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using the trial method by inserting each option in the equation. Inserting 21º: sin([5 x 21] - 28) = cos([3 x 21] - 50) sin(105 - 28) = cos (63 - 50) sin 77º = cos 13º where: sin 77º = 0.9744 cos 13º = 0.9744

The sum of angles in a triangle = 180º (180 - 108)º = 72º Isosceles triangle has both two equal sides and two equal angles. ∠OSN = ∠SON = \(\frac{72}{2}\) = 36º

The sum of angles in a triangle = 180º (180 - 108)º = 72º Isosceles triangle has both two equal sides and two equal angles. ∠OSN = \(\frac{72}{2}\) = 36º

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. ∠M = ∠R + ∠N → 141 = 41 + ∠N ∠N = 141 - 41 = 100º ∠QNR = 180 - 100 → 80º

where x=-4 and y = 16, 16 = -4m - 4 4m = -16 - 4 4m = -20 M = -5

Convert from base 5 to base 10 432\(_{five}\) = (4 x 5\(^2\)) + (3 x 5\(^1\)) + (2 x 5\(^0\)) = (4 x 25) + (3 x 5) + (2 x 1) = 100 + 15 + 2 = 117\(_{ten}\) Then convert from base 10 to base 3 3 117 3 39 r 0 3 13 r 0 3 4 r 1 3 1 r 1 0 r 1 Selecting the remainders from bottom to top: 117\(_{ten}\) = 11100\(_{three}\) Hence; 432\(_{five}\) = 11100\(_{three}\)

4\(^{3x}\) = 4\(^{2(x+1)}\) 3x = 2x + 2 3x - 2x = 2 x = 2

Recall that: log\(_3\) 27 → log\(_3\)3\(^3\) 3log\(_3\)3 → 3 * 1 = 3 Then log\(_3\) 27 = 2x + 1 → 3 = 2x + 1 3 - 1 = 2x 2 = 2x 1 = x

\sqrt24 + \sqrt96 - \sqrt600 = y\sqrt6 convert all to basic surds \sqrt24 = 2\sqrt6 \sqrt96 = 4\sqrt6 - \sqrt600 = -10\sqrt6 2\sqrt6 + 4\sqrt6 - 10\sqrt6 = -4\sqrt6 value of y = -4

(x\(^2\) - 4x + p) Use the coefficient of the middle variable(-4x) = (\(\frac{-4}{2}\))\(^2\) = (-2)\(^2\) = 4

573.06 x 184.25 = 105,586.305 1,05600.00 to four significant figure What are the Rules for significant figures? Significant Figures All non-zero numbers ARE significant. Zeros between two non-zero digits ARE significant. Leading zeros are NOT significant. Trailing zeros to the right of the decimal ARE significant. Trailing zeros in a whole number with the decimal shown ARE significant.

cost price = $50 Selling price = 15 * 8 = $120 percentage profit = \(\frac{sp-cp}{cp}\) * 100 → \(\frac{120-50}{50}\) * 100 percentage profit = 70 * 2 → 140%

Total proportion is 6+7+8 = 21 \(\frac{6 * 10500}{21}\) = 3000 \(\frac{7 * 10500}{21}\) = 3500 \(\frac{8 * 10500}{21}\) = 4000 The largest share is 4000

Error = 1.80 - 1.75 = 0.05 %error = \(\frac{error}{original length}\) = \(\frac{0.05 * 100}{1.75}\) = 2.85 or 2\(\frac{6}{7}\)

\(\frac{1}{x}\) +\(\frac{4}{3x}\) - \(\frac{5}{6x}\) + 1 = 0 using 6x as lcm → \(\frac{6+8-5+6x}{6x}\) → \(\frac{9+6x}{6x}\) = 0 9+6x = 0 6x = -9 x = \(\frac{-9}{6}\) or \(\frac{-3}{2}\)