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Maths
GCSE

A curve (a) has equation, y = x^2 + 3x + 1. A line (b) has equation, y = 2x + 3. Show that the line and the curve intersect at 2 distinct points and find the points of intersection. Do not use a graphical method.

a) y = x2 + 3x + 1b) y = 2x + 3At points of intersection (a) = (b).2x + 3 = x 2 + 3x + 1Note this is a quadratic expression which will solve for 2 unique solutions, providing the dis...

Answered by Joseph C. Maths tutor
3863 Views

Find the inverse of: f(x) = (2x + 3)/(x - 4)

To find the inverse of a function, f-1(x):1) set f(x) as y: y =  (2x + 3)/(x - 4)2) swap x and y: x = (2y + 3)/(y -4)3) solve the new equation for y: x(y -4) = 2y + 3 = xy -4x2y - xy = -4x - 3y...

Answered by Sophie I. Maths tutor
3961 Views

Can you explain when we flip the inequality direction when solving inequalities.

We solve inequalities exactly like normal equations except for Dividing by a Negative Coefficient where we Change the inequality directionE.gx+2>4 is ... x>2 (ask second ...

Answered by Matthew M. Maths tutor
1962 Views

Mixed rugby team of 20, 5 are female. 15 play at a time. i.) What is the percentage chance of a female playing. ii.)A minimum of three females must now be on the pitch. What is the percentage chance of 4 females playing?

i.) 5/20 * 15/20 *100 = 18.755%ii.) Since 3 have to be on the team, essentially the problem is percentage chance of one female getting onto a team of 12, therefore 2/17 * 12/17 * 100 = 8.30%

Answered by Alfie C. Maths tutor
1925 Views

f(x) = (2x+3)/(x-4). Work out f^-1 (x)

f-1(x) = inverseSet f-1(x) as y = (2x+3)/(x-4)y(x-4) = 2x+3yx-4y = 2x+3yx-2x = 3+4yx(y-2) = 3+4yx = (3+4y)/(y-2)f-1(x) = (3+4x)/(x-2)

Answered by Gurlina H. Maths tutor
4548 Views

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