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A cuboid has length x cm. The width of the cuboid is 4 cm less than its length. The height of the cuboid is half of its length. The surface area of the cuboid is 90 cm^2 . Show that 2x^2 − 6x − 45 = 0

Take each side of the cuboid as an algebraic expression and multiply each by 2 to account for both sides of the shape. For example, (x)(x-4), which could be expanded to x²-4x, and then multipl...

Answered by Tom M. • Maths tutor

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Solve the simultaneous equations: 3x + 2y = 4 and 4x + 5y = 17

Step 1: multiply one or both equations so that the 2 equations have the same coefficient for either x or y (pick easier one) 5(3x + 2y) = 5(4) --> 15x + 10y = 20 AND 2(4x + 5y) = 2(17) --> 8x + 10y ...

Answered by Rania D. • Maths tutor

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Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y − 2x = 5 (5 marks)

First consider each equation separately and label them with a number. x² + y² = 25 (1) y - 2x = 5 (2)This question is difficult as it involves squa...

Answered by Karisma S. • Maths tutor

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Factorise y^2 + 27y and simplify w^9/w^4

y² + 27y = y(y + 27)To factorise you need to find the common factor between each part of the equation. In this case y is common between the different parts of the equation. Therefore you take y...

Answered by Lucy M. • Maths tutor

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there are 11 sweets in a box four are soft centred and seven hard centred sweets two sweets are selected at random a)calculate the probability that both sweets are hard centred, b) one sweet is soft centred and one sweet is hard centred

a) First sweet you pick will be soft centred in 7 out of 11 cases, so the probability is 7/11when you are picking up a second sweet there are only 6 hard centred left and a total of 10, so the probability...

Answered by Artem T. • Maths tutor

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