Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
= 3·4ⁿ + 51
= 3·4ⁿ⁺¹ + 51
- = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
- = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ - is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since - is divisible by 9, we have;
- 
= 
- is divisible by 9
Therefore is divisible by 9 and is divisible by 9 for all positive integers n
Step-by-step explanation:
Answer:
80,000
Step-by-step explanation:
1/4(25%)×60,000=20,000
20,000+60,000=80,000
Answer:
A) Rational
B) Irrational
C) Rational
D) Irrational
Step-by-step explanation:
Irrational numbers cannot be expressed as a ratio of two number, whereas rational numbers can be. 81 can be expressed as 9*9 whereas, 89 cannot be expressed as ratio of two numbers.
Answer:
Vertical lines have undefined (or no) slope always, so this is a true statement. To see why, look at a horizontal line (which is perpendicular). They have zero slope. That comes from the y = mx + b slope intercept form and their equation being y = b, and b is some number.
Step-by-step explanation:
2w+2(5+2w)=33
2w+10+4w=33
6w=22
w=11/3 or 3 and 2/3
