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:
-2
Step-by-step explanation:
rise over run or, y2-y1/x2-x1
Answer:
TOTAL TAX IS: $19.25
TOTAL PRICE IS: $294.25
MONEY LEFT IS: $135.75
Step-by-step explanation:
First, you do a proportion:
?/275 = 7/100
the ?/275 represents how much money in $275
the 7/100 represents 7% (7 hundredths)
then you cross multiply:
275 x 7 = 1925
then you divide:
1925 divided by 100 = 19.25
<em><u>So $19.25 is the tax amount.</u></em>
<em><u></u></em>
To get the total price, you add:
Tax ($19.25) + Cost($275) = $294.25
<u><em>$294.25 is the total amount that Anna has to pay.</em></u>
<u><em></em></u>
To get what Anna has left over, you subtract:
Has($430) - Spend($294.25) = $135.75
<u><em>Anna has $135.75 left.</em></u>
<u><em></em></u>
I hope this helped you a lot!
Bri <3
Answer:
12x+4
Step-by-step explanation:
Cross multiply denominators by numerators so:
8(x)+ 4(x+1)
8x+4x+4
Collect like terms to get 12x+4
The cross-section of a sphere is a circle . The area of a circle can be calculated by the formula A=
Where r is the radius of the circle.
Given :
Solving for r we have:

Or r= 10.
The area of a sphere is calculated by the formula :

Substituting r value we have:
SA= 
The total surface area of this sphere is 400π .