# Solve the equation 2m2– 5m -3 = 0

a) Solve the equation 2m2– 5m -3 = 0

(3 marks )
b) Two adjacent sides of a rectangle are of lengths (x+4) cm and (x+6) cm. the area of the rectangle is equal to twice the area of the square whose side is x. what are the

dimensions of the rectangle?(5 marks )

c) A researcher in Kisumu City has randomly interviewed individuals in the city centre. The following are the data he collected: 40 of those interviewed are Christians; 25 were Kenyans; 10 were Kenyan Christians; 35 were neither Kenyan nor Christians. Using Venn diagram, find the following:

(i) The number of Christians non-Kenyans.

(ii) The number of Kenyan non-Christians.

(iii) The total number of individuals interviewed. (5marks)

d) Broadway has the capacity to produce three types of cookies X, Y and Z using ingredients P, Q and R. the recipe for each unit of cake is given as follows:

X – 20 , 15 and 40 grams of P, Q and R respectively

Y – 12 , 36 and 16 grams of P, Q and R respectively

Z – 30 , 15 and 40 grams of P, Q and R respectively

If 130, 225 and 200 units of P, Q and R respectively must be used. Formulate a set of simultaneous equations and solve them such that they would indicate the number of units of each cookie to produce in order to utilize completely the available ingredients.

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