Algebra - problems - page 86

  1. MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  2. Triangles
    496_triangle Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?
  3. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  4. The tank
    pipe2_4 The tank had 9 inflows to be filled in 21 days. After 9 days, 3 trips out. How many days did the remaining 6 tributaries fill the tank?
  5. Bricks pyramid
    The_Great_Pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
  6. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  7. Budget plan
    penize_49 In the construction of the building, the planned budget exceeded 13%, which was 32,500 euros. How many euros cost built the building?
  8. Cuboid walls
    cuboid_19 If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
  9. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  10. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  11. Workers
    workers_34 Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
  12. Parking
    cars_27 At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses?
  13. Cakes
    buhty_1 1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes?
  14. One kilogram
    jablka_19 The apple weighs 125 grams and half apple. How many apples weigh 1 kilogram?
  15. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  16. Triangle perimeter
    triangle_vysky_3 Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
  17. Soldier
    digging_1 An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together?
  18. Tractors
    tractors_2 5 tractors will plow the field for 8 hours. In 2 hours, 1 tractor broke down. How long do the remaining tractors complete the plow?
  19. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  20. Discount
    saty_1 The dress was discounted by CZK 115, which was 12% of the original price. What is the cost of the dress after the discount?

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