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)
\(2311_5\)
\(1131_5\)
\(1311_5\)
\(2132_5\)
Correct answer is C
\(413_7\) to base 5
convert first to base 10
\(417_7 = 4 × 7^2 + 1 × 7^1 + 3 × 7^0\)
= 4 × 49 + 1 × 7 + 3 × 1
= 196 + 7 + 3
= \(206_{10}\)
convert this result to base 5
| 5 | 206 |
| 5 | 41R1 |
| 5 | 8R1 |
| 5 | 1R3 |
| 0R1 |
\(∴ 413_7 = 1311_5\)
For what value of x is \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\) is undefined?
\(\frac{1}{5}, \frac{3}{2}\)
\(\frac{-1}{5}, \frac{3}{2}\)
\(\frac{1}{5}, \frac{-3}{2}\)
\(\frac{-1}{5}, \frac{-3}{2}\)
Correct answer is B
The fraction \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\) is undefined when the denominator is equal to zero
\(then 10x^2 - 13x - 3 = 0\)
by factorisation, \(10x^2 - 13x - 3\) = 0 becomes \( 10x^2 - 15x +2x -3\) = 0
\(5x(2x - 3) + 1(2x - 3) = 0\)
\((5x + 1)(2x - 3) = 0\)
\(then, x = \frac{-1}{5}\) or \(\frac{3}{2}\)