# Algebra - examples

- Hectares

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 - Cube surface and volume

Find the surface of the cube with a volume of 27 dm^{3}. - On line

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]. - Center of line segment

Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is . - Left handed

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? - Soldier

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? - The third

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? - MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - MO Z8-I-1 2018

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. - Prime number

Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number? - Powers 3

2 to the power of n divided by 4 to the power of -3 equal 4. What is the vaule of n? - Drying herbs

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? - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Equation 20

In given equation: 8/9-4/5=2/9+x, find x - 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. - Clubhouse

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 - Age

In 1960 my age was equal to the digits sum of the year of my birth. What is my age now? - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Square

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 dm^{2}?

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