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\((3x + 1)^{2} = (3x - 1)^{2} + x^{2}\) (Pythagoras's theorem) \(9x^{2} + 6x + 1 = 9x^{2} - 6x + 1 + x^{2}\) x2 - 12x = 0 x(x - 12) = 0 x = 0 or 12 The sides cannot be 0 hence x = 12.

When x = -2, y = x3 - x + 3 = -23 - (-2) + 3 = -8 + 2 + 3 = -3

6 + 10 + 14 + 16 + 26 = 72 \(\frac{6}{72}\) x 360 = 30o Similarly others give 30o, 50o, 70o, 80o and 130o respectively

log\(_7\)49 + log\(_7\)\(\frac{1}{7}\) = log\(_7\)7 = 1

An hexagon polygon is a six sided polygon n = 6 sum of all interior angles of hexagon polygon will be (2n - 4) x 90o = [2 x 6 - 4] x 90 = 720o If one angle is 170o and each of the remaining five angles is 5xo 5xo + 170o = 720o = 5x + 550 x = \(\frac{550}{5}\) = 110o

Circumference of PRS = \(\frac{\pi d}{2}\) = \(\frac{22}{7}\) x \(\frac{7}{1}\) x \(\frac{1}{2}\) = 11cm Side PT = 7cm, Side TR = 7cm Perimeter(PTRS) = 11cm + 7cm + 7cm = 25cm

By using cosine formula, p2 = Q2 + R2 - 2QR cos p Cos P = \(\frac{Q^2 + R^2 - p^2}{2 QR}\) = \(\frac{(3)^2 + 2(\sqrt{3})^2 - 3^2}{2\sqrt{3}}\) = \(\frac{3 + 12 - 9}{12}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\) = 0.5 Cos P = 0.5 p = cos-1 0.5 = 60o = < P = 60o If < P = 60o and < Q = 30 < R = 180o - 90o angle P = 60o and angle R is 90o

Speed = \(\frac{distance}{time}\) let x represent the speed, d represent distance x = \(\frac{d}{4}\) d = 4x 2x = \(\frac{600 - d}{3}\) 6x = 600 - d 6x = 600 - 4x 10x = 600 x = \(\frac{600}{10}\) = 60km/hr Since speed was doubled for the last three hours = 2 x 60km\hr = 120km\hr.

Angle subtended at any part of the circumference of the circle \(\frac{125^o}{2}\) at centre = 360o - 235o = 125o \(\bar{PQR}\) = \(\frac{125}{2}\) = 62\(\frac{1}{2}\)o

o, o o

tan\(\theta\) = \(\frac{0.8}{2}\) = (0.4) \(\theta\) = tan-1(0.4) From the diagram, the inclination of the diagonal PR to the horizontal is 10o 42'

From the diagram; The value of x = 360o - 2(130o) = 360 - 260 = 100o

Adding the values of all the items together, it gives 70 Okro sector = \(\frac{145}{270}\) x \(\frac{360^o}{1}\) = 19.33o = 19\(\frac{1}{3}\)o

Distance = 155 - 50 = 105km Time = 75mins = \(\frac{75}{60}\)hr = \(\frac{5}{4}\)hr Average speed = \(\frac{Distance}{time}\) = \(\frac{105}{\frac{5}{4}}\) = \(\frac{105 \times 4}{5}\) = 84km\h

Loss% = \(\frac{\text{actual loss}}{\text{cost price}}\) x 100% \(\frac{N150 - N120}{N150} \times 100%\) \(\frac{N30}{N150} \times 100%\) = 20%