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Equation through (5,7) parallel to the line 7x + 5y = 12 5y = 7x + 12 y = \(\frac{-7x}{5} + \frac{12}{5}\) Gradient = \(\frac{-7}{5}\) Required equation = \(\frac{y - 7}{x - 5} = \frac{-7}{5}\) i.e. 5y - 35 = -7x + 35 5y + 7x = 70

Principal = N225.00, interest = N27.00 Year = x, Rate = 4% 1 = \(\frac{PRT}{100}\) 27 = \(\frac{225 \times 4 \times x}{100}\) = 2700 = 900T T = \(\frac{2700}{900}\) = 3 years

x x - x (x - x)\(^2\) 7 8 9 10 11 12 13 -3 -2 -1 0 1 2 3 9 4 1 1 0 4 9 -------------- 28 S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\) = \(\sqrt{4}\) = 2

Possible outcomes are 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Prime numbers have only two factors, itself and 1. The prime numbers among the group are 23, 29. The probability of choosing a prime number = \(\frac{\text{Number of Prime}}{\text{No. of Total Possible Outcome}}\) = \(\frac{2}{11}\)

Gradient of line = \(\frac{\text{Change in y}}{\text{Change in x}}\) = \(\frac{y_2 - Y}{x_2 - x}\) y\(_2\) = 0\(_1\) Y\(_1\) = 4 x\(_2\) = 3 and x\(_1\) = 0 \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{3 - 0} = \frac{-4}{3}\) Equation of straight line y = mx + c Where m = gradient and c = y intercept = 4 y = -\(\frac{4}{3}\)x + 4 multiply through by 3 3y = -4x + 12

0.0014 = 1.4 \times 10\(^{-3}\) 0.011 = 1.1 \times 10\(^{-2}\) Product = (1.4 \times 1.1) \times 10\(^{-3}\) \times 10\(^{-2}\) = 1.54 \times 10\(^{-5}\)

h = 30 tan 60 = 30\(\sqrt{3}\)

I = \(\frac{PRT}{100}\) = 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\) = 8%

360\(^o\) - (60\(^o\) + 60\(^o\) + 67 + 50 = 237\(^o\)) 360\(^o\) - 237 = 123\(^o\) B. Salary = \(\frac{123}{360} X \frac{N6000}{1}\) = N2,050

\(\frac{1}{3x}\) + \(\frac{1}{2}\)x = \(\frac{2 + 3x}{6x}\) > \(\frac{1}{4x}\) = 4(2 + 3x) > 6x = 12x\(^2\) - 2x = 0 = 2x(6x - 1) > 0 = x(6x - 1) > 0 Case 1 (-, -) = x < 0, 6x - 1 > 0 = x < 0, x < \(\frac{1}{6}\) (solution) Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0 x > \(\frac{1}{6}\) Combining solutions in cases (1) and (2) = x > 0, x < \(\frac{1}{6}\) = 0 < x < \(\frac{1}{6}\)

\(\frac{\sqrt{2}}{x + 2}\) = x - \(\frac{1}{\sqrt{2}}\) x\(\sqrt{2}\) (x - \(\sqrt{2}\)) = x + \(\sqrt{2}\) (cross multiply) x\(\sqrt{2}\) - 2 = x + \(\sqrt{2}\) = x\(\sqrt{2}\) - x = 2 + \(\sqrt{2}\) x (\(\sqrt{2}\) - 1) = 2 + \(\sqrt{2}\) = \(\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}\) x = \(\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}\) = 3\(\sqrt{2}\) + 4

a = b = a\(^2\) a + 2 = a\(^2\).....(i) a + 2 = 2 - a..............(ii) a\(^2\) = 2 - a a\(^2\)+ a - 2 = a\(^2\) + a - 2 = 0 = (a + 2)(a - 1) = 0 a = 1 or - 2

\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\) \(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\) Length of arc (minor) ST = \(\frac{\theta}{360}\) x 2\(\pi r\) \(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\)

r = radius of the cone's base, R = radius of the circle r = \(\frac{R \theta}{360}\) = \(\frac{7.2 \times 300}{360}\) = 6cm

V = 2080cm\(^3\), h = ? r = 7cm V = V\(\pi r^2h\) h = \(\frac{V}{\pi r^2} = \frac{3080}{\frac{22}{7} \times 49}\) \(\frac{3080}{54}\) = 20cm