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\(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) = \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\) \(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\) p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2) p = -x + 5 or p = 5 - x

\(\frac{1}{2}\)(a - b + c) + \(\frac{1}{2}\)(a + b - c) - [\(\frac{1}{2}\) (a - b - c)] \(\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c\) = \(\frac{1}{2}(a + b + c)\)

There are 3 triangles: \(\bigtriangleup\)MRS, \(\bigtriangleup\) and \(\bigtriangleup\) PRQ Area PRMS has 2 triangles: \(\bigtriangleup\) MRS and \(\bigtriangleup\) RSP the fraction = \(\frac{2}{3}\)

No expanded working has been attached for this question yet. The verified answer is Option C.

To find the probability that the sum of a randomly selected number from \( P = \{1, 2, 3\} \) and \( Q = \{2, 3, 5\} \) is prime: Possible sums: 1 + 2 = 3 \(\text{prime})\) 1 + 3 = 4 \(\text{not prime})\) 1 + 5 = 6 \(\text{not prime})\) 2 + 2 = 4\(\text{not prime})\) 2 + 3 = 5 \(\text{prime})\) 2 + 5 = 7 \(\text{prime})\) 3 + 2 = 5 \(\text{prime})\) 3 + 3 = 6 \(\text{not prime})\) 3 + 5 = 8\(\text{not prime})\) Prime sums: \( 3, 5, 5, 7 \) (total: 4 favorable outcomes). Total outcomes: \( 3 \times 3 = 9 \). Probability: \(P = \frac{4}{9}\) Thus, the probability that the sum is prime is \(\frac{4}{9}\)

Log(0.0005957)\(^{\frac{1}{3}}\) = Log(\(\frac{5.957}{10000})^{\frac{1}{3}}\) = \(\frac{1}{3}\)Log(5.957) - \(\frac{1}{3}\)Log10\(^4\) = \(\frac{0.7750}{3}\) - \(\frac{4}{3}\) =\(\frac{\overline3.225}{3}\) = \(\overline{1}\).075

9 + 8 = 17 17 + mod 12 = 1 rem 5 it is mod 12

volume of cylinder = \(\pi r^2h\) volume of cylinder p = \(\pi r^2 \times 10\) = 10\(\pi r^2\) volume of cylinder Q = \(\pi (2r)^2 h\) = 4\(\pi r^2\)h 4\(\pi r^2h = 10 \pi r^2\) h = \(\frac{10}{4} = 2.5cm\)

score 0 = 4 students score 1 = 2 students score 2 = 5 students score 3 = 6 students score 4 = 3 students = 20 students

No expanded working has been attached for this question yet. The verified answer is Option C.

if m + n = 120o and n + r = 100o then m + n = 120o then r = 180o - 120o = 60o also n + r = 100o m = 180o = 80o m + r is = 80o + 60o = 140o

xo + zo = 180o (sum of o + zo = 180o zo = 180o - 45o z = 135o z + yo + 20o = 180o (sum of o + yo + 20o = 180o yo + 155o = 180o yo + 180o - 155o yo = 25o

Draw a straight line from point S to meet the y-axis, which cuts it at 2, and do the same for the x-axis which cuts it at 1. Therefore the coordinate of the point S is (1, 2) NOTE: for this graph, each box(square) = 2.5cm on both axes.

The minimum value of y is where the slope of the curve cuts the y - axis = - 1.25.

In the figure above, a + 80º = 180º ( opp

Source: Myschool Past Questions Archive (Record #37010)