A man bought 220 mangoes at N5x. He sold each for 3x kobo and made a gain of N8. Find the value of x
2
5
6
10
Correct answer is B
The cost price of the whole mangoes = N5x
The sold amount of the mangoes = 3x * 220 = N6.60x
The gain made on mangoes = N6.60x - N5x = N8.00 => N1.60x = N8 => \(x=\frac{8}{1.60}=\frac{1}{0.2}=\frac{10}{2}=5\)
Find the equation whose roots are 2 and \(-3\frac{1}{2}\)
2x2 + 3x + 14 = 0
2x2 + 5x + 7 = 0
2x2 + 5x - 7 = 0
2x2 + 3x - 14 = 0
Correct answer is D
x2 (sum of roots)x + (product of roots) = 0
Sum of roots \(2+-3\frac{1}{2} = -1\frac{1}{2}=-\frac{1}{2}\)
Product of roots \(=2 \times -3\frac{1}{2}=-7\\
x^2-\left(\frac{-3}{2}\right)x+(-7)=0\Rightarrow 2x^2 + 3x - 14 = 0\)
Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)
31.12
3.112
2
1
Correct answer is C
\(log_{10}18 - log_{10}2.88+log_{10}16\\
=log_{10}18 - log_{10}\left(\frac{288}{100}\right)+log_{10}16 = log_{10}\left(\frac{18\times 16}{1}\times \frac{100}{288}\right)\\
=log_{10}\left(\frac{288\times 100}{288}\right)=log_{10}100=log_{10}10^2=2log_{10}10=2\)
33
8
7
0
Correct answer is C
\(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div\frac{33}{2}\\
=\frac{15}{2}-\left(\frac{5}{2}+\frac{3}{1}\right)\times\frac{2}{33}\\
=\frac{15}{2}-\left(\frac{5+6}{2}\right)\times \frac{2}{33}=\frac{15}{2}-\frac{11}{2}\times \frac{2}{33}=\frac{15}{2}-\frac{1}{3}\\
=\frac{45-2}{6}=\frac{43}{6}\)
Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)
\(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
\(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
\(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
\(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)
Correct answer is D
\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\\
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)