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Write x^2+4x-12 in the form (x+a)^2+b where 'a' and 'b' are constants to be determined.

This question is asking us to complete the square. To find the value of a we must halve the coefficient of x. So, in this question: a = 4/2 = 2. To find the value of b we take the constant at the end of the ...
FA
Answered by Fizza A. • Maths tutor
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I think of a number. I multiply it by 3 and then subtract 5. I get an answer of 16. What was the number I first thought of?

This question is asking us to work our way back and find the original number. We can refer to this number as 'x'. If we multiply x by 3 we get 3x. The next step is to subtract 5, so our equation now is 3x-5....
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Answered by Fizza A. • Maths tutor
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Factorise x^2-x-12

To factorise this equation we want to get 2 brackets. We are looking for 2 numbers which multiply to make -12 and add to make -1. So, let's see some factors of -12: -12 = (-1) x 12; (-2) x 6; (-3) x 4; (-4) ...
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Answered by Fizza A. • Maths tutor
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Find the derivative of x(x+3)^5

First we use the product rule, so we multiply x by the derivative of (x+3) 5 . To find the derivative of (x+3) 5 we use the chain rule. So we have 5(x+3) 4 . So the first part of our product rule calculation...
JY
Answered by John Y. • Maths tutor
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Solve the simultaneous equations: 3x+4y=19, x-6y= -23.

In order to solve these simultaneous equations we first want to eliminate one of the variables (x or y) and find a solution to the variable remaining (y or x) and then use this solution to find the second va...
NL
Answered by Nathalie L. • Maths tutor
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