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How do you solve a quadratic equation e.g. x^2 - 5x - 14 = 0?

Quadratic equations take the form ax^2 + bx + c = 0. In the case above, a = 0, b = -5, c = -14. In order to solve it, we can factorise the equation into the form (x+c)(x+d) = 0. The answers are then x = -...

Answered by Manal P. • Maths tutor

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y = (x + 2)(x + 5)

steps as follows:x times x = x²2 times 5 = 102 times x = 2xx times 5 = 5xthen add these together:y = x²+ 7x +10x = -2, -5; y = 0, 10

Answered by Georgie L. • Maths tutor

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Use the addition formulas: sin(x+y)=sin(x)cos(y)+sin(y)cos(x), cos(x+y)=cos(x)cos(y)-sin(x)sin(y) to derive sin(2x), cos(2x), sin(x)+sin(y).

sin(2x)=sin(x+x) =sin(x)cos(x)+cos(x)sin(x) =2*sin(x)*cos(x); cos(2x)=cos(x+x) =cos(x)cos(x)-sin(x)sin(x) =[cos(x)]²-[sin(x)]² Now let x+y=a and x-y=b, then x=(a+b)/2 and y=(a-b)/2. ...

Answered by Ioana S. • Maths tutor

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Why do you need simultaneous equations?

This is an example of a simultaneous equation - 2X + Y = 5X + 3Y = 10 You can think of X and Y as apples and oranges from a market. You know that if you buy 2 apples and 1 orange it cost £5, but this does...

Answered by Amelia G. • Maths tutor

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Raya buys a van for £8500 plus VAT at 20%.Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of £531.25 each month. Find the ratio (in simplest form) of the deposit Raya pays to the total of the 12 equal payments.

Raya buys a van for £8,500 x 1.2 = £10,200. Total of 12 equal payments = 12 x £531.25 = £6375. Raya's deposit = £10,200 - £6375 = £3825. Ratio of the dep...

Answered by Andrew B. • Maths tutor

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