Explanation

(a) \(\frac{x^{2} - 4}{x^{2} + x} \div \frac{x^{2} - 4x + 4}{x + 1}\)

= \(\frac{x^{2} - 4}{x^{2} + x} \times \frac{x + 1}{x^{2} - 4x + 4}\)

= \(\frac{(x - 2)(x + 2)}{x(x + 1)} \times \frac{x + 1}{x^{2} - 2x - 2x + 4}\) (Using difference of two squares)

= \(\frac{(x - 2)(x + 2)}{x} \times \frac{1}{(x - 2)^{2}}\)

= \(\frac{(x + 2)}{x(x - 2)}.

(b) Roots of \(ax^{2} +bx + c = mx + k\)

For graph \(y = ax^{2} + bx + c\),

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

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

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

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

\(x^{2} - x - 2 = 0 ..... (i)\)

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

For graph \(y = mx + k\)

\(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{1 - (-1)}{1.3 - (-1.3)}\)

\(m = \frac{2}{2.6} = 0.769\)

\(k = 0.25\)

\(x^{2} - x - 2 = 0.769x + 0.25\)

\(x^{2} - x - 0.769x - 2 - 0.25 = 0\)

\(x^{2} - 1.769x - 2.25 = 0\)

Using formula method, \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

\(x = \frac{-(-1.769) \pm \sqrt{(-1.769)^{2} - 4(1)(-2.25)}}{2(1)}\)

\(x = \frac{1.769 \pm \sqrt{3.1294 + 9}}{2}\)

\(x = \frac{1.769 \pm 3.483}{2}\)

\(x = \frac{1.769 + 3.483}{2}\) or \(x = \frac{1.769 - 3.483}{2}\)

\(x = \frac{5.252}{2} \approxeq 2.626\) or \(x = \frac{-1.714}{2} \approxeq -0.857\)

(ii) The coordinates of points L, M and N are (-1, 0), (0, 2) and (2, 0) respectively.

Using coordinate for L:

\(0 = a(-1^{2}) + b(-1) + c \implies 0 = a - b + c ..... (1)\)

Using M :

\(2 = a(0^{2}) + b(0) + c \implies c = 2 ...... (2)\)

Using N :

\(0 = a(2^{2}) + b(2) + c \implies 0 = 4a + 2b + c .... (3)\)

From (2), c = 2

\(\therefore (1) : a - b + 2 = 0 \implies a - b = -2 .... (1a)\)

\(\therefore (3) : 4a + 2b + 2 = 0 \implies 4a + 2b = -2 ..... (3a)\)

Solving equations (1a) and (3a) simultaneously, we get

\(a = -1 , b = 1 , c = 2\)

\(\therefore\) Equation of the curve : \(-x^{2} + x + 2 = 0\)

(iii) Line of symmetry = \(x = \frac{-b}{2a}\)

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

Line of symmetry = \(\frac{-1}{2(-1)}\)

\(x = \frac{1}{2}\)

Correct Answer: C. Fertilization

Correct Answer: C. simile

Explanation

The phrase 'She swallowed it all, just like a nasty pill' employs the literary device of simile. A simile is a figure of speech that makes a comparison between two different things using the words 'like' or 'as'. In this case, the author compares the act of swallowing a nasty pill to accepting a difficult situation.

Correct Answer: B. hutches

Correct Answer: D. legitimacy

Correct Answer: C. book keeping records data accounting interprets it

Explanation

In the simplest of terms, bookkeeping is responsible for the recording of financial transactions whereas accounting is responsible for interpreting, classifying, analyzing, reporting, and summarizing the financial data.

Correct Answer: A) Millet

Correct Answer: A. hand Amuka over to the police

Correct Answer: B) study of viruses

Correct Answer: B. Worshiping Baal