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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 factor...

Answered by Scott S. • Maths tutor

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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(x²y-2x+3) and this is your answer.

Answered by Amber S. • Maths tutor

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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...

Answered by Jack W. • Maths tutor

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How do you solve a quadratic inequality?

Treat it as a normal quadratic equation and solve by factorising: eg. x² - 5x - 24 > 0 x² - 5x - 24 = 0 (x + 3)(x - 8) = 0 x = -3 or x = 82) Sketch the curve, showing the po...

Answered by Abeda A. • Maths tutor

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