# Examples for secondary school students - page 17

- Segments

Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - Party

At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party? - Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Pizza

A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - 2nd class combinations

From how many elements you can create 4560 combinations of the second class? - Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. - Geometric mean

Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines. - Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^{2}. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers. - Two runners

Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi - Icerink

Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water. - Tiles

From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles. - Aircraft

The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Kids

How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge? - Triangle TBC

TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - ISO trapezium

Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees. - Fall

The body was thrown vertically upward at speed v_{0}= 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach? - Lines

In how many points will intersect 14 different lines, where no two are parallel? - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length.

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