Answer:
Step-by-step explanation:
We have been given two expressions 
and
Now we need to find out least common multiple of these two expressions.
First we need to find out what is common factor of both expressions. and
Least common multiple means find the expression which can be divided by both expressions.
15 and 6 both goes into 30
so 30 is part of LCM (least common multiple )
Now pickup the highest exponent of each variable.
So we get 
Hence required least common multiple is
Answer:
65
Step-by-step explanation:
because it is vertically opposite angles
20/10 is same as 20:10 so the whole number is 2
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
Answer:
4
Step-by-step explanation:
4 is the answer
