Simplify \(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\)
\(\frac{3}{5}\)
\(\frac{2}{5}\)
\(\frac{2m - u}{5m + u}\)
\(\frac{m - 2u}{m + 5u}\)
Correct answer is A
\(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\)
= \(\frac{2m - u + m - 2u)(2m - u - m + 2u)}{5(m + u)(m - u)}\)
= \(\frac{3(m - u)(m + u)}{5(m + u)(m - u)}\)
= \(\frac{3}{5}\)
Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\)
0.141
0.301
0.667
0.707
Correct answer is D
\(\frac{1}{\sqrt{2}}\) = \(\frac{1}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\)
= \(\frac{1.414}{2}\)
= 0.707
Simplify \(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)
5√3
6√3
8√3
18√3
Correct answer is B
\(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)
Rearrange = \(\sqrt{48}\) + \(\sqrt{75}\) - \(\frac{9}{\sqrt{3}}\)
= (√16 x √3) + (√25 x √3) - \(\frac{9}{\sqrt{3}}\)
=4√3 + 5√3 - \(\frac{9}{\sqrt{3}}\)
Rationalize \(\to\) 9√3 = \(\frac{9}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)
= \(\frac{9\sqrt{3}}{\sqrt{9}}\) - \(\frac{9\sqrt{3}}{\sqrt{3}}\)
= 3√3
Without using table, solve the equation 8x-2 = \(\frac{2}{25}\)
4
6
8
10
Correct answer is D
8x-2 = \(\frac{2}{25}\)
= 200x-2 = 2
= 100x-2 = 1
x-2 = \(\frac{1}{100}\)
x-2 = 10-2
x = 10
Evaluate \(\frac{log_5 (0.04)}{log_3 18 - log_3 2}\)
1
-1
\(\frac{2}{3}\)
-\(\frac{2}{3}\)
Correct answer is B
\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)
= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\)
= \(\frac{log_5 0.04}{log_3 9}\)
= \(\frac{-2}{2}\)
= -1
Let log5 0.04 = x
5x = 0.04
x = \(\frac{4}{100}\) = 5-2
Let log3 9 = z
32 = 32
z = 3