# New math problems - page 6

- Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2.}Determine the area of the trapezoid A - Two cyclists

Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder? - Cube

One cube has edge increased 5 times. How many times will larger its surface area and volume? - Doubling

The message is spreading that each day has doubled the number of people who know about it. All know message for 20 days. How long known it eighth people? - Modulo

Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 . - Two friends

Two friends met as a good man perish together for a beer. After recovery the most important topics (politics, women, football ...), one asks: - And how many do you have children? - I have 3 children. - And how many years have? Friend already not want to an - One percent

One percent of all the lights in the city are LED, the remaining 99% are conventional. Other types are not there. John counted them honestly but he had counted only conventional. After a good dinner he registered numbers and he have notice that from all t - Cakes Z8-I-5

Mom brought 10 cakes of three types: kokosek was less than laskonek and most were caramel cubes. John chose two different kinds of cakes, Stephan did the same and for Margerith leave only the cakes of the same type. How many kokosek, laskonek and caramel c - Two diagonals

The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal? - Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m^{3}to have painted/bricked walls with least amount of material. - Probably member

Look at the series 2,6,25,96,285, ? What number should come next? - Rainfall

The annual average rainfall in India was in Cherrapunji in the year 1981 26 461 mm. How many hectoliters of water fell on 1 m^{2}? Would fit this amount of water into a cube of three meters? - Minimum of sum

Find a positive number that the sum of the number and its inverted value was minimal. - Hello adding

Fill letters instead of digits so the indicated sum (equal letters represent equal digits). What number is hidden under the letter J? A A H A H O A H O J -------------------------- 4 3 2 1 - Rectangle diagonals

It is given rectangle with area 24 cm^{2}a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Hypotenuse

Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters. - Star equation

Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗ - Christmas trees

Salesman sold Christmas trees: spruce for € 22, pine for € 25 and fir for € 33. At the morning he had the same number of spruce, fir and pine. At the evening he had all the trees entirely sold for € 3,600. How many trees that day salesman sold? - MO-Z5-3-66 tiles

The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.

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