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Maths
GCSE

Solve the simultaneous equations “x^2+y^2=4” and “x=2-y”. What does this tell us about the circle centred on the origin, with radius 2, and the straight line with y-intercept 2 and gradient -1?

In order to solve the pair of simultaneous equations, we must find a single set of values for x and y which fulfils both at once. By substituting “x=2-y” into “x2+y2=4”, we obtain a ...

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Answered by Aaron D. Maths tutor
11646 Views

What is the length of the hypotenuse in the right angled triangle to one decimal place? (a=5cm, b=4cm)

Step 1. Use the formula a2+b2=c2

Step 2. Square a and b to find a2=25 and b2=16

Step 3. Add a2 and b2 to find c

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Answered by Eleanor R. Maths tutor
3731 Views

Prove the quadratic formula for ax^2 + bx + c = 0, where a is non 0 and a,b and c are reals.

By completing the square: ax^2 + bx + c = 0 => x^2 + (bx)/a + c/a = 0 (divide both side by a, since a is non-zero) => (x + b/(2a))^2 + c...

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Answered by ShenZhen N. Maths tutor
8936 Views

By factorising, solve the quadratic equation x^2-8x+15=0

First we find two numbers that that add up to -8 and multiply to make 15. In this case the numbers are -3 and -5. This means we can now factorise the quadratic to give (x - 5) (x - 3) = 0. For the above t...

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Answered by Ivo N. Maths tutor
3338 Views

How do you use the completing the square method to solve a quadratic equation?

First you need to get the quadratic equation in completed square form. 
This looks like: (x+p)^2 + q 

To put an expression in completed square form you can use this formula: x^2 + 2bx + c = (...

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Answered by Caroline P. Maths tutor
3362 Views

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