Explanation

(a) \(\frac{\log_28 + \log_216 - 4\log_22}{\log_416}\) = \(\frac{\log_22^3 + \log_2 2^4 - 4\log_22}{\log_44^2}\)

= \(\frac{3 \log_2 2 + 4\log_22 - 4 \log_2^2}{2 \log 4^4}\)

But log\(_2\) 2 = \(\log_44 = 1\)

Then, \(\frac{\log_28+\log_216 - 4 \log_2^2}{\log_416}\) = \(\frac{3 + 4 - 4}{2}\) = 1\(\frac{1}{2}\)

(b) Subtract 241\(_{five}\) to get 1101\(_{five}\). Thereafter, converting to base ten to find the value of x = (5\(^3\) x 1) + (5\(^2\) x 1 + (5\(^1\) x 0) + (5\(^o\) x 1) = 125 + 25 + 0 + 1 = 151

(b) They subtracted 241\(_{five}\) from 1342\(_{five}\) to get 1101\(_{five}\). Thereafter, converting to base ten to find the value of x = (5\(^3\) x 1) + (5\(^2\) x 1) + (5\(^1\) x 0) + (5°x 1) = 125 + 25 + + 1 = 151.

Correct Answer: B. 45

Explanation

\(^{3^2 + 1}\)C\(_{3+5}\)

\(^{9 + 1}\)C\(_{3+5}\)

\(^{10}\)C\(_{8}\) = \(\frac{10!}{8! 2!}\)

\(\frac{10 * 9 * 8!}{8! 2!}\) = \(\frac{10 * 9}{2}\)

= 45

Correct Answer: b. 9/20

Correct Answer: D. N260

Correct Answer: B. 2x² - 11x + 15

Explanation

(2x - 5)(x - 3)

2x² - 5x - 6x + 15

2x² - 11x + 15

Correct Answer: A. 45°

Explanation

Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\)

\(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\)

\(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\)

P + 8 - 8 = \(\frac{\theta \pi}{456o}\)

\(\pi = \frac{\theta \pi}{45^o}\)

\(\theta \pi = 45^o\)

Correct Answer: D. 2√5

Explanation

p(4, 3) Q(2 - 1)

distance = \(\sqrt{(x_2 - x_1)^2 + (Y_2 - y_1)^2}\)

= \(\sqrt{(2 - 4)^2 + (-1 - 3)^2}\)

= \(\sqrt{(-2)^2 = (-4)^2}\)

= \(\sqrt{4 + 16}\)

= \(\sqrt{20}\)

= \(\sqrt{4 \times 5}\)

= 2\(\sqrt{5}\)

Correct Answer: D. x = 4 and y = 1

Explanation

3x - 2y = 10 - - x 3

x + 3y = 7 ---x 2

------------------------

9x - 6y = 30

2x + 6y = 14

-------------------------

\(\frac{11x}{11} \frac{44}{11}\)

x = 4

From x + 3y = 7

3y = 7 - 4

\(\frac{3y}{3}\) = \(\frac{3}{3}\)

y = 1

Correct Answer: A. (3 N, 020°)

Correct Answer: B. 81