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Prove that the square of an odd number is always 1 more than a multiple of 4

2n+1 will always be an odd number (e.g. if n is equal to 3 the answer would be 7, an odd number) So, we square 2n+1 and write this as (2n+1) 2 2n +12n 4n 2 2n+1 2n 1Then multiple out the brackets to give 4n ...
Answered by • Maths tutor
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There are 495 coins in a bottle. 1/3 of the coins are £1 coins. 124 of the coins are 50p coins. The rest of the coins are 20p coins. Work out the total value of the 495 coins

495/3 = 165 => £165 worth of £1 coins 124 x 0.5 = 62 => £62 worth of 50p coins We know the number of coins that are NOT 20p coins. Therefore, we can subtract the number of non-20p coins from the total ...
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Answered by Sim B. • Maths tutor
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25* 3/2

25 3/2 = 25 (3x 1/2) (25 1/2 ) 3 = (square root of 25) 3 (5) 3 = 125
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Answered by Aisha B. • Maths tutor
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Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x^(2) + y^(2) = 5

If a line is a tangent to a circle, it will have exactly one point where the line intersects the circle. Therefore, when we set the equation of the straight line equal to the equation of the circle, we shoul...
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Answered by Rawdah H. • Maths tutor
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y is inversely proportional to d^2 and when d = 10, y = 4. d is directly proportional to x^2 and when x = 2, d = 24. Find a formula for y in terms of x. Give your answer in its simplest form.

Firstly, find proportionality equation between the two variables. This should be shown as d = kx^2 and y = b/d^2.Solve to find constants of proportionality of a=6 and b=400. Eliminating for d, find that y=10...
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