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Write x² + 4x -16 = 0 in the form (x+a)² - b = 0. Solve the equation giving your answer in surd form as simply as possible.

x² + 4x -16 = 0 (x+2)² -20 = 0 We note that the coefficient of x 2 is 1 and the coefficient of x is 4. Therefore we say the that square is (x+2). This leaves us with an additional 4 from this expansion. We m...
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Answered by Henry H. • Maths tutor
4890 Views

When is an arrangement a combination, and when a permutation?

An arrangement is a permutation when we care about the order of the elements in it, and a combination when we do not. So if we are for example choosing a group of 3 people from 10 students, we do not care ab...
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Answered by Liora W. • Maths tutor
7351 Views

When do we add and when do we multiply probabilities?

We add probabilities when the corresponding events are alternatives, e.g. P(rolling a 4 on a pair of dice) = P(rolling a 1 and a 3) + P(rolling a 2 and a 2). These are mutually exclusive events which can't h...
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Answered by Liora W. • Maths tutor
5498 Views

In what useful ways can you rearrange a quadratic equation?

Factorisation: x 2 - 5x + 6 = (x - 2)(x - 3) This method is the quickest to perform if the roots are simple but does rely on a bit of trial and error. The method lets you find the roots of a quadratic equati...
Answered by • Maths tutor
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Find the area under the curve with equation y = 5x - 2x^2 - 2, bounded by the x-axis and the points at which the curve reach the x-axis.

First, we must find the two points at which the curve crosses the boundary. To do this, set y=0 and solve.0 = 5x - 2x 2 - 20 = (2x - 1)(-x+2)This gives that x = 0.5 and x = 2Next, we integrate with these bou...
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Answered by Natassja K. • Maths tutor
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