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

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 10^2. √10² = … Read more

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

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

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

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

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

The formula to calculate the present amount including compound interest is A = P(1 + ^r/_n)^nt , where P is the principal amount, r is the annual rate expressed as a decimal , t is the number of years, and n is number of times per year that interest is compounded. NOTE : It is … Read more

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

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

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

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)

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

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

The question appears incomplete but certain facts can be deduced. As Time (T) varies inversely with Horsepower (P) then, T ∝ 1/P which implies T = k/P where k is a constant. When T = 10, P = 200 therefore , 10 = k/200 : K = 200 x 10 = 2000 The formula now … Read more

(w-8/w-9)  - (w+1/w-9)  + (w-27/w²-81) As the first two terms have the same denominator they can be combined : (w-8/w-9)  - (w+1/w-9) = -9 / w - 9 The denominator for the third term can be factored :- (w-27/w²-81) = w - 27 / (w + 9)(w - 9) Combining the new expressions gives :- … Read more

Let John's age now be J and his son's current age be S. The looking at the ages now, J + 13 = 3S : Thus S = (J + 13) ÷ 3 And looking at 6 years ago, (J - 6) - 14 = 2(S - 6) : J - 20 = 2S - … Read more

The equation of the circle can be written (x - p)² + (y - q)² = r², where r is the radius and (p,q) is the centre of the circle. Then, (x - 3)² + (y + 1)² = 9², is the equation of the circle with its centre at (3, -1)and radius 9.

FELIX Fe is the Chemical Symbol for Iron LIX is 59 in Roman Numerals.

Let the 5 digit number be represented by abcde. Then the 6 digit number, 1abcde x 3 = abcde1 (another 6 digit number) Now let Y = abcde.00 Then (100000 + Y) x 3 = (Y x 10) + 1 300000 + 3Y = 10Y + 1 7Y = 299999 Y = 299999 ÷ 7 … Read more