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Questions which ask for you to rationalize the denominator usually includes an integer and a square root of a number (x+sqrt(y)).We can use the following formula to our advantage: (a+b)(a-b)=a^2-b^2. ...
A triangle number is a number such that it is the sum of n consecutive integers, starting from 0. Eg 1, 1+2, 1+2+3... are the first 3 triangle numbers. The formula for the nth triangle number is well-know...
We have that x2 + y2 + 6x - 2y - 10 = (x+3)2 + (y-1)2 - 20 = 0 (step was motivated by the equation of a general circle (x-a)2 + (y-b)2 = ...
First we need to find the cost of one arc from the information we already have about the arc (20 straight lines cost £12). To do this divide the £12 total cost by the number of lines 20.12 ÷ 20 = £0.60 ea...
(x+6)(x+5)=20. x2 + 11x +30=20. x2+ 11x + 10 = 0. (x+10)(x+1)=0 . x=-1 and x=-10. width= -10+5=-5 (invalid solution). width =-1+5= 4. Checking through: (-1+6)*(-1+5)=20.
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