9514 1404 393
Answer:
D.
Step-by-step explanation:
The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)
When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.
The only reasonable choice is D.
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Your calculator can check this for you.
√12/(√3 +3) ≈ 3.4641/(1.7321 +3)
= 3.4641/4.7321 ≈ 0.7321 = -1 +√3
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If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.

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<em>Additional comment</em>
We "rationalize the denominator" in this way to take advantage of the relation ...
(a -b)(a +b) = a² -b²
Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.
We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).
Answer:
Step-by-step explanation:
1. ABE bc the both have a right angle. plus when added together, they make a square which means they are the same.
2. id remember how to do the second one i am so sorry
Odd integers are represented by 2n+1 where n is a whole number
consecutive odd are 2 apart so
they are 2n+1 and 2n+1+2
the sum of them is at least 16
2n+1+2n+1+2<u>></u>16
4n+4<u>></u>16
minus 4
4n<u>></u>12
divide 4
n<u>></u>3
sub back
2n+1 and 2n+3
2(3)+1 and 2(3)+3
6+1 and 6+3
7 and 9
they have to be at least 7 and 9
20:20 since the number of boy is even to the girls
I think the answer is 300+20+8
and 400+7 :)