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First we need to understand what the range is. It is the difference between the smallest and largest numbers in a sample or list or numbers. If we add the range on to the smallest number we get the larges...

Angle AOB = 2x + 28. An angle at the circumference is half that at the centre, so angle ACB = x + 14. Opposite angles of a cyclic quadrilateral sum 180° , so ACB + ADB = 180. ADB is given as 3x - 70. This...

Rearrange (2): x=(-7y-4)/9Substitute the value of x from (2) into (1): 3y=7+5*(-7y-4)/9 Simplify and rearrange for y: y+(35y/27)=(7/3) -(20/27)Resolve for y: y=43/62Substitute y into (1): (3*63)/62=7+5xRe...

Expand the brackets to find x²-x-12=0Factorise the equation to find (x-4)(x+3)=0Check it expands to equal x²-x-12=0Find the value of x as:x+4=0 therefore X=4x-3=0 therefore X=-3

Factorising means reducing an equation to a set of brackets, in the form (x+a)(x+b), where a and b are constants. To factorise this equation, we must find two numbers that add to make -6, and multiply to ...