Correct Answer: D. -1

Explanation

16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\)

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

--> 4 + x + 1 = 2x + 3 - 3x

collect like terms

--> x - 2x + 3x = 3 - 1 - 4

--> 2x = -2

--> x = -1

Correct Answer: B. 72°

Explanation

\(a . b = |a||b| \cos \theta\)

\(\begin{pmatrix} 13 \\ 1 \end{pmatrix}. \begin{pmatrix} 1 \\ 4 \end{pmatrix} = 13 \times 1 + 1 \times 4 = 13 + 4 = 17\)

\(17 = (\sqrt{13^{2} + 1^{2}})(\sqrt{1^{2} + 4^{2}}) \cos \theta\)

\(17 = (\sqrt{170})(\sqrt{17}) \cos \theta\)

\(\cos \theta = \frac{17}{17\sqrt{10}} = \frac{\sqrt{10}}{10} = 0.3162\)

\(\theta = \cos^{-1} 0.3162 = 72°\)

Explanation

(a) They completed the table of values as shown

(b)(i) The graph

(b)(ii)(\(\alpha\), deduce that 4x\(^2\) - 8x - 21 = 3 - 21 so that y = -18. From the graph, the point of intersection of y = -18 and y = 4x\(^2\) - 8x - 21 was atx = {-0.35 \(\pm\) 0.1, 2.3 \(\pm\) 0.1}

(b)(ii)(\(\beta\)), the equation 4x\(^2\) - 8x - 21 = 0 which can be written as 4x\(^2\) - x - 7x - 21 = -x. This implies that 4x\(^2\) - 8x - 21 = -x.

But, y = 4x\(^2\) - 8x - 21 so that y = -x, Next was to draw the line y = -x and from the graph, the point of intersection with the curve y = 4x\(^2\) - 8x - 21 was at x = {3.3 \(\pm\) 0.1, -1.6 \(\pm\) 0.1}

Correct Answer: A. 22cm²

Correct Answer: C. 25

Correct Answer: C. 5

Explanation

\((x * y) = \frac{x+y}{2}\)

\((3 * b) = \frac{3+b}{2}\)

\(x \circ y = \frac{x^{2}}{y}\)

\((\frac{3+b}{2}) \circ 48 = \frac{(\frac{3+b}{2})^{2}}{48} = \frac{1}{3}\)

\(\frac{(3+b)^{2}}{48 \times 4} = \frac{1}{3}\)

\((3 + b)^{2} = \frac{48 \times 4}{3} = 64\)

\(b^{2} + 6b + 9 = 64 \implies b^{2} + 6b + 9 - 64 = 0\)

\(b^{2} + 6b - 55 = 0 \implies b^{2} - 5b + 11b - 55 = 0\)

\(b(b - 5) + 11(b - 5) = 0 \implies (b - 5) = \text{0 or (} b + 11) = 0\)

Since b > 0, b - 5 = 0

b = 5.

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

Correct Answer: c) 5/7

Explanation

Tan 75\(^o\) = Tan (45\(^o\) + 30\(^o\))

= \(\frac{\tan 45^o + \tan 30^o}{1 - \tan 45^o \tan 30^o}\)

= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)

RATIONALIZE THE DENOMINATOR

= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\) X \(\frac{\sqrt{3} + 1}{\sqrt{3} +1}\)

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

= \(\frac{2(2 + \sqrt{3})}{2}\)

= 2 + \(\sqrt{3}\)

Correct Answer: A. 10.1 years

Explanation

x = 10 ; 10 = \(\frac{x}{25}\)

x = 250

x = \(\frac{250 + 12.4}{26}\)

x = 10.09

x = 10.1 years