If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\)
\(\frac{4}{3}\)
\(\frac{5}{3}\)
\(\frac{3}{4}\)
\(\frac{3}{5}\)
Correct answer is B
m = 2, n = 1
\(\frac{3m^2 - 2n^2}{m^2 _ mn}\)
= \(\frac{3(2)^2 - 2(1)^2}{2^2 + 2(1)}\)
= \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\)
= \(\frac{5}{3}\)
Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)
4\(\sqrt{7} - 21 \sqrt{2}\)
4\(\sqrt{7} - 11 \sqrt{2}\)
4\(\sqrt{7} - 9 \sqrt{2}\)
4\(\sqrt{7} + \sqrt{2}\)
Correct answer is C
2\(\sqrt{28} - 3\sqrt{50} + \sqrt{22}\)
4\(\sqrt{7} - 15\sqrt{2} + 6\sqrt{2}\)
6\(\sqrt{7} - 9\sqrt{2}\)
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
9
10
6
8
Correct answer is B
6, p, 14
14 - p = p - 6
14 + 6 = p - 6
14 + 6 = p + p
\(\frac{2p}{2}\)
= \(\frac{20}{2}\)
p = 10
If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y
4
5
6
7
Correct answer is C
23\(_y\) = 1111\(_{\text{two}}\),
2 x y\(^1\) + 3 x y\(^0\) = 1 x 2\(^3\) + 1 x 2\(^1\) + 1 x 2\(^o\)
2y + 3 = 8 + 4 + 2 + 1
2y + 3 = 15
\(\frac{2y}{2}\)
\(\frac{12}{2}\)
y = 6
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
-\(\frac{1}{3}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
-\(\frac{1}{2}\)
Correct answer is D
\(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
= \(\frac{\log_3 3^2 - \log_2 2^3}{\log_3 3^2}\)
= \(\frac{2 -3}{2}\)
= \(\frac{-1}{2}\)