# Examples for 9th grade - page 47

1. Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
2. Teams
How many ways can divide 16 players into two teams of 8 member?
3. Three piles
100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil
4. 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?
5. 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
6. Hexa prism
Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
Determine the numbers b, c that the numbers x1 = -1 and x2 = 3 were roots of quadratic equation: ?
8. 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?
9. Equilateral triangle v2
Equilateral triangle has a perimeter 36 dm. What is its area?
10. 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.
11. 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?
12. Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
13. 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?
14. Cuboid - complicatef
Three walls of the same cuboid has content 6 cm2, 10 cm2 and 15 cm2. Calculate the volume of the cuboid.
15. 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.
16. 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?
17. Cube 7
Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
18. 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.
19. 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.
20. 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?

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