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Solve the simultaneous equations: x^2 + y^2 = 5 and y = 3x + 1

x 2 + y 2 = 5 1 y = 3x + 1 2 Inserting 2 into 1 : x 2 + (3x +1) 2 = 5 Expanding the brackets: x 2 + 9x 2 + 3x + 3x + 1 = 5Collecting like terms: 10x 2 + 6x - 4 = 0Using the quadratic formula: x = (-6 ± √(6 2...
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Answered by Sophie B. • Maths tutor
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A jug containing 0.250 kg of liquid is put into a refrigerator. Its temperature decreased from 20°C to 15°C. The amount of energy transferred from the liquid was 5,250 J. Calculate the specific heat capacity of the liquid.

specific heat capacity = change in energy ÷ (mass × change in temperature) [1]= 5,250 ÷ (0.250 × 5) [1]= 4,200 J/kg°C [1]
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Answered by Benjamin P. • Physics tutor
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Solve ((3x-2)/4) - ((2x+5)/3) = ((1-x)/6)

The important concept here is that in order to add or subtract fractions, they must have a common denominator. The easiest way of finding a common denominator for three or more fractions is usually to multip...
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Answered by Peta D. • Maths tutor
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Plot the graph, y=2x^2 -7x +4

3 Mehods:Step 1: Does the function factorise. In this case yes it does. giving y=(2x+1)(x-4)Method: Find the factors of the contract in this case (4). Which are (2,2) , (4,1)We know that a quadratic must fac...
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Answered by Theodore W. • Maths tutor
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Prove algebraically that (2n + 1) to the power of 2 - (2n-1) is an even number

(2n + 1) 2 - (2n-1)can also be written be as (2n +1)(2n + 1) - (2n-1) Two brackets next to each other indicate that you must multiple them by each other, this is also known as expanding the brackets. To do t...
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Answered by Otiti O. • Maths tutor
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