2. Use the associative property to make the equation equal (2 + 5) + 3 =
2 answers:
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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!!!
To find our solution, we can start off by creating a string of 27 boxes, all followed by the letters of the alphabet. Underneath the boxes, we can place 6 pairs of boxes and 15 empty boxes.The stars represent the six letters we pick. The empty boxes to the left of the stars provide the "padding" needed to ensure that no two adjacent letters are chosen. We can create this -
Thus, the answer is that there are
ways to choose a set of six letters such that no two letters in the set are adjacent in the alphabet. Hope this helped and have a phenomenal New Year! <em>2018</em>
Thus, the answer is that there are