Answer:
This proof can be done by contradiction.
Let us assume that 2 - √2 is rational number.
So, by the definition of rational number, we can write it as
where a & b are any integer.
⇒ 
Since, a and b are integers 
is also rational.
and therefore √2 is rational number.
This contradicts the fact that √2 is irrational number.
Hence our assumption that 2 - √2 is rational number is false.
Therefore, 2 - √2 is irrational number.
Answer:
- short-term: $90,000
- long-term: $70,000
Step-by-step explanation:
Let x represent the amount borrowed on the short term. Then 160000-x is the amount of the long-term note. The total interest is ...
0.11x +0.08(160000-x) = 15500
0.03x + 12800 = 15500 . . . . simplify
0.03x = 2700 . . . . . . . . . subtract 12800
x = 2700/.03 = 90,000 . . . . short-term note
160,000 -90,000 = 70,000 . . . . long-term note
The short-term note was for $90,000; the long-term note was for $70,000.
84 x .70 = $58.80
Or if you want to do it the long way you can calculate the actual discount (your savings from this purchase first then subtract it from the original price of $84. It`s just easier to figure out what is left (which is 70% of $84).
Do what is in brackets first, then the multiplication.
