Width ?8 Length ?20 Width < 3ft Length <6ft below. Width >3ft Length >6ft First integer <10 Second integer <11 First integer ? 7 Second integer ? 9 Width < 3 meters Length <30 meters PROBLEMS 1. The product of two positive integers has a minimum value of 63. The second integer is 2 more than the first integer. Find the possible values of the integers. 2. The area of a pathway is at most 90 m². Its length is 10 times longer than its width. What are the possible measures of the length? 3. The product of two consecutive positive inters is less than 100. Find the inters. 4. The area of a garden is at most 160 m². The length of the garden is 4 more than SOLUTIONS
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The product of two positive integers has a minimum value of 63. The second integer is 2 more than the first integer. Find the possible values of the integers. Let's assume the first integer is x. Then the second integer is x + 2. The product of these two integers Show more…
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MELC Evaluation. The CODE: relationship between the coefficients and the roots of quadratic equation. COMPETENCY: The learner is able to solve routine and non-routine problems involving quadratic equation roots. NAME: SECTION: SCORE: Directions: What do you think is important in order to sustain life's journey? Solve each problem and write the problem letter above each correct answer. Units for the answers are stated in every problem. A. The longest side of a right triangle is 4 more than the shortest side. The middle side is 2 more than the shortest side. Find the lengths of the sides of the right triangle. R. A tennis court for four players has an area of 230 square meters. The perimeter of the court is 66 meters. Find the dimensions of the court. I. The product of two consecutive odd integers is 1 less than ten times their sum. Find the integers. T. Last year, Mario planted potatoes in a rectangular plot whose length was 4m more than its width. Encouraged by a plentiful harvest, he increased the width of his plot by 3m and also increased the length to twice this width, thus having 83m² more in area. What are the dimensions of his plot now? P. Find two positive consecutive integers that are multiples of 5 and whose product is 300. E. The length of a rectangle is one meter longer than its width. Its diagonal is 29 meters. Find the dimensions of the rectangle. S. The length of a rectangle is 1 ½ meters more than its width. The area of the rectangle is known to be 27 square meters. Find the dimensions of the rectangle. Y. The sum of two numbers is 28 and their product is 96. Find the numbers. H. A rectangular table has an area of 27 ft² and a perimeter of 24 ft. What are the dimensions of the table? K. An amusement park wants to place a new rectangular billboard to inform visitors of their new attractions. Suppose the length of the billboard to be placed is 4m longer than its width and the area is 96m². What will be the length and the width of the billboard? 15,20 23,10 6,8,10 24,4 20,21 23,10 19,21 4 ½,6 8.16 3,9 20,21 8,12 20,21 4,24
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Items 13 - 16, refer to the problem inside the box. Then, answer the questions that follow. The length of a tarpaulin is 4 more than twice the width. Its area is no less than 96 meters. 13.) Which of the following represents the length of the tarpaulin? A. x B. x + 4 C. 2x + 4 D. 2x 14.) Which of the following expressions represents the width of the tarpaulin? A. x B. x + 4 C. 2x + 4 D. 2x 15.) Which inequality represents the situation? A. x(x) ≥ 96 B. x(2x + 4) ≥ 96 C. x(x + 4) ≥ 96 D. x(2x) ≥ 96 16.) What is the least length of the tarpaulin? A. 16-meters B. 10-meters C. 6-meters D. 4-meters 17.) The product of the two positive consecutive integers is no less than 56. Find the pairs of the integers. A. 7 and 8 B. 7 and - 8 C. - 7 and 8 D. - 7 and - 8 18.) The length of the swimming pool is 2-meters more than its width. If the area of the wall is no less than 48m², which of the following could be its length? A. 4-meters B. 6-meters C. 8-meters D. 10-meters 19.) The monthly profit P(in thousand pesos) that a Sari-Sari Store earns is determined by the equation P = 10x² - 280x - 1000. What is the lowest possible value of x that will give the store a profit of at least ₱10, 000.00? A. 5 B. 22 C. 50 D. 52 20.) The width of the lot is 4-meters shorter than its length. How long should its width be to have an area of no more than 60m²? A. 16-meters B. 10-meters C. 6-meters D. 4-meters
1. Find two positive numbers whose sum is 300 and whose product is a maximum. 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum. 3. Let x and y be two positive numbers such that x + 2y = 50 and (x + 1)(y + 2) is a maximum. 4. We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft. If we have $700 determine the dimensions of the field that will maximize the enclosed area. 5. We have 45 m² of material to build a box with a square base and no top. Determine the dimensions of the box that will maximize the enclosed volume. 6. We want to build a box whose base length is 6 times the base width and the box will enclose 20 in³. The cost of the material of the sides is $3/in² and the cost of the top and bottom is $15/in². Determine the dimensions of the box that will minimize the cost. 7. We want to construct a cylindrical can with a bottom but no top that will have a volume of 30 cm³. Determine the dimensions of the can that will minimize the amount of material needed to construct the can.
Kathleen C.
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