# Examples for 9th grade - page 35

- Sequence 2

Write the first 4 members of an arithmetic sequence a_{5}=-18, d=-7 - Trousers

Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high. - Iron fence

One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m^{3.} - Hiker and cyclist

At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker? - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - Pot

Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm. - Warehouse cars

From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck? - Disinfecting solution

How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution? - 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. - Square Number

If to a square of integer number add 49, we get the square of next integer number. What is the original number? - Pytagoriade

Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed - Freight and passenger car

The truck starts at 8 pm at 30 km/h. Passenger car starts at 8 pm at 40 km/h. Passenger arrives in the destination city 1 hour and 45 min earlier. What is the distance between the city of departure and destination city? - Medal

Calculate the approximate weight of the gold Olympics medal, if its diameter is 9 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet. - Cups

We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then - Angles of the triangle

ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC. - Word problem

384 students were on holiday in Hungary. 146 bought pizza, chips 25 pupils, 39 pupils bought soda, butter 15 pupils, 18 pupils fruits, vegetables 29 students. How much pay for all the food, if every meal cost 4.9 euros? - Pedestrian and the cyclist

Pedestrian and cyclist went against each from the two cities that are distant 40 km. Pedestrian started 30 minutes before the cyclist and walk an average speed of 5 km/h. What speed went cyclist when met after 120 minutes from the start of the pedestrian? - Mr Novak

Mr Novak earns an average 638 euros. When increasing the salary they gave him a choice: ? What is better choice for Mr Novak? - Pool 2

The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later? - Round table

Round table with diameter d = 95 cm is coated by square tablecloth with a side length 122 cm. About how many cm is higher center of tablecloth than its cornes?

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