Adding 42 to a given positive number gives the same result as squaring the number. Find the number
14
13
7
6
Correct answer is C
Let the given positive number be x
Then 4 + x = x2
0 = x2 - x - 42
or x2 - x - 42 = 0
x2 - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
= (x + 6)(x - 7) = 0
x = -6 or x = 7
Hence, x = 7
If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
1\(\frac{5}{16}\)
1\(\frac{1}{16}\)
\(\frac{5}{16}\)
- 1\(\frac{37}{48}\)
Correct answer is D
If m = 4, n = 9, r = 16,
then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)
= \(\frac{64 - 256 + 81}{144}\)
= \(\frac{-111}{144}\)
= - 1\(\frac{37}{48}\)
Find the equation whose roots are \(\frac{3}{4}\) and -4
4x2 - 13x + 12 = 0
4x2 - 13x - 12 = 0
4x2 + 13x - 12 = 0
4x2 + 13x + 12 = 0
Correct answer is C
Let x = \(\frac{3}{4}\) or x = -4
i.e. 4x = 3 or x = -4
(4x - 3)(x + 4) = 0
therefore, 4x2 + 13x - 12 = 0
Factorize completely: 6ax - 12by - 9ay + 8bx
(2a - 3b)(4x + 3y)
(3a + 4b)(2x - 3y)
(3a - 4b)(2x + 3y)
(2a + 3b)(4x -3y)
Correct answer is B
6ax - 12by - 9ay + 8bx
= 6ax - 9ay + 8bx - 12by
= 3a(2x - 3y) + 4b(2x - 3y)
= (3a + 4b)(2x - 3y)
If 2n = y, Find 2\(^{(2 + \frac{n}{3})}\)
4y\(^\frac{1}{3}\)
4y\(^-3\)
2y\(^\frac{1}{3}\)
2y\(^-3\)
Correct answer is A
If 2n = y,
then, 2\(^{(2 + \frac{n}{3})}\) = 22 x 2\(^\frac{n}{3}\)
= 4 x (2n)\(^{\frac{1}{3}}\)
But y = 2n, hence
2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\)
= 4y\(^\frac{1}{3}\)