Factorize the expression 2s\(^2\) - 3st - 2t\(^2\).
(2s - t)(s + 2t)
(2s + t)(s - 2t)
(s + t)(2s - 1)
(2s + t)(s -t)
(2s + t)(s + 2t)
Correct answer is B
2s\(^2\) - 3st - 2t\(^2\)
= 2s\(^2\) - 4st + st - 2t\(^2\)
= 2s(s - 2t) + t(s - 2t)
= (2s + t)(s - 2t)
Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)
1/6
3/8
1/2
3/4
6
Correct answer is B
\(\frac{\log \sqrt{27}}{\log 81}\)
= \(\frac{\log \sqrt{3^3}}{\log 3^4}\)
= \(\frac{\log 3^{\frac{3}{2}}}{\log 3^4}\)
= \(\frac{\frac{3}{2} \log 3}{4 \log 3}\)
= \(\frac{\frac{3}{2}}{4}\)
= \(\frac{3}{8}\)
Simplify: \(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
1/4
0
1
2
4
Correct answer is D
\(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
= \(\frac{16^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}\)
= \(\frac{(2^4)^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}\)
= \(\frac{2^3}{4}\)
-2
1
2
6
12
Correct answer is A
when n = 2
(-1)\(^{n-2}\) 2\(^{n+1}\) = 2
When n = 3
(-1)\(^{n-2}\) 2\(^{n+1}\) = -4
Sum = 2 - 4 = -2
A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement
27/9%
26/7%
5%
277/9%
284/7%.
Correct answer is B