# Examples for 9th grade - page 47

1. Rectangles - sides One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
2. Truck PRG-BA Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway ki
3. Two numbers The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
4. Cottages The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?
5. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area? Determine the numbers b, c that the numbers x1 = -1 and x2 = 3 were roots of quadratic equation: ?
7. Cyclist Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
8. Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
9. Two trains meet From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet?
10. Square vs rectangle Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
11. Cube 7 Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
12. Cuboid - complicatef Three walls of the same cuboid has content 6 cm2, 10 cm2 and 15 cm2. Calculate the volume of the cuboid.
13. Cars 2 Opava is 360 km distance from Prešov. At 8:00 hour two cars started against each other from this cities at average speeds 88 km/h and 121 km/h. At what hour its will meet and what distance its travel if car started from Prešov is faster?
14. Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
15. Holidays Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany.
16. Silver medal To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
17. Solution What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
18. Ring The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
19. Alfa, beta, gama In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
20. 12 Moons Good Marry came to ask twelve moons for help with collecting strawberries. All twelve moons 1200 strawberries picked in 20 minutes. But lazy months July and August cease tear after 5 minutes. How many minutes in total will take collect strawberries?

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