# Examples for 9th grade - page 23

- Parallelogram

Parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides. - Wood

Wood contains 12% water. 1 m^{3}of wood weighs 650 kg. How many liters of water it contains? - Cargo

Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load? - 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? - Three workers

Three workers were rewarded CZK 7200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received? - Unknown integer

Find the smallest integer that: divided by 2, the remainder is 1 divided by 3 the remainder is 2, divided by 4 remainder is 3, ... divided by eight reminder is 7, by 9 reminder is 8. - Mother and daughter

Three years ago mother was three times older than daughter. After nine years she will be only twice old. How old is mother (and daughter)? - Leveling

Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 28 m^{2}to the "height" 12 mm if consumtion is 1.7 kg per square meter and millimeter thickness. - Flowerbed

On the flowerbed was planted 310 flowers - pansies and crayons. During the first week wilts quarter of pansies and an eighth crayons, which is 20% of all flowers. How many pansies were planted on the flowerbed? - Horizon

The top of a lighthouse is 12 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Vectors

For vector w is true: w = 2u+2v. Determine coordinates of vector w if u=(-8, -5), v=(18, 19) - Series

Your task is express the sum of the following arithmetic series for n = 36: S(n) = 11 + 13 + 15 + 17 + ... + 2n+9 + 2n+11 - R Trapezium

Rectangular trapezium has bases 17 and 7 and area 80 cm^{2.}What is its perimeter? - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it? - Triangle TBC

TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB? - Chord

In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 1:7 and perimeter is 735. - RT - hypotenuse and altitude

Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments? - Pears

Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears. - Water reservoir

The water reservoir is filled with one pump for 4 days by the second one for 9 days. Outlet can drain tank in 12 days. How long take fill the reservoir if both pumps are running and not closed outlet channel.

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