Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\), find the value of (x + y)
1\(\frac{3}{5}\)
1\(\frac{2}{5}\)
1\(\frac{1}{5}\)
\(\frac{1}{5}\)
Correct answer is C
\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\)
cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) = x\(\sqrt{5}\) + 5y\(\sqrt{3}\)
Collect like roots : x\(\sqrt{5}\) = \(\sqrt{5}\) → x = 1
5y\(\sqrt{3}\) = \(\sqrt{3}\) → y = \(\frac{1}{5}\)
∴ ( x + y ) = 1 + \(\frac{1}{5}\)
= 1\(\frac{1}{5}\)
N470,000.00
N480,000.00
N490,000.00
N500,000.00
Correct answer is D
S.I = \(\frac{x \times 2 \times 5}{100}\) = 0.1x
A = P + S.I
550,000 = x + 0.1x
\(\frac{550,000}{1.1} = \frac{1.1x}{1.1}\)
x = N500,000
If 101\(_{\text{two}}\) + 12y = 3.3\(_{\text{five}}\). Find the value of y
8
7
6
5
Correct answer is C
012 + 01 = 01
101\(_2\) + 12\(_y\) = 2.3\(_5\)
1 x 2\(^o\) + 0 x 2\(^o\) + 1 x2\(^2\) + 1 x y\(^o\) + 2 x y\(^1\) = 3 x 5\(^o\) + 3 x 5\(^1\)
1 + 4 + 1 + 2y = 3 + 15
6 + 2y = 18
2y = 18 - 6
\(\frac{2y}{2} = \frac{12}{2}\)
y = 6
Express 1 + 2 log10\(^3\) in the form log10\(^9\)
log10\(^{90}\)
log10\(^{19}\)
log10\(^{9}\)
log10\(^{6}\)
Correct answer is A
1 + 2log\(_{10}^3\)
= log\(_{10}^{10} + log_{10}^{3^2}\)
= log\(_{10}^{10} + log_{10}^{9}\)
= log\(_{10}^{10 \times 90}\) = log\(_{10}^{90}\)
Simplify; [(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
\(\frac{3}{4}\)
\(\frac{9}{16}\)
\(\frac{3}{8}\)
\(\frac{1}{4}\)
Correct answer is C
[(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\frac{9}{16}\))]\(^{\frac{3}{2}}\) x [(\(\frac{1}{16}\))\(^{\frac{3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\sqrt{\frac{9}{10}}\))\(^3\) x (4\(\sqrt{\frac{1}{16}})^3\)]\(^{\frac{1}{3}}\)
= [(\(\frac{3}{4})^3 \times (\frac{1}{2})^3\)]\(^\frac{1}{3}\)
(\(\frac{27}{64} \times \frac{1}{8}\))\(^\frac{1}{3}\) = \({3}\sqrt{\frac{27}{64} \times \frac{1}{8}}\)
= \(\frac{3}{4} \times \frac{1}{2}\) = \(\frac{3}{8}\)