Correct Answer: C. anger

Explanation

(a) From y = (x\(^2\) - x + 1)(x - 2) - x + 1)(x - 2)

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

dy/dx = 3x\(^2\) - 6x + 3

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

(x - 1) = 0 twice ; x = 1

y = (1\(^2\) - 1 + 1) (1-2) ; y = -1

Gradient m\(_1\) of tangent = y/x = -1/1 = -1

Using m\(_1\)m\(_2\) = -1

Gradient, m\(_2\) of normal =1

Using y-y\(_1\) = m\(_2\)(x - x\(_1\))

y + 1 = x - 1; x - y - 2 = 0

x\(_1\),y\(_1\) = ( -1, 2), , x\(_2\),y\(_2\), =(3, -4)

Mid point of PR =\(\frac{3-1,-4+2}{2,2}\)

= (1-1)

Using \(\frac{y_2 - y_1}{x_2 - x_1}\) = \(\frac{y - y_1}{x - x_1}\)

\(\frac{1-{-1}}{5-1}\) = \(\frac{y-1}{x-5}\);

\(\frac{2}{4}\) = \(\frac{y-1}{x-5}\)

2(y-1) = x - 5; 2y - 2 = x - 5

2y - x = -3

x - 2y -3 =0

Correct Answer: D. Prospectus

Correct Answer: D. 12

Explanation

To answer this question, you need to know the first ten prime numbers! Remember, prime numbers are all of the integers that are divisible only by themselves and by 1. They do not include 1. So, our list is: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 The median is the middle value. There is no proper middle since we have an even number of values. We need to take the 5th and the 6th elements (the middle two values) and average them. The 5th term is 11 and the 6th is 13; therefore, the median is: 11+13/2=24/2=12

Correct Answer: A. political sovereignty

Correct Answer: D. loss

Correct Answer: D) That Gentiles should abstain from love of the world

Explanation

The question is asking you to identify the decision that was not reached at the Council of Jerusalem regarding Gentiles who became Christians. The Council of Jerusalem was a meeting of the early Christian leaders to discuss the issue of whether Gentile converts to Christianity needed to follow Jewish customs and laws, such as circumcision.

Option A states that Gentiles should abstain from what has been sacrificed to idols, which was one of the decisions made at the Council. Option B states that Gentiles should abstain from blood, which was also one of the decisions made. Option C states that Gentiles should abstain from what is strangled, which was also decided upon at the Council.

Option D is the correct answer, as the Council did not make a decision that Gentiles should abstain from the love of the world. This option is not related to the issue being discussed at the Council, which was about whether Gentile converts needed to follow Jewish customs and laws.

In summary, the decision that was not reached at the Council of Jerusalem regarding Gentiles who became Christians is that they should abstain from the love of the world. The other decisions made were that Gentiles should abstain from what has been sacrificed to idols, blood, and what is strangled.

Correct Answer: C. aggravated

Correct Answer: B. energy

Explanation

stamina; the ability to sustain prolonged physical or mental effort..

synonyms; energy, vigour, perseverance, strength.

Correct Answer: C. \(\frac{7}{40}\)

Explanation

\(\frac{5}{8} - \frac{3}{4} ÷ \frac{5}{12} x \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{3}{4} ÷ \frac{5}{12}) \times \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{3}{4} \times \frac{12}{5}) \times \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{9}{5} \times \frac{1}{4})\)

⇒ \(\frac{5}{8} - \frac{9}{20}\)

∴ \(\frac{7}{40}\)