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
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<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:
6
Step-by-step explanation:
Add all the numbers together and divide by the amount of numbers
6+9+3+8+9+3+4= 42
42/7 = 6
Answer:
C. straight
Step-by-step explanation:
A Linear Pair is two adjacent angles whose non-common sides form opposite rays.
If two angles form a linear pair, the angles are supplementary.
A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.
In the figure given in attachment, AB and BC are two non common sides of ∠ABD and ∠DBC.
∠1 and ∠2 form a linear pair.
The line through points A, B and C is a straight line.
∠1 and ∠2 are supplementary.
Thus two non-common sides of adjacent supplementary angles form a <u>straight</u> angle.
60 total fourth graders and 43 are girls. To find the number of boys, subtract.
60 - 43 = 17 boys
If 5 girls were absent, subtract.
43 - 5 = 38 girls present
If 4 boys were absent, subtract.
17 - 4 = 13 boys present
Therefore, there were 13 boys present.
Best of Luck!
<span>Naming of rays
Rays are commonly named in two ways:
By two points.
In the figure at the top of the page, the ray would be called AB because starts at point A and passes through B on it's way to infinity. Recall that points are usually labelled with single upper-case (capital) letters. There is a symbol for this which looks like this: AB This is read as "ray AB". The arrow over the two letters indicates it is a ray, and the arrow direction indicates that A is the point where the ray starts.
By a single letter. (I have not seen this done.)
The ray above would be called simply "q". By convention, this is usually a single lower case (small) letter. This is normally used when the ray does not pass through another labeled point.</span>
