Covert to a common denominator to help:
A LCD is 24.
12/24, 20/24, and 15/24
So 12/24, 15/24, 20/24
Convert back into their original denominators:
1/2, 5/8, 5/6.
F.
Answer:
- vertical scaling by a factor of 1/3 (compression)
- reflection over the y-axis
- horizontal scaling by a factor of 3 (expansion)
- translation left 1 unit
- translation up 3 units
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
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Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
- vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
- reflection over the y-axis . . . 1/3f(-x)
- horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
- translation left 1 unit . . . 1/3f(-1/3(x+1))
- translation up 3 units . . . 1/3f(-1/3(x+1)) +3
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
- translation right 1/3 unit . . . f(x -1/3)
- reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
Answer:
66
Step-by-step explanation:
multiply everything together
Each persons ticket costs $34.00(D)
all you have to do is subtract $6.80 from $142.80
then you divide the answer by 4
Answer:
C. II, III, and IV only
Step-by-step explanation:
Lol I haven't done one of these in a while, so thanks for the practice!
It's important to note that a dilation does NOT change the angles of the shape whatsoever. By this, you know that II and III are automatically correct, which rules out A and B. After that, you can look at I, which is the only difference between C and D. Since the dilation factor is 2/3, the parallelogram you see is smaller than the original. Since in I, the original would be larger than the denominator, the correct answer would be at least greater than one (to be precise, it'd be 3/2). To make everything easier, you can find the value by assigning the original side a value of 1, which would make the prime value 2/3. 1/(2/3) is going to be 3/2.