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Inequalities can be treated just like equations with one major difference - if you multiply or divide both sides using a negative number then  the Inequality Sign is reversed. This doesn't actually apply in these questions. 1) 8x + 9 < 9x -  8...add 8 to both sides and subtract 8x from both sides 17 … Read more
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Assuming that you can't use a calculator etc. And that the answer is an integer. 1) Express 11664 in terms of its prime factors. 11664 = 2^4 x 3^6 = (22)2 x (33)2 Then, √11664 = 22 x 33 = 4 x 27 = 108 2) Write 11664 as 116.64 x 102. √102 = … Read more
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As the expression is a radical (a root of another quantity) and figures within the square root are multiplied then see is any of them can be expressed as perfect squares. If this can be done then the square root of these perfect squares can be taken outside the square root sign. X2 is clearly … Read more
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We can regard the ladder, the floor and the house wall as forming a right angled triangle with the ladder representing the hypotenuse. Using Pythagoras' Theorem and letting H be the height of the ladder then, 102 = 52 + H2 H2 = 100 - 25 = 75 H = √75 = 9.21954 (5dp) As … Read more
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The required equation is, 325 = 1/2(n2 + n)...then 650 = n2 + n...and the equation can be written:- n2 + n - 650 = 0...which can be factored (n + 26)(n - 25) = 0 As we are only concerned with a positive integer solution, this occurs when n - 25 = 0, thus … Read more
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The wholesale cost can be regarded as 100%. After a markup of 130% the retail price is equivalent to 230% (100 + 130) of the wholesale cost. If the retail price = 213.90 then the wholesale price = 100 x (213.90/230) = \$93.00
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3x = 8y + 11 x + 6y - 8 = 0...which can be written as x = -6y + 8 We now have both equations in the same format. It can be seen that we can make the coefficients of x equal in both equations by multiplying the 2nd equation by 3. 3x = … Read more
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2x2 + 10x + 7 = 0 Bring the coefficient of x2 to 1 by dividing throughout by 2. 2(x2 + 5x + 7/2) = 0      Note : (x + h)2 = x2 + 2hx + h2...so h = half the coefficient of x 2(x + 5/2)2 - 22/4 = 0 2(x + … Read more
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If , a/b = 7/20 then 20a = 7b and we can write... 20a - 7b = 0 As a + b = 135 then multiplying throughout by 7 gives 7a + 7b = 945 Adding these two equations gives, ...27a  = 945 : Then a = 945/27 = 35 Substituting this value for a … Read more
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4x + 32 / x2 + 9x + 8 4 is a factor of both terms in the numerator. 4(x + 8) / x2 + 9x + 8 The quadratic expression in the denominator can be factored : X2 + 9x + 8 = (x + 1)(x + 8) 4(x + 8) / (x + … Read more
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The Slope/Intercept form of equation for a straight line is y = mx + c, where m is the slope(gradient) and c is the y-intercept (when x = 0). 4x - 10y = 11 10y = 4x - 11 y = 4x/10 - 11/10 y = 2x/5 - 11/10 (or y = 0.4x - 1.1)
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Let the width of the original rectangle be W, then the length = (W + 5) The area of this rectangle = W(W + 5) = W2 +5W The modified rectangle has a length 2(W + 5) and a width (W - 2) The area of the modified rectangle = 2(W + 5)(W - 2) … Read more
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The factored formula for the polynomial is, (x - 3)(x - 3)x(x + 4) = 0, given that it has two equal roots when x = 3, a further root when x = 0 and another when x = -4. This expands to x4 - 2x3 - 15x2 + 36x = 0 As the lead … Read more