JAMB Mathematics Past Questions & Answers - Page 312

(x + 15)° + (2x - 45)° + (x + 10)° = (2n - 4)90°

when n = 4

x + 15° + 2x - 45° + x - 30° + x + 10° = (2 x 4 - 4) 90°

5x - 50° = (8 - 4)90°

5x - 50° = 4 x 90° = 360°

5x = 360° + 50°

5x = 410°

x = \(\frac{410^o}{5}\)

= 82°

Hence, the value of the least interior angle is (x - 30°)

= (82 - 30)°

= 52°

P = \(\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}\)

|P| = 2 - 1 x -3 = 5

P-1 = \(\frac{1}{5}\)\(\begin{pmatrix} 1 & 3 \\ -1 & 2 \end{pmatrix}\)

= \(\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}\)

\(\begin{vmatrix} 2 & 0 & 5 \\ 4 & 6 & 3 \\ 8 & 9 & 1 \end{vmatrix}\)

= 2(6 - 27) - 0(4 - 24) + 5(36 - 48)

= 2(-21) - 0 + 5(-12)

= -42 + 5(-12)

= -42 - 60

= -102

Using S\(\infty\) = \(\frac{a}{1 - r}\)

r = \(\frac{0.05}{0.5}\) = \(\frac{1}{10}\)

S\(\infty\) = \(\frac{0.5}{{\frac{1}{10}}}\)


= \(\frac{0.5}{({\frac{9}{10}})}\)

= \(\frac{0.5 \times 10}{9}\)

= \(\frac{5}{9}\)

-6 \(\leq\) 4 - 2x < 5 - x
split inequalities into two and solve each part as follows:

-6 \(\leq\) 4 - 2x = -6 - 4 \(\leq\) -2x

-10 \(\leq\) -2x

\(\frac{-10}{-2}\) \(\geq\) \(\frac{-2x}{-2}\)

giving 5 \(\geq\) x or x \(\leq\) 5

4 - 2x < 5 - x

-2x + x < 5 - 4

-x < 1

\(\frac{-x}{-1}\) > \(\frac{1}{-1}\)

giving x > -1 or -1 < x

Combining the two results, gives -1 < x \(\leq\) 5