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x^2 - 10x + 33 ≡ (x - a)^2 + b. Work out the value of a and b.

x² - 10x + 33 ≡ (x - a)² + b Work out the value of a and b. Our aim here is to write the expression on the left in the same form as the one on the...

Answered by Joshua C. • Maths tutor

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How do you solve algebraic fractions with quadratics?

First you need to remove the fractions from each side,

take the equation: (x+1)/(x+3) = (2x-1)/(3x-1)

now multiply by x+3 to give x+1 = (2x-1)(x+3)/(3x-1)

now multiply by (3x-1) to gi...

Answered by Eleanor R. • Maths tutor

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The line l is a tangent to the circle x^2 + y^2 = 40 at the point A. A is the point (2,6). The line l crosses the x-axis at the point P. Work out the area of the triangle OAP.

Firstly to work out the area of the triangle OAP we need to know the coordinates of the individual points O, A and P. O is the centre of the axis hence has coordinates (0,0). The coordinates of the point ...

Answered by Mohammad Q. • Maths tutor

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Solve the simultaneous equations: 2x-y=x+4; x^2+4y^2=37

taking equation 1 and solving for x: 2x-y=x+4 x-y=4 x=y+4 Sub our new equation into equation 2 from the question: (y+4)²+4y²=37 Expand and simplify: y²+8y+16+4y²

Answered by Alexander W. • Maths tutor

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A line passes through coordinates (-2,4) and (8,9). Does the point with coordinates (32,55) fall on this line?

To work out if a given point with coordinates (X,Y) falls on a line you must work out the equation for the line. All straight lines follow the formula: y=mx+c with 'y' being the Y coordinate, 'x' being th...

Answered by Nicholas S. • Maths tutor

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