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A triangle T With vertices A (2,4), B (6,2) and C (4,8) is mapped onto triangle T’ with vertices A’(l0,0) , B'(8,—4) and C'(14,—2) by a rotation. (a) On the grid provided draw triangle T and its image. (2 marks) (b) Determine the centre and angle of rotation that maps T onto T’.
A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the firm hired 4 technicians and 1 artisan and paid a total of Ksh 9500‘ Calculate the cost of hiring 2 technicians and 5 artisans in a day
Suppose that X takes values between 0 and 1 and has probability density function 2x. Compute Var(X) and Var(X2).
Two lines L1: 2y — 3x 6 = 0 and L2: 3y + x — 20 = 0 intersect at a point A. (a) Find the coordinates of A. (3 marks) (b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants. (3 marks) (c) Another line L4 is parallel to L1 and passes through (—l,3). Find the x and y intercepts of L 4
The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°. (a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D. (4 marks) (b) Use the scale drawing to determine: (i) the bearing of A from D; (1 mark) (ii) the distance BD in kilometres.
. Convert 2πC/9 into degrees.
A trader bought maize for Ksh 20 per kilogram and beans for Ksh 60 per kilogram. She mixed the maize and beans and sold the mixture at Ksh 48 per kilogram. If she made a 60% profit, determine the ratio maize to beans per kilogram in the mixture
Evaluate correct to four decimal places, hence Write the answer in standard form.