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:
5 per hour
Step-by-step explanation:
15 miles the total amount he ran divided by 3 the total amount of time
15/3=5 so John ran 5 mph
A
this is because it is not infinite since there are not arrows and domain is all the possible c values while range is all the possible y values. Therefore when analyzing the graph we can see it starts at x=2 and ends at x=10 which is the domain. we can also see the lowest y value is 1 while the highest is 3 which is the range :)
ANSWER
The area of square ABCD is
EXPLANATION
The area of square ABCD is the square of the length of one side.
That is the area of ABCD is |AD|²
From Pythagoras theorem,
We can read from the graph that, each box is one unit.
This implies that,
Therefore the area of square ABCD is 25 square units.
The correct answer is option C.
Step-by-step explanation:
enjoy brooooooooooooo
