Answer:
1. A
2. 9
Step-by-step explanation:
Answer:
The Slope= -13/3
y-intercept= (0,5/3)
Step-by-step explanation:
m= change in y/change in x
m= y2-y1/x2-x1
m=6-(-7)/ -1-(2)
m=-13/3
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:
The explicit formula is 15 + (n-1) -4
Step-by-step explanation:
The formula for an explicit formula is an = First number of the sequence (15) + (n-1)(times the amount of integers separating two different sequential numbers) which is -4.
For instance, since 15 is the first number, it will be a1 or 15. Next will be + (n-1) which is the same for every explicit sequence and the multiplier will be the difference between each number, which is -4 in the recursive sequence. As a result, the answer is 15 + (n-1) -4.
Answer:
33
Step-by-step explanation:
35*3-8+33=33
