Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
-2
-1
\(-\frac{1}{2}\)
1
Correct answer is D
\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)
= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\)
= \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\)
= \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\)
= \(\frac{x + 2}{2x + 3}\)
At x = -1,
= \(\frac{-1 + 2}{2(-1) + 3}\)
= \(\frac{1}{1}\)
= 1
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q.
p = 1, q = 3
p = 1, q = 2
p = -2, q = 3
p = 3, q = -2
Correct answer is B
y = px + q
5 = 3p + q ... (i)
4 = 2p + q ... (ii)
(i) - (ii) : p = 1
∴∴ 5 = 3(1) + q
⟹⟹ q = 5 - 3 = 2
(p, q) = (1, 2)
45 years
48 years
60 years
74 years
Correct answer is C
Let the sons age be x. The father is 4x ∴ 4x - x = 36; 3x = 36; x = 12 The son is 12 years and the father is 12 x 4 = 48. The sum of their ages (12 + 48) years = 60years
Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\)
\(\frac{15}{16}\)
\(\frac{11}{16}\)
\(\frac{49}{50}\)
\(3\frac{1}{5}\)
Correct answer is B
\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)
= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\)
= \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\)
= \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\)
= \(\frac{1}{2} + \frac{3}{16}\)
= \(\frac{11}{16}\)
The nth term of a sequence is \(2^{2n-1}\). Which term of the sequence is \(2^9?\)
3rd
4th
5th
6th
Correct answer is C
\(T_{n} = 2^{2n - 1}\)
\(2^{2n - 1} = 2^9\)
\(2n - 1 = 9 \implies 2n = 9 + 1\)
\(2n = 10 \implies n = 5\)
The 5th term = 2\(^9\)