If f(x) = x² − 4x + 3, find
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the domain and range of f(x)
Find the maximum value of the quadratic equation 2 + 30t − 5t²
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Siti is thinking of two whole numbers x and y. Twice the first is greater than or equal to 3. But the first number is greater than three times the second. Furthermore, three times the first number is at most equal to 6 plus the second number. Find the two numbers.
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A shopkeeper buys two types of sugar; white sugar and brown sugar. The white sugar is sold at shs. 40,000/= per bag and the brown sugar is sold at shs. 60,000/= per bag. He has shs. 1,500,000/= available and decides to buy at least 30 bags altogether. He has also decided that at least one third of the bags should be brown sugar. He buys x bags of white sugar and y bags of brown sugar.
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(a) Write down three (3) inequalities which will summarize the above information.
(b) Represent these inequalities graphically.
(c) The shopkeeper makes a profit of shs. 10,000/= from a bag of white sugar and shs. 20,000/= from a bag of brown ...
Two types of food, A and B, contain 4 and 6 units of proteins, and 5 and 3 units of starch per kg respectively. The cost of A is shs. 400.00 per kg. The cost of B is shs. 500.00 per kg. If the minimum daily intake is 16 units of protein and 11 units of starch, how much food should be bought in order to meet these conditions?
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A certain secondary school intends to buy two types of Basic Mathematics reference books. The school wants between 10 and 15 books (inclusive) of author A which cost 8,000/= each. Books from author B cost 10,000/= each. If the school has 240,000/=, what is the maximum number of books that the school can buy?
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A bread dealer can buy up to 150 loaves of bread. Premium bread costs 200/= per loaf and Royal bread costs 250/= per loaf. The dealer can spend not more than 36,000/= in the business. Premium bread sells at a profit of 40/= per loaf, while Royal bread sells at a profit of 50/= per loaf. How many loaves of bread of each type should the dealer buy in order to generate a maximum profit?
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M & P Contractor has 150 tons of sand and 90 tons of cement for building structures A and B for business. Structure A requires 1 ton of sand and 2 tons of cement whereas structure B requires 3 tons of sand and 1 ton of cement. If structure A is sold at shs. 40,000/= and structure B at shs. 60,000/=, how many structures of each type should be made in order to get maximum profit?
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Find the image of point A(3, 4) after its reflection in the line y+x = 0 followed by another reflection in the line y = 0.
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Find the image of the line 2x − 7y + 14 = 0 under a reflection in the x-axis.
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