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Show the curve y = 4x^2 + 5x + 3 and the line y = x + 2 have exactly one point of intersection

The curve and the line will intersect when the two expressions are equal, so:4x²+ 5x + 3 = x + 2 (eliminating y and putting the expressions in terms of one variable).4x²+ 4x + 1 = 0(...

Answered by Jacob H. • Maths tutor

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Factorise and find the solutions of the equation 6x^2 + 4x -10 = 0

6x² + 4x - 10 = 0
6x² + 10x - 6x - 10 = 0
2x(3x + 5) - 2(3x + 5) = 0
(2x - 2)(3x + 5) = 0
Case 1:
2x - 2 = 0
2x = 2
x = 1
Case 2:
3x +...

Answered by Cathy H. • Maths tutor

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Simplify the expression: (2a + a)x(5a - a)

Evaluate each bracket first. We have:(2a + a)x(5a - a) = (3a)x(4a)Then, multiply both brackets.(3a)x(4a) = 12a²

Answered by Jonas O. • Maths tutor

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Solve 6/(x-3) + x/(x+4) = 1

(6(x+4) + x(x-3) )/ ((x-3)(x+4)) = 1 obtain a common denominator and write as one fraction. (6x+24+x²-3x ) /( x²-3x+4x-12) = 1 multiply out the brackets. (x²+3x+24)/ (x

Answered by Jana R. • Maths tutor

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Solve these simultaneous equations: 2x + 3y = 19 and x + 4y = 17.

By multiplying everything in equation 2 by 2, you get 2x + 8y = 34. If you then subtract equation 1 from this you get 5y = 15. Thus y = 3, going back to equation two, and subbing y back in, x + 12 = 17, t...

Answered by James H. • Maths tutor

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