Explanation

To find the determinant of \(\begin{pmatrix} 5 & -6 & 4\\ 7 & 4 & -3\\ 2 & 1 & 6 \end{pmatrix}\) which is 5(24 + 3) + 6(4 + 6) + 4(7 - 8) = 135 + 288 - 4 = 419.

Then, substitude the column of the coefficient of x by the right - hand side of the equations and find the determinant of \(\begin{pmatrix} 5 & -6 & 4\\ 7 & 4 & -3\\ 46 & 1 & 6 \end{pmatrix}\) = 15(24 + 3) + 6(114 + 138) + 4(19 - 184) = 405 + 1512 - 660 = 1257.

Similarly, to find the coefficient of y, find the determinant of \(\begin{pmatrix} 5 & 15 & 4\\ 7 & 19 & -3\\ 2 & 46 & 6 \end{pmatrix}\)

= 5(114 + 138) - 13(42 + 6) - 4(322 - 38) = 1260 - 720 + 1136 = 1676.

Finally, for the coefficient of z find the determinant of \(\begin{pmatrix} 5 & -6 & 15\\ 7 & 19 & -3\\ 2 & 46 & 6 \end{pmatrix}\)

= 5(184 - 19) + 6(322 - 38) + 15(7 - 8) = 825 + 1704 - 15 = 2514

Therefore, x = \(\frac{1257}{419}\) = 3, y = \(\frac{1676}{419}\) = 4

and z = \(\frac{2514}{419}\) = 6

Correct Answer: B. \(\frac{5}{3}\)

Explanation

m = 2, n = 1

\(\frac{3m^2 - 2n^2}{m^2 _ mn}\)

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

= \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\)

= \(\frac{5}{3}\)

Explanation

(a)(i) < PTS = 38° (alternate angle)

42° + x + 38° = 180° (angles on a straight line)

80° + x = 180°

x = 180° - 80° = 100°

(ii) < SQT = 42° (alternate angle)

< SQR = 60° (sum of angles in a triangle)

y + 42° + 60° = 180° (angle on a straight line)

y + 102° = 180°

y = 180° - 102° = 78°

(b) \(< QSP = \frac{150}{2}\) (angle at the centre is twicw angle at the circumference)

\(< QSP = 75°\)

\(\hat{R} + \hat{P} = 180°\) (opposite angles in a cyclic quad are supplementary)

\(\hat{P} + 75° + 45° = 180°\) (sum of angle in a triangle)

\(\hat{P} = 180° - 120°\)

\(\hat{P} = 60°\)

\(\hat{R} + \hat{P} = 180°\)

\(\hat{R} = 180° - 60°\)

\(\hat{R} = 120°\)

\(< RQS + < QRS + < QSR = 180°\) (sum of angle in a triangle)

\(< RQS = 180° - (40° + 120°)\)

= \(180° - 160°\)

\(< RQS = 20°\)

Correct Answer: A. 19%

Correct Answer: C. 1001011²

Correct Answer: B. 12% preference share capital account ₦187,500

Correct Answer: C. 540°

Explanation

Sum = (5 - ) 180\(^o\)

= (5 - 2) 180\(^o\) = 3 x 180\(^o\)

= 540\(^o\)

Correct Answer: C. 6.4cm

Explanation

\(\frac{PR}{QR} = \frac{QR}{QY} = \frac{QP}{YR}\) (SSS Congruence)

\(\frac{QR}{4} = \frac{8}{5}\)

\(QR = \frac{4 \times 8}{5}\)

= 6.4 cm

Correct Answer: D. 0.003

Correct Answer: C. 7

Explanation

\(M5_{ten} = 1001011_{two}\\

=1 \times 2^6 + 0\times 2^5 + 0\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 \\

=64+8+2+1=75_{ten}\\

? m = 7 \)