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.
Use the Pythagorean theorem: a² + b² = c²
c = hypotenuse (which means) = 53
a and b are equal to the side length
So a = 21.
Use the formula and solve.
21² + b² = 53²
441 + b² = 2809
b² = 2368
b = 48.66210024238575 or 8√37
Answer:
sad to be honest
Step-by-step explanation:
Population size:9
Lower quartile (xL): 3.5
Upper quartile (xU): 7
<span>Interquartile range (xU-xL): 3.5</span>
(cross multiply)
(371)(x) = (120)(100) (multiply)
371x = 12000 (divide by 371 on both sides)
x = 32.25