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Factorise x^2 - 14x + 49

(x - 7)^2

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A curve has the equation y = 4x^2 + 5x + 3 and a line has the equation y = x + 2. Show that the line and the curve have one point of intersection.

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...

Answered by Francesca G. • Maths tutor

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A curve has the equation y=x^2+4x+4 and a line has the equation y=2x+3. Show the line and curve have only one point of intersection and find its coordinate..

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...

Answered by Ewan F. • Maths tutor

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Name and describe the type of bonding in H2O

The bonds in H₂O are covalent bonds. Covalent bonds are formed when two atoms share a pair of electrons, often where one electron is donated by each atom. This forms a bond as there is an elect...

Answered by William S. • Chemistry tutor

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MRSA and C. difficile are resistant bacterial strains which cause life-threatening infections in hospitals. Explain how MRSA/ C. difficile could arise from non-resistant bacteria. [6 marks]

Natural SelectionCompetition for survival between bacterial colonies/ Selection pressure is survivalVariation between colonies linking to phenotype of resistanceSpontaneo...

Answered by Ijaz C. • Biology tutor

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