Mathematics Questions and Answers

(m + \(\sqrt{3}\))(1 - \(\sqrt{3}\))² = 6 - 2\(\sqrt{2}\)

(m + \(\sqrt{3}\))(4 - 2\(\sqrt{3}\)) = 6 - 2\(\sqrt{2}\)

= 6 - 2\(\sqrt{3}\)

4m - 6 + 4 - 2m\(\sqrt{3}\) = 6 - 2\(\sqrt{3}\)

comparing co-efficients,

4m - 6 = 6.......(i)

4 - 2m = -2.......(ii)

in both equations, m = 3

If \(log_{10} 2 = 0.3010\) and \(log_{10} 3 = 0.4771\),

\(\log_{10} 4.5 = \log_{10}  (\frac{3 \times 3}{2})\)

\(log_{10} 3 + log_{10} 3 - log_{10} 2 = 0.4771 + 0.4771 - 0.3010\)

= 0.6532

\(\frac{8^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{\frac{2}{10^3}}\) = \(\frac{(2^3)^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{(2 \times 5)^{\frac{2}{3}}}\)

= \(\frac{2 \times 5}{2^{\frac{2}{3}} \times 5^{\frac{3}{2}}}\)

= 21 - \(\frac{2}{3}\)

= 2\(\frac{1}{3}\)

= 3\(\sqrt{2}\)

He pays tax on 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)th of his income

20% is 490, 100% is \(\frac{100}{20}\) x 490, N2,450.00

= \(\frac{7}{8}\) of his income = N2,450.00


\(\frac{1}{\frac{7}{8}}\) x 2450

= \(\frac{8 \times 2450}{7}\)

= \(\frac{19600}{7}\)

= N2800.00

Let x represent total number of balls in the basket.

If there are 10 blue balls, \(\frac{1}{8}\) of x = 10

x = 10 x 8 = 80 balls

Green balls will be \(\frac{5}{8}\) x 80 = 50 and black balls = \(\frac{2}{8}\) x 80 = 20

Ratio = Green : black : blue

50 : 20 : 10

-10 : -10 : -
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New Ratio 40 : 10 : 10

4 : 1 : 1