Correct Answer: A. 9

Correct Answer: D. 1/2

Explanation

\(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)

\(\frac{3}{4} \div \frac{5}{4} \times (\frac{9 - 4}{6})\)

= \(\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}\)

= \(\frac{1}{2}\)

Correct Answer: C. (1, - \(\frac{3}{2}\))

Explanation

\(\frac{3x^2}{3} + \frac{3y^2}{3} - \frac{6x}{3} + \frac{9y}{3} - \frac{5}{3}\) = 0

2gx = -2x, 2 fy = 3y

g = -1, f = \(\frac{3}{2}\)

Centre (1, - \(\frac{3}{2}\))

Correct Answer: C) 15

Explanation

(a) Worth of raw materials = N30,450.00

Worth of raw material to get processed materials = N87.00

Amount of raw material to get processed material = \(\frac{30,450}{87}\)

Time required for direct labour = 3 hours

Amount that will be budgeted for direct labour at N18.25 per hour =

\(3 \times 18.25 \times \frac{30,450}{87}\)

= \(\frac{1667137.5}{87}\)

= N19,162.50

(b) Total amount invested \(N(x + y) = N8,000,000 ....(1)\)

Interest from bank M = \(\frac{x \times 4 \times 6}{100} = 0.24x\)

Interest from bank N = \(\frac{y \times 4 \times 8}{100} = 0.32y\)

\(0.24x + 0.32y = 2,320,000 .... (2)\)

(i) Multiplying (1) by 0.24 in order to eliminate x, we have

\(0.24(x + y) = 0.24(8,000,000.00)\)

\(0.24x + 0.24y = 1,920,000.00 .... (3)\)

(2) - (3) : \(0.32y - 0.24y = 2,320,000 - 1,920,000 = 400,000\)

\(0.08y = 400,000 \implies y = \frac{400,000}{0.08} = N5,000,000\)

\(x = 8,000,000 - y\)

= \(8,000,000 - 5,000,000\)

= \(N3,000,000\)

Therefore, x = N3,000,000 and y = N5,000,000.

(ii) Interest paid by bank N = 0.32y

= \(0.32 \times N5,000,000\)

= \(N1,600,000\)

Correct Answer: A. 12

Explanation

(a) (i) (3 - x), 6, (7 - 5x).

First term = a = (3 - x)

common ratio = \(\frac{6}{3 - x} = \frac{7 - 5x}{6}\)

\(36 = (3 - x)(7 - 5x)\)

\(36 = 21 - 15x - 7x + 5x^{2}\)

\(36 = 21 - 22x + 5x^{2}\)

\(5x^{2} - 22x + 21 - 36 = 0\)

\(5x^{2} - 22x - 15 = 0\)

\(5x^{2} - 25x + 3x - 15 = 0 \implies 5x(x - 5) + 3(x - 5) = 0\)

\((x - 5)(5x + 3) = 0\)

\(x = -\frac{3}{5} \text{ or = } 5\)

(ii) Constant ratio = \(\frac{6}{3 - x} = \frac{7 - 5x}{6}\)

Using x = 5,

\(r = \frac{7 - 5(5)}{6} = \frac{-18}{6}\)

= \(-3\)

(b)Considering \(\Delta\) AOC

\(b^{2} = 4^{2} + 3^{2}\)

\(b^{2} = 16 + 9 = 25\)

\(b = \sqrt{25} = 5 cm\)

Considering \(\Delta\) ACD,

Using cosine rule,

\(\cos D = \frac{a^{2} + b^{2} - c^{2}}{2ab} = \frac{a^{2} + c^{2} - b^{2}}{2ac}\)

= \(\frac{6^{2} + 7^{2} - 5^{2}}{2 (6)(7)}\)

= \(\frac{36 + 49 - 25}{84}\)

\(\cos D = \frac{60}{84}\)

\(\cos D = 0.714\)

\(D = \cos^{-1} (0.714)\)

\(D = 44.4° \approxeq 44°\) (to the nearest degree)

Correct Answer: C. 48°

Explanation

x = 180° - 123° = 57°

z = 180° - 105° = 75°

y = 180° - 57° - 75° = 48°

Correct Answer: B. -4

Explanation

2x - 3y = 22 ---- eqn I

3x + 2y = 7 ---- eqn II

multiply eqn I by 2

4x - 6y = 44 ---- eqn III

multiply eqn II by 3

9x + 6y = 21 ---- eqn IV

Adding eqn III and IV

=> 13x = 65 => x = 5

Substituting 5 for x in eqn II

3x5 + 2y = 7 => 2y = -8

y = -4

Correct Answer: A. 0

Explanation

p = {-3

Q = {-1

P n Q = {0} or {-1