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Write x^2+6x-7 in the form (x+a)^2+b where a and b are integers

Complete the square.We want a quadratic we can simplify.Halve the linear term coefficient (6) and square it.Add it to the (x²+6x) term and subtract it from the 7.x²+6x+(6/2)²

Answered by George B. • Maths tutor

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Write as a single fraction in it's simplest form: 2/(y+3)-1/(y-6)

The aim is to find a common denominator, we first therefore cross multiply to get:(2(y-6)-(y+3))/((y+3)(y-6))After expanding the relevant brackets we are left with:(2y-12-y-3)/((y+3)(y-6))Which is simply:...

Answered by James F. • Maths tutor

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A curve, C, has equation y =(2x-3)^5. A point, P, lies on C at (w,-32). Find the value of w and the equation of the tangent of C at point, P in the form y =mx+c.

To find the value of w, let x = w and y = -32. Substitute these values into the equation of the curve, C: y = (2x-3)^5 => -32 = (2(w) - 3 )^5. Note: the symbol, =>, means "implies that." F...

Answered by Lewis M. • Maths tutor

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Solve the simultaneous equations to find x and y: 2x - 2y = 20, x + 4y = 5

Equation1: 2x - 2y = 20, equation 2: x + 4y = 5First method (subtraction):Multiply equation1 by 2: 4x - 4y = 40Add the two equations together canceling out the y unknowns: 4x + x = 40 + 5Solve for ...

Answered by John S. • Maths tutor

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A curve has equation y = f(x) and passes through the point (4, 22). Given that f ′(x) = 3x^2 – 3x^(1/2) – 7, use integration to find f(x), giving each term in its simplest form.

Firstly we can use the difference rule to split f'(x) into three components which we can consider separately. Then using the knowledge that the integral of x^n is 1/(n+1)*x^(n+1) we get the expression for...

Answered by Abbey S. • Maths tutor

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