Reason - practice for 14 year olds - page 3 of 40
Number of problems found: 798
- Quadrilateral calc
The square ABCD is given. The midpoint of AB is E, the midpoint of BC is F, CD is G, and the midpoint of DA is H. Join AF, BG, CH, and DE. Inside the square (approximately in the middle), the intersections of these line segments form a quadrilateral. Calc - Probability 81446
What is the probability that each digit is different in a five-digit number? - Several resistors
We have a box with the same resistors, so all of them have a resistance value of 200 ohms. Draw the connection of several resistors so that the resulting resistance is: a) 100 b) 120 (only 4 resistors) - Equilateral 81142
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body.
- Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ - Thanks 81022
Pavla is 2x older than Irena. Four years ago, Pavla was 6 times older than Irena was then. In how many years will the ages of Pavla and Irena be in the ratio of 4:3? Thanks - Multiply 80797
When I multiply two equal natural numbers, I get the same result as when I add them together. Which ones are they? - Increases 80774
A bus travels between places A and B. If it increases its average speed by 5 km/h, the travel time will be reduced by 20 minutes. If he reduces his original speed by 4 km/h, the driving time is increased by 20 minutes. What is the average speed of the bus
- Parallelogram 80761
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Determine 80714
Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the t - Single-digit 80674
There are cows, ducks, and geese on the farm. They have a total of 126 legs. Ducks are 3 more than houses. And there are 20 cows. If we count all the animals, we have to divide them by the number three, and we should get a single-digit number. - Grandchildren 80639
The average age of the grandfather, grandmother, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is a year younger than grandpa. How old is grandma? - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵
- Nightmares 80568
At the dream market, she offered the Sphinx to a traveler for four dreams, seven illusions, two naps, and one nightmare. Another has seven dreams, four illusions, four naps, and two nightmares. The Sphinx always measures the same for all travelers. How ma - Differences 80551
Bolek and Lolek each had their own arithmetic sequence. Both Lolek and Bolek's sequence started with the number 2023 and ended with the number 3023. The two sequences had 26 numbers in common. The ratio of Bolek's and Lolka's difference was 5:2. What is t - Chessboard 80533
How many ways can one white and one black square be selected on an 8x8 chessboard if the selected squares cannot lie in the same row or column? - Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - Five-digit 80104
How many different five-digit numbers with different digits can be made from the digits 0, 2, 4, 6, 7, 8, and 9? How many of them are divisible by 4? How many of them are divisible by 10? How many of them are even?
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