Correct Answer: B. 7

Explanation

A heptagon is a 7-sided shape.

Correct Answer: B. 7

Correct Answer: D) van der Waal's forces

Correct Answer: B) Revaluation reserve

Explanation

(i) Constitutional division of powers: Powers are constitutional shared between the central authority and other subordinate units, e.g state and local government

(ii) Derivation of powers from the constitution: The central, state and local governments derive their powers from the constitution

(iii) Supremacy of the constitution: The constitution of a Federal state is powerful and supreme.

(iv) Written and Rigid: The constitution of most federal systems are written and rigid

(v) Separation of powers: The constitution separate the functions and powers among three organs of government, namely: executive, legislature, and judiciary

(vi) Bicameral legislature: Most of the federal constitutions have bicameral legislature. For example, in Nigeria and the USA, there are the senate and the House of Representatives.

(vii) The supreme court: There is always a supreme court that interprets the constitution and decides on any conflict between the Centre and the constituents units

(viii) Equal representation: Every interest group is recognized and represented in federalism.

Correct Answer: A. homicide

Explanation

The correct word to complete the sentence is 'homicide'. The defendant was charged with homicide because he caused his neighbour's death. This is because 'homicide' is a legal term for any killing of a human being by another human being. In this context, it refers to the crime the defendant was charged with for causing his neighbour's death.

Correct Answer: C. ozone layer depletion

Explanation

(a) \(x = 3i - j ; y = 2i + kj\)

\(x \cdot y = |x||y| \cos \theta\)

\((3i - j) \cdot (2i + kj) = (\sqrt{3^{2} + (-1)^{2}})(\sqrt{2^{2} + k^{2}}) \cos \theta\)

\(6 - k = (\sqrt{10})(\sqrt{4 + k^{2}})(\frac{\sqrt{5}}{5})\)

\(5(6 - k) = \sqrt{10(4 + k^{2})(5)}\)

\(30 - 5k = \sqrt{200 + 50k^{2}}\)

\((30 - 5k)^{2} = 200 + 50k^{2}\)

\(900 - 300k + 25k^{2} = 200 + 50k^{2}\)

\(900 - 200 - 300k + 25k^{2} - 50k^{2} = 0\)

\(25k^{2} + 300k - 700 = 0 \implies k^{2} + 12k - 28 = 0\)

\(k^{2} - 2k + 14k - 28 = 0 \implies k(k - 2) + 14(k - 2) = 0\)

\(\text{k = 2 or -14}\).

(b)

ABCD is a parallelogram if AD = BC.

\(\overrightarrow{AD} = \overrightarrow{AB} + \overrightarrow{BD}\)

= \(\begin{pmatrix} -5 \\ -1 \end{pmatrix} + \begin{pmatrix} 4 \\ -7 \end{pmatrix}\)

= \(\begin{pmatrix} -1 \\ -8 \end{pmatrix}\)

\(\overrightarrow{BC} = \overrightarrow{BA} + \overrightarrow{AC}\)

= \(\begin{pmatrix} 5 \\ 1 \end{pmatrix} + \begin{pmatrix} -6 \\ -9 \end{pmatrix}\)

= \(\begin{pmatrix} -1 \\ -8 \end{pmatrix}\).

\(\overrightarrow{AD} = \overrightarrow{BC}\). ABCD is a parallelogram.

Correct Answer: C. inspite of the old covenant, Israel has proved faithless to God

Correct Answer: C. Col

Correct Answer: C. N2,141