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:
Our radius is already given, 8.
8 x 3.14 x 2 = 50.24cm <-------- perimeter/circumference
8^2 x 3.14
64 x 3.14 = 200.96cm2 <------- area
Formula of a circumference:
2πr
2 x pie x radius (pie can be used as 22/7 or 3/4 most likely 3.14)
Formula of an area of a Circle:
πr^2
pie x radius squared (pie can be used as 22/7 or 3.14)
Answer:
456/12= 38 means 38 kids share a locker
Step-by-step explanation:
Answer:
Negative numbers
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
Yes , if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram . The parallelogram has opposite sides equal and parallel . Diagonals bisect each other . The sum of alternate angles is 180° and the opposite angles are equal .
