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At what points does the line y = x +1 intersect the circle x^2 + y^2 + 18x + 20y + 81 = 0.

The method we shall use is substitution. We shall replace y each term by 'x + 1' so we are able to obtain an equation in one variable. x^2 + (x+1)^2 + 18x + 20(x+1) + 81 = 0. We now expand the brackets. x^2 ...
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Answered by Harry R. • Maths tutor
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(2x + 3)/(x-4) - (2x - 8)/(2x + 1) = 1

Multiply through by both denominators, giving us the equation (2x + 3)(2x + 1) - (2x - 8)(x - 4) = (x-4)(2x +1). If we expand the brackets, we arrive at 4x^2 + 8x + 3 - (2x^2 -16x + 32) = 2x^2 -7x -4. If we ...
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Answered by Harry R. • Maths tutor
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Solve the simultaneous equations: 3a + 2b = 17 and 4a - b = 30

Here we have a pair of simultaneous equations with two unknowns. There are two methods of going about this question: substitution or elimination. Today, we shall be focusing on the latter. We need a pair of ...
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Answered by Yashna R. • Maths tutor
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X-rays and gamma rays are two types of electromagnetic radiation, state two ways in which they differ from microwave radiation

microwaves come from a different region in the electromagnetic spectrum to X-rays and gamma rays, meaning that they have a different wavelength. Since wavelength and energy are related, this also means that ...
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Answered by Hannah S. • Physics tutor
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Factorise x^2+7x+10 to find the roots of the equatino x^2+7x+10=0

When we are asked to solve a quadratic, we can use the formula, but we are here specifically asked to use factorisation. First of all, we need to know the format of factorisation: usually, it's (x+ )(x+ ), a...
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Answered by Felix H. • Maths tutor
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