could 7.2 inches and 28 inches be the diameter and circumference of the same circle? Explain why or why not.
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Let's analyze the changes made to the parent function one by one:
STEP 1: Horizontal translation.
If we transform
We're performing a change in the form of
This kind of changes result in a horizontal translation, k units to the left if k is positive, k units to the right if k is negative. In this case, k=2, so the original graph is shifted 2 units to the left.
STEP 3: Vertical stretch.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical stretch with scale factor k. If k is negative, the function is also reflected across the x axis. In this case, k=3, so the original graph is stretched vertically, with scale factor 3.
STEP 3: Vertical translation.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical translation, k units down if k is positive, k units up if k is negative. In this case, k= -4, so the graph is shifted 4 units down.
All, in all, the original graph is shifted 2 units to the right, then it's stretched vertically with scale 3, and then it's shifted 4 units down. The order is important!
part A
if the paperbacks are 40% less, that means 100% - 40% = 60%, they actually are 60% of the price of the hardcover ones.
part B
so, if they return it, they get 1/3 credit, if they try to sell it, is half off, which is more than 1/3. 22 got damaged.
part C
I don't think she is incorrect, $17.5 is close to $20, she didn't say it was exactly $20, just thereabouts, and 17.5 is around that much.