# Examples for 9th grade - page 33

1. Skier At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first?
2. The professor's birthday Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc
3. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
4. ISO Triangle V2 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
5. Again saw From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
6. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
7. Gon functions Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
8. Math logic There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w
9. Pennies 800 pennies have the same value as 100 ducats. 100 pennies have the same value as 250 tolars. How many ducats has the same value as 100 tolars?
10. Clock What distance will pass end of 8 cm long hour hand for 15 minutes?
11. Sequence Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
12. Pyramid 8 Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
13. Retail At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 4% of weight of the goods and retail still have a profit of 6.3%? Goods are sold at retail for 25 euro per kg.
14. Compare II Which of the numbers 710, 107 is greater?
15. Friends in cinema 5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
16. Snowman In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
17. Isosceles trapezoid Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
18. Loans, loan ... In Slovakia, launched a short-term non-bank loans, of which few people have their "take" are considered unfavorable. Often, the borrower ends up in a spiral of debt, which takes more and more onerous loan used to repay earlier loans. Calculate how many 9-
19. Shadow and light Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
20. Rectangular triangles The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c

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