Ms. Hussain told her class that some dilations make figures bigger, some make figures smaller, and some make figures stay the sa
me size.
Select two of the scale factors that support Ms. Hussain's claim that some dilations make figures smaller.
Select two of the scale factors that support Ms. Hussain's claim that some dilations make figures smaller.
1 answer:
Answer:
To make the figures smaller, scale factor must be divided.
Step-by-step explanation:
1) Firstly, consider a pentagon ABCDE, if we take the scale factor 1\3, the dilations will be smaller.
As distance between A and B = 6
after dilation, distance between A' and B' = 2
Similarly continuing for each side, we get the figure smaller A'B'C'D'E' which is smaller than the original figure.
2) Secondly, consider a hexagon ABCDEF, if we take scale factor 1\2, the dilated figure will be smaller.
A s distance between A and B = 4
After dilations, distance between A' and B' = 2
Similarly continuing for each side, we get the figure A'B'C'D'E'F' which is smaller than the original figure.
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Answer:
Third choice from the top is the one you want
Step-by-step explanation:
This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out. For example:
and another example:
Let's take this step by step. First we will rewrite both the numerator and the denominator in rational exponential equivalencies:
In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number. The LCM of 3 and 4 is 12. So we rewrite as
Now we will put it back into radical form so we can rationalize the denominator:
In order to rationalize the denominator, we need the power on the 2 to be a 12. Right now it's a 4, so we are "missing" 8. The rule for multiplying like bases is that you add the exponents. Therefore,
We will rationalize by multiplying in a unit multiplier equal to 1 in the form of
That looks like this:
This simplifies down to
Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2! Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:
Phew!!!