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Prove that the sum of two consecutive integers is always odd

And integer is a whole numberLet the integer = 2X meaning it is even and the next number is (2X+1) making it oddTherefore the sum of the two consecutive integers is2X + 2X + 1=4X+1As this cannot be factorise...
SS
Answered by Scott S. • Maths tutor
20019 Views

Factorise 3x^3y^2-6x^2y+9xy

look for a common factor. See that 3 divides 3, -6 and 9. Then see that x and y divide the equation also. so write 3xy(x 2 y-2x+3) and this is your answer.
AS
Answered by Amber S. • Maths tutor
4659 Views

The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

Draw a diagramRearrange the given equation into the form y = mx + cy = -3/2x+7/2Gradients of perpendicular lines - m1*m2=-1, so gradient of PQ = 2/3PQ : y=mx+c -> 4=(2/3)*3+cc=2, therefore PQ: y=2/3x+2 b=...
JW
Answered by Jack W. • Maths tutor
3190 Views

How do you solve a quadratic inequality?

Treat it as a normal quadratic equation and solve by factorising: eg. x 2 - 5x - 24 > 0 x 2 - 5x - 24 = 0 (x + 3)(x - 8) = 0 x = -3 or x = 82) Sketch the curve, showing the points where the curve crosses ...
AA
Answered by Abeda A. • Maths tutor
4116 Views

Tim flies on a plane from London to Tokyo. The plane flies a distance of 9000 km. The flight time is 11 hours 15 minutes. Work out the average speed of the plane in kilometres per hour.

Speed = Distance/TimeSpeed = 9000/11.25Speed = 800 km/h
NE
Answered by Nicholas E. • Maths tutor
4461 Views