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5^a = 1/25, 5^b = 25sqrt(5), 5^c = 1/sqrt(5). What is the value of a + b + c?

Two ways to do it. Manually work them all out: 5 a = 1/25 means a = -2, 5 b =25sqrt(5) means b = 2.5, 5 c = 1/sqrt(5) means c = -0.5. So a + b + c = -2 + 2.5 + 0.5 = 0. Can alternatively remember that (x t )...
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Answered by Connor H. • Maths tutor
3396 Views

Katie wants to buy 4 adult show tickets for £10 each and 2 child show tickets for £3 each. There is a 10% booking fee and 3% is then added for paying by credit card. Work out the total charge for Katie if she pays with a credit card.

Firstly, work out the cost of the tickets without any additional charges.(£10 x 4) + (£3 x 2) = £40 + £6 = £46Now, add on the 10% booking fee. 10 % of £46 = £46 x 0.10 = £4.60New cost = £46 + £4.60 = £50.60F...
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Answered by Riana P. • Maths tutor
2700 Views

Solve algebraically the simultaneous equations: (x^2)+(y^2) = 25 , y-3x = 13

Step 1: First rearrange second equation for either x or y (in this example it is easier to make y the subject of the equation: y = 13+3xStep 2: Substitute the expression obtained for y into the first equatio...
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Answered by Spondan B. • Maths tutor
2874 Views

6x + 2y = 22, 2x + y = 8. Find x and y.

Times second equation by 2.6x + 2y = 22 4x + 2y = 16Cancel the y's to gain equation of just x's. 6x + 2y =22 4x + 2y = 16 - ------------------- 2x = 6 ; x = 3Substitute x into an equation.(2×3) + y = 8y = 8-...
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Answered by Jacob O. • Maths tutor
3628 Views

How can you factorise quadratics with a an x^2 coefficient higher than one?

If we take an example question such as 20x 2 - 130 x = -20020x 2 - 130 x = -200 Divide by 10 to simplify2x 2 - 13x = -20 Take all of the terms to the left2x 2 - 13x +20 = 0 Now use this technique. Multiply a...
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Answered by Vahgisha T. • Maths tutor
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