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Find the roots of 2x^2-2x=3, leaving your answer in it's simplest exact form.

First we need to rearrange our equation so it is in the correct form of ax 2 +bx+c=0.So we'd move the 3 over to the left hand side to give us 2x2-2x-3=0.We need to use the quadratic formula. Using x=( -b+/-(...
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Answered by Jake A. • Maths tutor
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Solve the inequality x^2 + 4x ≥ 77

First step is to rearrange to make the quadratic easier to work with: in a familiar form. x 2 + 4x ≥ 77, -77 from both sides x 2 + 4x - 77 ≥ 0 Now the quadratic can be solved, by simplifying into double brac...
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Answered by Alex D. • Maths tutor
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Show that the square of any odd number is an odd number

We can talk about any integer (or whole number) with the variable n. n could be any integer, 2, 3 or 100 or 5 billion and 1!If n is any integer, then what numbers could be written as 2n? These are the even n...
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Answered by Alice T. • Maths tutor
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Solve simultaneously, 2x-3y=16 and x+2y=-6

In order to solve this we need to make two of the terms the same and use an elimination method so we are left with only one unknown rather than two. We will multiply x + 2y = -6 by 2 in order to get 2x + 4y ...
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Answered by Gemma G. • Maths tutor
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The y-intercept of A is 7. A also passes through point (7, 2). (a) Find an equation of A in the form y = mx + c. (b) B is perpendicular to A and also has a y-intercept of 7. Write down the equation for B in the form y = mx + c.

(a) y-intercept = (0,7); other point = (7,2) ; gradient, m = change in y / change in x ; m = (0 - 7) / (7 - 2) => m = -7/5 ; y = mx + c (we know from the question that c=7) ; y = (-7/5)x + 7(b) gradient o...
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Answered by Oliver T. • Maths tutor
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