Correct Answer: B. \(-1\)

Explanation

\(f(x) = \frac{3x + 1}{x^{2} - 1}\)

\(f(-3) = \frac{3(-3) + 1}{(-3)^{2} - 1} = \frac{-8}{8} = -1\)

Correct Answer: B. baptized into His death

Correct Answer: B. is convicted of a serious crime

Correct Answer: A. Rock fall

Correct Answer: C) overshadowed by

Explanation

The most logical and precise choice to complete the text would be C) overshadowed by. The sentence states that when considering an interstate move, state taxes are overshadowed by other factors such as employment opportunities, housing availability, and climate. This implies that state taxes have little influence or significance compared to those other factors.

Explanation

Properties of cathode rays that show particle nature of matter:

- Casting of shadows of objects along their path.

- They have momentum

- Heat up objects that stop thorn, that is they obey energy conservation law.

- They are deflected in electric or magnetic fields, showing they are tiny particles of matter, etc.

Explanation

(a) Personal selling; is a direct, face-to-face or person-to-person communication with the customer. A personnel of the firm comes into contact with the customer and shows the customer how to use the product. The salesperson must be courteous, tactful and have a clear knowledge of the product being marketed.

(b) Reasons why firms engage in personal selling are:

(i) It allows the sales person to foresee a customer's particular needs and problems.

(ii) It makes it possible for immediate feedback from the customers.

(iii) It is also an important public relations tool utilized by firms to project their image.

(iv) It is good when a new product is to be introduced.

(v) It is also used by firms that sell technical goods requiring installation and demonstration on how to use such technical product.

(vi) Personal selling provides the firm the opportunity to obtain firm orders and also sales are made on the spot.

Explanation

Cultivation of maize (a) Land Preparation: (1) land should be cleared (ii) land should be ploughed. (iii) land should be harrowed (iv) ridges can also be prepared

(b) Propagation: (i) propagated by seed. (ii) may be planted manually. (iii) may be planted machanically.

(c) Planting Date: (i) early maize is planted between March and April. (ii) late maize is planted in August. (iii) maize (early or late) is also planted depending on location and rainfall.

(d) Seed Rate: (i) 25 - 30kg maize seed is recommended per hectare. (ii) 2 - 3 seeds are also recommended per hole. (iii) quantity usually depends on spacing I plant population desired.

(e) Spacing: (i) as sole crop, is 25cm along the the row and 75cm between the row, that is 25cm x 75cm. (iii) also 30cm x 90cm along and between the row respectively.

(f) Fertilizer Requirements: (i) apply 200kg (4 bags) of NPK 15:15:15 per hectare at planting. (ii) apply 250kg (5 bags) of CAN or 150kg (3 bags) of Urea per hectar, 5 - 6 weeks after planting. (iii) apply farmyard/poultry dropping/ organic manure as side dressing or by broadcast method.

(g) Weeding: (i) should be done regularly and manually (hoeing, cutlassing.) (iii) done chemically. (iv) done mechanically.

(h) Harvesting: (i) matures 90 - 120 days after planting. (ii) harvested either green or dry. (iii) mostly harvested green for consumption when the silk dries and turns brown. (iv) harvested by plucking the cobs on a small scale and by machines such as corn-picker on a large scale.

(i) a Storage: (i) cobs are stored in cribs, on a small scale (ii) cobs are stored in rhumbus, on a small scale. (iii) cobs are stored in a fire-place, on a small scale (iv) dry grains are stored in silos, on a large scale. (v) store in air - tight

Correct Answer: D. faith in Christ crucified

Explanation

(ai) Let the quadratic equation be \(ax^2+bx+c\)

\(g(x)=ax^2+bx+c\)

Since \((2x+1)\) is a factor,\(x=-\frac{1}{2}\)is a root

\(∴g(-\frac{1}{2})=a(-\frac{1}{2})^2+b(-\frac{1}{2})+c=0\)

\(=a(\frac{1}{4})-b(\frac{1}{2})+c=0\)

Multiply through by 4

=a-2b+4c=0-----(i)

For(x-1)and(x-2),x=1 and x = 2 respectively

So,

\(g(1)=a(1)^2+b(1)+c=-6\)

=a+b+c=-6-----(ii)

and

\(g(2)=a(2)^2+b(2)+c=-5\)

= 4a+2b+c=-5

Adding equations (i) and (iii) gives;

=5a+5b=-5

Divide through by 5

=a+b=-1......(iv)

Adding equation (i) to 2 times equation (iv) gives:

3a+6c=-12.....(v)

Equation (v) minus three times equation (iv) gives:

=3c=-12-(-3)

=3c=-9

=c\(\frac{-9}{3}=-3\)

Substitute (-3) for c in equation (v)

=3a+6(-3)=-12

=3a-18=-12

=3a=-12+18

=3a=6

=a=\(\frac{6}{3}=2\)

Substitute 2 for a and (-3) for c in equation (ii)

=2+6-3=-6

=b-1=-6

=b=-6+1

=b=-5

\(\therefore g(x)=2x^2-5x-3\)

(aii) \(2\times2 - 5x - 3\)

\(= 2\times2 - 6x + x - 3\)

\(= 2x(x - 3) + 1(x - 3)\)

\(= (x - 3)(2x + 1)\)

zeros of \(g(x)\) are \(2x + 1 = 0\) and \(x - 3 = 0\)

∴ zeros of \(g(x)\) are -\frac{1}{2}\) and \(3\)

(b) \((\frac{x}{2}-1)^8\)

rth term is given as \(^nC_r-1 a^n-(r-1)b^r-1\)

\(a=\frac{x}{2},b=-1,n=8,r=3,r-1=2\)

3rd term = \(^8C_2(\frac{x}{2})^8-2(-1)^2\)

= \(28×(\frac{x}{2})^6\times1\)

∴3rd term = \(28\times \frac{x^6}{64}=\frac{7x^6}{16}\)