Answer:
A
Step-by-step explanation:
We are given two rational functions m(x) and n(x) that have the same vertical asymptotes both with a single x-intercept at x = 5.
The correct choice will be A.
Recall the transformations of functions.
B represents m(x) being shifted up 5 units. If the function is shifted up, the vertical asymptotes will be the same, but the x-intercept will change.
C represents m(x) being shifted 5 units to the right. This changes both the x-intercept and the vertical asymptotes.
Likewise, D represents m(x) being shifted 5 units to the left. Again, this will change both the x-intercept and the vertical asymptotes.
Therefore, the only choice left is A. It represents a vertical stretch by a factor of 5. This preserves the x-intercepts and the vertical asymptotes. Consider the function:
If n(x)=5m(x), we can see that:
So, the x-interceps and vertical asymptotes are preserved.
You do the distance times by the amount of time
Dilation doesn't change slopes. But slope of AD is 2/1 while slope of JM is 5/2, different.
Last choice:
No, because sides JM and KL have different slopes from sides AD and BC.
Answer:
M
Step-by-step explanation:
M is in the middle of the alphabet, so it would be the midpoint of A-Z if they were placed on a coordinate plane.
Answer:
The area of the patio without the tub is 53.44 ft²
Step-by-step explanation:
In order to calculate the area of the patio that is not covered by the hot tub we need to calculate the total area of the patio and subtract it by the area of the tub. Since the patio is rectangular it's area is given by "area = length*width" and the area of the tub is given by "area = pi*r²".
area patio = length*width = 11*6 = 66 ft²
area tub = pi*r² = pi*(48/2)² = pi*(24)² = 1,808.64 in²
To compare the area we need to convert the areas to the same unit, to do that we will convert the area of the tub from in² to ft², in order to do that we need to divide the value by 144. We have:
area tub = 1,808.64/144 = 12.56 ft²
The area of the patio without the tub is:
x = area patio - area tub = 66 - 12.56 = 53.44 ft²
