# Examples for 9th grade - page 102

1. Construct Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
2. Father and son Father and son weigh together 108kg. The father weighs 2.6 times more than his son. How much does weight my father and son count?
3. No smoke Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant
4. Parallelogram Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
5. An oil An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
6. Banknotes Eva deposit 7800 USD in 50 banknotes in the bank. They had value 100 USD and 200 USD. How many were they?
7. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
8. Cows and calves There are 168 cows and calves in the cowshed. Cows are in nine stalls and calves in four stalls. Same count cows are in every cow stall and three more in each calf stall than in a cow stall. What is the capacity of the stalls for cows and what for calves?
9. Train speed Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
10. Winery The wine processing plant sold 8/15 of its total wine production to the domestic market, 2/7 to the foreign the rest of the wine. How many percents are still in stock?
11. Equations - simple Solve system of linear equations: x-2y=6 3x+2y=4
12. The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
13. Discount sale At Christmas Sale after a 20% discount cosmetic package was priced at a price of 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount?
14. Alice Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
15. Together If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee)
16. 12 apples 12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread?
17. A car A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
18. Three workshops There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
19. Hectoliters How deep is the pool if there are 2025 hectoliters of water and the bottom dimensions are a = 15 meters b = 7,5 meters and the water level is up to 9/10 (nine-tenths) of height.
20. Right isosceles triangle Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?

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