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Solve the inequality x^2 < -8x + 9

Notice that the inequality may be rearranged to give the quadratic x^2 + 8x - 9 &lt; 0.Factorise the quadratic to give (x-1)(x+9) &lt; 0.Treating the expression as an equality, recall that if the product of ...
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Answered by Isaac S. • Maths tutor
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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 miles. (80p = £0....
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Answered by Euan M. • Maths tutor
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Briefly describe the different steps of mitosis (6 marks)

There are 4 clear phases in mitosis that need to occur in a specific order so that a cell can successfully copy it's DNA and then divide. They are; prophase, metaphase, anaphase telophase and cytokinesis . I...
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Answered by Ben H. • Biology tutor
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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 transform...
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Answered by James T. • Maths tutor
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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 =9/4
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Answered by James T. • Maths tutor
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