Explanation

(a) 3 log\(_2\) x = y \(\to\) 2\(^y\) = x\(^3\).............(1)

Similarly, log\(_2\) 4x = y + 4 can be written as 2\(^{y + 4}\) = 4x............(2)

Substituting for 2y in equation (2) to have 16x\(^3\) = 4x and to form a cubic equation 16x\(^3\) - 4x = 0.

Then, using factorizing to have 4x(4x\(^2\) - 1) = 0 and solving for x to get x = 0 or x = \(\frac{1}{2}\) or \(\frac{1}{2}\)

Next, substituting for x in equation (1), when x = 0, y has no solution.

Also, when x = -\(\frac{1}{2}\) y has no solution and when x = \(\frac{1}{2}\), 2\(^y\) = (\(\frac{1}{2}\))\(^3\) = 2\(^{-3}\)

Therefore, y = -3

(b). Substitute to have -3*5 = (-3)\(^2\) - 2(-3) (5) + 5\(^2\) = 2\(^n\) and when simplified to get 64 = 2\(^n\). However, 2\(^6\) = 2\(^n\) so that n = 6.

Correct Answer: C. x - 2

Explanation

\(2x^2 + 3x - 14\)

\(2x^2 + 7x - 4x - 14\)

\(x(2x + 7) - 2(2x + 7)\)

= \((x - 2)(2x + 7)\)

The other factor = (x - 2).

Correct Answer: C. -102

Correct Answer: C. 4

Correct Answer: A. \(\frac{x^2}{2}-2\sqrt{x}+K\)

Correct Answer: B. 9

Explanation

Mean = \(\frac{\sum f x}{\sum f}\)

= \(\frac{350}{10}\)

= 35

= \(\frac{\sum f |d|}{\sum f}\)

= \(\frac{90}{10}\)

= 9

Correct Answer: C. 6.5

Explanation

Firstly; solving for x

6 = \(\frac{2 + 5 + x+1 + x+2 + 7 + 9}{6}\)

cross multiply to have:

6 * 6 = 2 + 5 + x+1 + x+2 + 7 + 9

36 = 2x + 26

36 - 26 = 2x

10 = 2x

x = 5

Median = \(\frac{7+6}{2}\)

→ 6.5

Correct Answer: B. 80

Explanation

Sum of interior angles in a quadrilateral is 360

(x + 20)^o + (x+ 10)^o + (2x - 45)^o + (x - 25)^o = 360^o

5x^o - 40^o = 360^o

x = 400/5 = 80^o

Correct Answer: A. (1, 2)

Explanation

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

\(\implies 2^{2 + x^{2}} = 2^{3x}\)

Comparing bases, we have

\(2 + x^{2} = 3x \implies x^{2} - 3x + 2 = 0\)

\(x^{2} - 2x - x + 2 = 0 \)

\(x(x - 2) - 1(x - 2) = 0\)

\((x - 1) = 0\) or \((x - 2) = 0\)

\(x = \text{1 or 2}\)

Correct Answer: D. 60

Explanation

Let number of children's ticket at N250.00 each = \(x\)

∴ Number of adult tickets at ?520.00 each = 5\(x\)

Then,

Total amount of money received from children's tickets = 250\(x\)

Total amount of money received from adult tickets = 520(5\(x\))

⇒ 250\(x\) + 520(5\(x\)) = 171,000

⇒ 250\(x\) + 2600\(x\) = 171,000

⇒ 2850\(x\) = 171,000

⇒ \(x = \frac{171,000}{2850} = 60\)

∴ 60 tickets were sold at N250.00 and 300 tickets were sold at N520.00