Examples for 9th grade - page 84

  1. Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
  2. Rhombus construction
    rhombus_7 Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
  3. 6 terms
    arithmet_seq Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
  4. Modulo
    modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
  5. Photocopier
    picture A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
  6. Fence and scale
    ctverec_mo_4 The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
  7. Competitors
    ski_2 In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
  8. Rhombus
    kosostvorec_1 The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
  9. Surface of cubes
    cubes3_6 Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
  10. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  11. Percentages 5
    usd_1 $5.25 is 7 1/2% of what number?
  12. Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
  13. Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  14. Scale factor
    cuboid_7 A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
  15. A bridge
    arc123 A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
  16. Inscribed sphere
    cubes2_7 How many percents of the cube volume takes the sphere inscribed into it?
  17. Windbreak
    vichrica A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
  18. Ratio of sides
    trojuholnik_5 The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
  19. Two forces
    forces_1 The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
  20. Paul earned
    workers_35 Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t

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