Examples for secondary school students - page 159 of 230

Number of problems found: 4586

Equilateral 4486
If we increase one side of the triangle by 11 cm and reduce the other by 11 cm, we get an equilateral triangle. Four times the shortest side of the triangle is 10 cm greater than three times the triangle's longest side. Find all the lengths of the sides o
Population 4485
The population is 22000 people. With an annual increase of 1.4%, there will be 25,000 people. How many years will it be?
Cycling 4482
Cycling races had 4 stages. The length of the first was 1/3 of the length of the entire track. The length of the second stage was 2/9 of the length of the entire track, and the length of the third stage was 1/4 of the track. The fourth stage was 15 km sho
Pharmacy
The pharmacy adds 3 liters of 95 percent alcohol and 5 liters of 38.04 percent alcohol. How much percent alcohol did the pharmacy get?
Connections 4473
The distance between the two airports is 3480 km. There are regular connections from airport 1. The plane takes off at 6:30 am at an average speed of 600 km/h. From airport two at 7:00 am at a speed of 540 km/h. When will they meet?
One-fifth 4469
Two hundred boxes of washing powder were lined up in 3 rows in the store. There were 13 more boxes in the first row than in the second row, one-fifth more in the second row than in the third row. How many boxes were there in each row?
Right triangle eq2
The hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
Average speed
The first third of the track was driven by a car at a speed of 15 km/h, the second third at a speed of 30 km/h, and the last third at a speed of 90 km/h. Find the average speed of the car.
Largest number n
Find the largest natural number d that has that property for any natural number n; the number V(n) is the value of the expression: V (n) = n ^ 4 + 11n²−12 is divisible by d.
Resulting 4446
A square with a side length of 3 cm rotates around its diagonal. Calculate the volume and surface area of the resulting body.
Coefficients 4445
Find all triplets P (x) = a * x² + b * x + c with the integer coefficients a, b, and c to which it applies P (1)
Inequality triangle
The heel of height from the vertex C in the triangle ABC divides the side AB in the ratio 1:2. Prove that in the usual notation of the lengths of the sides of the triangle ABC, the inequality 3 | a-b | < c.
Calculate 4425
In the triangle ABC with the center of gravity T, b = 7cm, median to c: tc = 9cm, the ATC angle is 112 degrees. Calculate the length of the line ta.
Calculate 4424
Calculate the area of the triangle ABC if a = 10 cm, c = 8 cm, ta = 6 cm.
Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees.
Concentration - salt solution
We added 300 g of water to 400 g of salt solution, reducing the solution's concentration by 5%. How much water did the original solution contain, and what was its concentration?
Determine 4414
Determine how many rows the 7th-order square matrix contains.
Third-order 4413
Determine how many elements a third-order square matrix contains.
Cuboids
Two separate cuboids with different orientations are in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
Rhombus and diagonals
The rhombus area is 150 cm², and the ratio of the diagonals is 3:4. Calculate the length of its height.

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