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Question:

Part A:

Find the measure of the following angles:

<1

<2

<3.

Show your work to justify your answers. Earn up to 1 point for each missing angle with the correct answer and work shown.

Part B:

Answer the following question in 1-2 complete sentences. How is the measure of <1 and the measure of <2 related to the exterior 123° angle?

An electric cable of length 150 m is cut into pieces in such a way that the length of each piece follows the arithmetic progression. If the shortest piece is 0.20 m and the longest piece is 1 m;

a) how many pieces of electric cable can be made out? ( 7 marks )

b) find the sum of the first 20 pieces of electrical cable. ( 3 marks )

a) how many pieces of electric cable can be made out? ( 7 marks )

b) find the sum of the first 20 pieces of electrical cable. ( 3 marks )

1. Find the point of intersection of the following pairs of linea whose equations are given.

a) x + 3y = 9 and 5x - 2y = 11

b) 4x + 3y =8 and 6x - 2y = - 14

c) 3x + 2y - 7 =0 and 5x - 6y = 7

2. Find the equation of the straight line which passes through the origin and through the point of intersection of the lines 4x - y- 3 =0 and x + 2y - 12=0

3. The sides of a triangle are given by the equations 2x + y = 5, x + 2y = 7 and

x - y = 1 find the vertices of the triangle and illustrate with a sketch.

4. Show that the three lines given by the equations 3x + 5y + 7 = 0, x + 2y + 2 = 0 and 2x - y + 9 =0 are concurrent (i. e. Pass through the one point)

a) x + 3y = 9 and 5x - 2y = 11

b) 4x + 3y =8 and 6x - 2y = - 14

c) 3x + 2y - 7 =0 and 5x - 6y = 7

2. Find the equation of the straight line which passes through the origin and through the point of intersection of the lines 4x - y- 3 =0 and x + 2y - 12=0

3. The sides of a triangle are given by the equations 2x + y = 5, x + 2y = 7 and

x - y = 1 find the vertices of the triangle and illustrate with a sketch.

4. Show that the three lines given by the equations 3x + 5y + 7 = 0, x + 2y + 2 = 0 and 2x - y + 9 =0 are concurrent (i. e. Pass through the one point)

The table below gives the proposed prices for two competing airlines

Airline A

Airline B

A1

A2

A3

A4

B1

B2

B3

B4

0.12

-0.23

0.59

-0.05

0.61

0.28

0.19

-0.21

0.18

0.19

0.17

0.01

0.41

0.53

0.13

0.03

Required:

i. Determine the mixed strategies (4 marks)

Calculate the value of the game.

Airline A

Airline B

A1

A2

A3

A4

B1

B2

B3

B4

0.12

-0.23

0.59

-0.05

0.61

0.28

0.19

-0.21

0.18

0.19

0.17

0.01

0.41

0.53

0.13

0.03

Required:

i. Determine the mixed strategies (4 marks)

Calculate the value of the game.

A manufacturing company needs 2500 units of a particular component every year. The company buys it at the rate of Sh. 30 per unit. The order processing cost for this part is estimated at Sh. 15 and the cost of carrying a part in stock comes to about Sh.4 per year. The company can manufacture this part internally. In that case, it saves 20% of the price of the product. However, it estimates a set-up cost of Sh. 250 per production run. The annual production rate would be 4800 units. However, the inventory holding costs remain unchanged.

i. Determine the EOQ and the optimal number of orders placed in a year. (3 marks)

ii. Determine the optimum production lot size and the average duration of the production run. (4 marks)

iii. Should the company manufacture the component internally or continue to purchase it from the supplier? (5 marks)

i. Determine the EOQ and the optimal number of orders placed in a year. (3 marks)

ii. Determine the optimum production lot size and the average duration of the production run. (4 marks)

iii. Should the company manufacture the component internally or continue to purchase it from the supplier? (5 marks)

By use of relevant examples explain the benefits acquired by a business student at the university by taking a unit in Principles of Management

Convert (36.532)8 into an equivalent hexadecimal number.

Convert (4 B F 8)16 into equivalent octal numbers.

A firm uses two inputs, K and L to manufacture final product. The price per unit of these inputs are sh. 20 and sh. 4 respectively. What combination of inputs should a firm use to maximize output given that the budget is fixed at sh. 390?

Find distance of the centre of the circle

x^2+y^2+z^2+x-2y+2z=3, 2x+y+2z=1 from the plane ax+by+cz=d where a,b,c,d are constants. Then Find the equation of the right circular cylinder whose base curve is the circle given above.

x^2+y^2+z^2+x-2y+2z=3, 2x+y+2z=1 from the plane ax+by+cz=d where a,b,c,d are constants. Then Find the equation of the right circular cylinder whose base curve is the circle given above.