Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)
\(( -5, \frac{-13}{3})\)
\(( 5, \frac{-13}{3})\)
\(( 5, \frac{13}{3})\)
\(( -5, \frac{13}{3})\)
Correct answer is B
Find the roots of the equations: \(3m^2 - 2m - 65 = 0\)
= \( m^2 - 15m + 13m - 65 = 0\)
= 3m(m - 5) + 13( m - 5) = 0
( m - 5)(3m + 13) = 0
m-5 = 0 or 3m + 13 = 0
therefore, m = 5 or \(\frac{-13}{3}\)
therefore the roots of the quadratic equation = ( 5, \(\frac{-13}{3})\)
If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
\(m^2 + p \)
2m + p
m + 2p
\(m + p^2\)
Correct answer is C
Given: \(log_a 3\) = m and \(log_a 5\) = p
\(log_a 75\) = \(log_a (3 × 25)\)
= \(log_a (3 × 5^2)\)
= \(log_a 3 + log_a 5^2\)
= \(log_a 3 + 2log_a 5\)
Since \(log_a 3\) = m and \(log_a 5\) = p
∴ \(log_a 75\) = m + 2p
Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
\(\frac{3}{2}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{5}{3}\)
Correct answer is B
\(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
applying the laws of indices
\(2^{5x - x} = 2^{10(1/5)}\)
\(2^{4x} = 2^{10(1/5)}\)
\(2^{4x} = 2^2\)
Equating the powers
then 4x = 2
therefore, x = \(\frac{2}{4}\) = \(\frac{1}{2}\)
12
15
10
14
Correct answer is D
each interior angle of a polygon = \(\frac{(n - 2)\times 180}{n}\) where n = no of side of a polygon
each exterior angle of a polygon = \(\frac{360}{n}\)
then \(\frac{(n - 2)\times 180}{n}\) = 6\(\times\) \(\frac{360}{n}\)
= (n - 2) 180 = 2160
= 180n - 360 = 2160
= 180n = 2160 + 360
= 180n = 2520
therefore, n = \(\frac{2520}{180}\) = 14.
Evaluate, correct to three decimal place \(\frac{4.314 × 0.000056}{0.0067}\)
0.037
0.004
0.361
0.036
Correct answer is D
\(\frac{4.314 × 0.000056}{0.0067}\)
\(\frac{0.000242}{0.0067}\)
= 0.036 ( to 3 decimal places)