# Examples for 9th grade - page 86

1. Percentages 5 \$5.25 is 7 1/2% of what number?
2. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?
3. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
4. Is right-angled Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle?
5. Windbreak A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
6. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
7. Scale factor A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
8. Ratio of sides The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
9. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
10. Garden fence The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
11. Distance of numbers Which number has the same distance from the numbers -5.65 and 7.25 on the numerical axis?
12. Tea mixture Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed?
13. Equation with abs Solve this equation with absolute value member: ?
14. Dried fruit The manufacturer produces a mixture of dried fruit. He purchased: 10kg pineapple for 200 Kc/kg 2kg papaya for 180 kc/kg 1kg of banana for 400 Kc/kg How many kgs of raisin for 80 Kc/kg must be put into the mix by the manufacturer so that the production pr In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
16. Average speed 4 Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?
17. Flying The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
18. Two workers Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself?
19. Repair pipe 20 workers had to repair broken pipes in 30 days. After fourteen days, four laborers joined them. How long did the pipe repair work last?
20. Five pumps Three same pumps fill the tank with 50400 liters of diesel in 7 hours. How many liters of diesel will it take in 4 hours if we add two more of the same pumps and pump them the same way? How much more (or less) will they get if we add 2 of the same pumps a

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