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kiruha [24]
4 years ago
11

Prove this conjecture

Mathematics
1 answer:
steposvetlana [31]4 years ago
7 0

Answer:

See explanation

Step-by-step explanation:

Consider the natural number n(n+1)(n+2).

If n is the natural number, then n+1, \ n+2 are next two natural numbers, so numbers n,\ n+1 and n+2 are three consecutive numbers.

Given three consecutive natural numbers, one of them is always even number and one of them is always multiple of 3, so the product

n(n+1)(n+2)

is divisible by 6.

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F(6,2) G(2,4)<br> Write equation in slope intercept form
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Answer:

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Step-by-step explanation:

Formula for slope intercept form is y = mx + b

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.............................

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...........................

m = (y2 - y1)/(x2-x1)

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m = (4-2)/2-6)

m = 2/(-4)

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.......................

Solving for b

.........................

Using point F(6,2) as reference

y = 2, x = 6, m = -½

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Substituting 2 for y and 6 for x in the above equation

2 = -½ * 6 + b

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OR

Using Point G(2,4) as reference

y = 4, x = 2, m = -½

if y = mx + b

Substituting 4 for y and 2 for x in the above equation

4 = -½*2 + b

4 = - 1 + b

4+1 = b

5 = b

b = 5

.............................................

Finally, we have to write the equation in slope form

Using y = mx + b

where m = -½ and b =5 ................ (Calculated)

y = -½x + 5

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