Answer: Choice B) 
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Work Shown:

This shows why choice B is the answer.
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Explanation:
- In the second step, I multiplied top and bottom by

- This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
- In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.
So in general, if the denominator is
and you want to rationalize the denominator, then you should multiply top and bottom by
. The same applies in reverse as well.
This leads to the denominator becoming 
Keep in mind that
and 
Answer:
a. 4600
b. 6200
c. 6193
Step-by-step explanation:
Let
the number of elements in A.
Remember, the number of elements in
satisfies

Then,
a) If
, and if 
Since 
So

b) Since the sets are pairwise disjoint

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

Answer:
14cm, 16 cm, 18 cm
Step-by-step explanation:
Note that
= a:b: c = 7:8:9
We have to find the sum of the proportion
Sum of proportion = 7 + 8 + 9
= 24
Length of side a
7/24 × 48 = 14 cm
Length of side b
8 /24 × 48 = 16cm
Length of side a
9/24 × 48 = 18 cm
What are the lengths of the sides?
The lengths of the sides of the triangle in cm are
14cm, 16 cm, 18 cm