Helps maths!? blah blah blah?

J

Josie

New member
ok I have a few questions please I need method and the rule is first person to answer all get the best answer thingy !!

9i) prove that 12 is a factor of 3n^2 + 6n for all positve intergers.
11. write x^2 - 5x + 8 in the form (x - a)^2 + b and hence show that x^2 - 5x + 8 > 0 for all values of x
12. (x-4)^2 + (x-2)^2 =49
show the origin lies inside this circle
 
9)
Let n be a positive integer.
From there, work out the long division, and you get a result with no remainder, hence 12 is a factor of the given expression.

[ (3n^2 + 6n) / 12 ] = { [(n^2) / 4] + (n/2) } .
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11.
( x^2 - 5x + 8 ) = [ (x - 2.5)^2 + 1.75 ]

and the right-hand side is greater than 0 for all x .
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12.
The center of the circle is at (4 , 2) .
The radius of the circle is sqrt(49) = 7.

The distance from the center of the circle to the origin is
sqrt[ 4^2 + 2^2 ] = sqrt(20) ? 4.47 , which is less than the radius of the circle, so the origin lies inside the circle.
 
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