Algebra - examples

  1. Hectares
    tractor_8 The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor
  2. Cube surface and volume
    cube_shield_6 Find the surface of the cube with a volume of 27 dm3.
  3. On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  4. Center of line segment
    stredna_priecka_1 Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
  5. Left handed
    pens_1 It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
  6. 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?
  7. The third
    meter_16 The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?
  8. 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.
  9. MO Z8-I-1 2018
    age_6 Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
  10. Prime number
    prime_2 Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
  11. Powers 3
    exp_4 2 to the power of n divided by 4 to the power of -3 equal 4. What is the vaule of n?
  12. Drying herbs
    vaha_18 Herbs lose 75% weight By drying. How many fresh herbs do you have to collect if you want to make 1.5 kg of dried herbs?
  13. Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  14. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  15. Equation 20
    eq222_21 In given equation: 8/9-4/5=2/9+x, find x
  16. Microorganisms
    microorganisms The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
  17. Clubhouse
    stol_2 There were only chairs and table in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs w
  18. Age
    age_5 In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
  19. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  20. Square
    namestie_tr_iso Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?

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