# Examples for 9th grade - page 47

- 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) - Teams

How many ways can divide 16 players into two teams of 8 member? - 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 - 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 cm^{2}. What are the dimensions of the original rectangle? - 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 - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Quadratic equation

Determine the numbers b, c that the numbers x_{1}= -1 and x_{2}= 3 were roots of quadratic equation: ? - 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? - Equilateral triangle v2

Equilateral triangle has a perimeter 36 dm. What is its area? - 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. - 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? - Circle inscribed

Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm. - 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? - Cuboid - complicatef

Three walls of the same cuboid has content 6 cm^{2}, 10 cm^{2}and 15 cm^{2}. Calculate the volume of the cuboid. - 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. - 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? - Cube 7

Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm. - 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. - 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. - 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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