimum value of y = 3, where 1/2·x - 2 = 0 and x = 4
Therefore, in moving one unit to the left, we have at the y-intercept where slope of the graph has become inverted (reflection of the real graph) we add one to the x value as follows;
![y = \left | \dfrac{1}{2}\cdot (x+1) - 2 \right |+3 = \left | \dfrac{x}{2} + \dfrac{1}{2} - 2 \right |+3 = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%20%7C%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%28x%2B1%29%20-%202%20%5Cright%20%7C%2B3%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20%2B%20%5Cdfrac%7B1%7D%7B2%7D%20%20-%202%20%5Cright%20%7C%2B3%20%3D%20%20%5Cleft%20%7C%20%5Cdfrac%7Bx%7D%7B2%7D%20-%20%5Cdfrac%7B3%7D%7B2%7D%20%20%5Cright%20%7C%2B3)
The equation of the graph becomes;
.
Answer:
1012
Step-by-step explanation:
Given:
pitch 'p' = 460 vibrations per second
wavelength 'w'= 2.2m
'k' represent constant of variation
'k' can be determined by taking the product of pitch and wavelength
k= p.w
k= 460 x 2.2
k= 1012
Therefore,
the constant of variation is 1012
QPR = 1/2 (31 + 98)
Angle QPR = 64.5 degrees
Answer: 5 + 5w
Step-by-step explanation:
We can use the variable <em>x </em>to describe each additional hour, although the vairable can be substituted for any other vairable.
We know that the main cost for one hour is $5, and that each additional hour will cost $5.
Therefore, the equation to reflect this situation would be 5 + 5w, because the first 5 represents the first hour, and the 5w represents how much each hour costs. If you rent two extra hours, then the cost would end up being 15, because the equation would become: 5 + (5x2) = 15.
The equation is 5 + 5w. Hope this helps, and good luck!