Explanation

\(\frac{625(\frac{3x}{4} - 1) + 125^{(x - 1)}}{5^{(3x - 2)}}\)

\(\frac{5^4(\frac{3x}{4} - 1) + 5^{3(x - 1)}}{5^{(3x - 2)}}\)

\(\frac{5^{3x - 4} + 5^{3x - 3}}{5^{3x} \times 5^{-2}}\)

= \(\frac{5^{3x}(5^{-4} + 5^{-3})}{5^{3x} \times 5{-2}}\)

= \(\frac{5^{-3}(5^{-1} + 1)}{5^{-2}}\)

= 5\(^{-1} (5^{-1} + 1)\)

= \(\frac{1}{5}(\frac{1}{5} + \frac{1}{1}\))

= \(\frac{1}{5} \times \frac{6}{5} = \frac{6}{25}\)

Correct Answer: A. Q`(5, -8)

Explanation

Q(3 -3, 2) = [-(-3) + 2, -4(2)]

= (3 + 2, -8)

= (5, -8)

Explanation

M = \(\begin {pmatrix} 0 & 7 \\ 3 & -1 \end {pmatrix}\)

N = \(\begin {pmatrix} 2 & -1 \\ 5 & 3 \end {pmatrix}\)

(b) p(2,-3) = (2(2) + 3, 5(2) + 3(-3))

= (7, 10 - 9) = (7, 1)

p(7, 1) = (7(1), 2(7) - 1)

= (7, 21, -1) = (7, 20)

(c) Q`(2, 4) = (2(2) - 4, 5(2) + 14)

= (4 - 4, 10 + 12)

= (0, 22)

Correct Answer: C. 6

Explanation

\(^nC_2\) = 15

\(\frac{n!}{(n - 3)! 2!}\) = 15

\(\frac{n(n - 1)(n - 2)!}{(n - 2)!2}\) = 15

n\(^2\) - n = 30

n\(^2\) - n - 30 = 0

(n - 6)(n + 5) = 0

n = 6 or n = -5

Explanation

Frequency Distribution Table

Correct Answer: B. -1

Explanation

8\(^{x - 2}\) = 4\(^{3x}\)

2\(^{3(x - 2)}\) = 2\(^{2(3x)}\)

2 \(^{3x - 4}\) = 2\(^{6x}\)

2 \(^{x - 4}\) = 6\(^x\)

\(\frac{-4x}{-4}\) = \(\frac{4}{-4}\)

x = -1

Correct Answer: C. (1, - \(\frac{3}{2}\))

Explanation

\(\frac{3x^2}{3} + \frac{3y^2}{3} - \frac{6x}{3} + \frac{9y}{3} - \frac{5}{3}\) = 0

2gx = -2x, 2 fy = 3y

g = -1, f = \(\frac{3}{2}\)

Centre (1, - \(\frac{3}{2}\))

Explanation

Substitute x by (x + h) to have f(x + h) = 3(x + h)\(^2\) + 2x + 2h - 1 - 3x\(^2\) - 2x + 1

= 6\(x\)h + 3h\(^2\) + 2h

Divided through by h and obtained \(\frac{f(x + h) - f(x)}{h} = \frac{6 \times h + 3h^2 + 2h}{h} = 6x + 3h + 2\)

Taking limit as h tends to zero, lim\(_{h \to o}\) \(\frac{f(x+h) -f(x)}{h}\)

= lim\(_{h \to o}\) (6x + 3h + 2) so that f\(^1\)(x) = 6x + 2

Correct Answer: C. p = 6, k = 6

Explanation

\(\frac{P}{2} + \frac{k}{3}\) = 5

\(\frac{3p + 2k}{6}\) = 5

2p + 3k = 30

- 2p - k = 6

\(\overline{\frac{4k}{4} = \frac{24}{4}}\)

k = 6

From 2p - k = 6

2p - 6 = 6

\(\frac{2p}{2} = \frac{12}{2}\)

p = 6

Correct Answer: D. 30

Explanation

54 x 40 = 35 x 10 + 60F

160 = 350 + 60F

F = \(\frac{1810}{60}\)

= 30N