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Maths
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For any given journey, ABC Taxis charge customers a base fare of £5 plus 80p per mile. XYZ Taxis charge a base fare of £3 plus £1.20 per mile. Find the number of miles, x, that must be traveled in order for ABC taxis to be the cheaper journey option.

This question can represented in algebraic form:
ABC Taxis = 0.8x + 5XYZ Taxis = 1.2x + 3
Noting that the units must be consistent throughout the question, so we have changed the pence into mile...

EM
Answered by Euan M. Maths tutor
3100 Views

Sketch the graph of y=3sin(2x +pi/2)

Understand what each tranformation does.Sketch in progressive steps, by considering what happens to important points, intersections and max/min values. i.e First 3sin(x)Then pi/2 translationThen 2x transf...

JT
Answered by James T. Maths tutor
3372 Views

Determine (27/8)^3/2

Understanding we can split it into numerator and denominator and find individually.Understanding that ^1/3 is same as cube root and why, by considering that ^2 is squaring27^2/3 = 3^2 = 98^2/3 = 2^2 = 4 =...

JT
Answered by James T. Maths tutor
3385 Views

Solve the simultaneous equations for x and y: 3x+2y = 14 and 5x-y = 6

3x + 2y = 14 -> 15x - y = 6 -> 2Answer: x = 2 and y =4Solution:multiply both sides of equation 2 by 2: 10x - 2y = 12add this to equation 1: 3x + 10x + 2y -2y = 14 +12simplify: 13x = 26divide by 13: ...

MF
Answered by Megan F. Maths tutor
5108 Views

x - 2y = 1 , x^2 + y^2 = 13 find the solutions to this quadratic equation

equation 1) x - 2y = 1equation 2) x2 + y2 = 13
Rearrange equation 1 to: x = 1+2ysubstitute into equation 2: (1+2y)2 + y2=13expand first bracket: (1+2y)(1+2...

CS
Answered by Caitlin S. Maths tutor
3125 Views

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