# Grade - examples - page 27

1. Circle
Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
2. KLMN
In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
3. Garden
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
4. Efficiency of rail
With subsidies are business easy. Calculate how much must cost rail ticket (x) in today's ticket price € 11 and if the trains was not subsidized, if it is known that without subsidies would cost three times today's ticket prices. Calculate the value of.
5. Posters
Column with posters in the form of a cylinder is 2 m high and its diameter is 1.7 m. What is the content area for which it is possible to stick posters?
6. Sugar - cuboid
Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
7. Playing cards
How many possible ways are to shuffle 7 playing cards?
8. Wood in the forest
The amount of wood in the forest was estimated at 28000 m3. How much wood will be in forest after 4 years if the annual growth of wood is 3.1% each year and logging 140 m3 each year?
9. Coins
Harvey had saved up a number of 2-euro coins. He stored coins in a single layer in a square. Left 6 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
10. Barrel 3
Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
11. Rhombus
Find the length of each side of rhombus if the perimeter is 49 dm long.
12. Pyramid
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
13. Free fall
Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s2
14. Trains
On double track line between stations K and M went against each other two trains. The first train passed the distance between stations for 3.5 hours, the second, which had an average speed of 12 km/h more passed for 3.05 hours. Calculate the distance betw
15. Trio
Trio of workers earn 750 euros. Money divided by the work that each of them made​​. First received twice as the second, the second received three times more than the third. How many got everyone from workers?
16. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
17. Built-up area
John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
18. Greek railwayman
Wesley works for the Slovak railways since 1986. His salary is 864 €. His colleague, Evgenias works in the Greek State Railways from 1991. Earns 5010 € per month. Calculate how many hours a day must Evgenias work to earn as much as Wesley and if they w
19. Reservoir + water
Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir.
20. Height
Is right that in any right triangle height is less or equal half of the hypotenuse?

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