<h3>
Answer: Always true</h3>
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Explanation:
We can prove this by contradiction.
Let's say
- A = some rational number
- B = some irrational number
- C = some other rational number
and
A+B = C
We'll show that a contradiction happens based on this.
If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.
If C is rational, then C = r/s for some other integers. We can't have s be zero.
Note the following
A+B = C
B = C - A
B = r/s - p/q
B = qr/qs - ps/qs
B = (qr - ps)/qs
B = (some integer)/(some other integer)
This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".
In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.
The template is
rational + rational = rational
Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.
Another template is
rational + irrational = irrational
Every hour at 12km/h I would go 12km. Simple.
The distance traveled in km is equal to 12 times how many hours you go.
If I go 27 km, I can go in reverse and divide by 12 to get 2.25 hours.
A quarter of an hour is 15 minutes, so the answer would be 2 hours and 15 minutes.
446,221 rounded to the nearest ten thousands would be 450,000
^ this is the correct answer
54+36=90<span>90÷6=15
So 15 is your answer</span>