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First we need to factorise the numerator into two expressions. We can see one expression must start (3x + ?) and the other therefore must hold (x + ?), we know this because the two bracke...

A sector represents a fraction of a circle. The fraction depends on the angle of the sector, X, and the total angle in a circle which is 360, such that the fraction is x/360. In this case the fraction is ...

(x - 7)^2

Set the equations equal to each other: 4x^2 + 5x + 3 = x + 2Collect terms and set equal to 0: 4x^2 + 4x + 1 = 0Factorise the equation: (2x + 1)(2x + 1) = 0Can now find the value of x: 2x + 1 = 0, therefor...

First set the equations equal to each other: x^2+4x+4 = 2x+3.Rearrange for x in form ax^2+bx+c : x^2+2x+1=0Factorise: (x+1)^2=0. Repeated root, hence only one intersection. x=-1. Using y=2x+3, y=1. So coo...