# Examples for 9th grade - page 14

- Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=69°. What sizes have other angles in a triangle? - n-gon

Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon? - Seven tractors

Seven tractor plowed 308 ha field in four days. How many hectares of fields will plowe 9 tractors in 3 days at the same power? - Barrel 2

Empty barrel weighs 12 kg. When it filled with water up to 46% height, weighs 68 kg. How heavy is barrel full of water? - Circle

Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes? - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - Common chord

Two circles with radius 15 cm and 11 cm are intersect at two points. Its common chord is long 20 cm. What is the distance of the centers of these circles? - 9.A

9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5? - Painters

One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself? - Workman - shift

The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components? - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1095 cm^{3}and a base radii r_{1}= 5.1 cm and r_{2}= 5.2 cm. - Gutter

How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material. - Greek railwayman

Rafael works for the Slovak railways since 1987. His salary is 874 €. His colleague, Asterios works in the Greek State Railways from 2001. Earns 5670 € per month. Calculate how many times earns Asterios more than Asterios? - Tmp workers

Three temporary workers cleaned 60 m of walkway in 5 hours. How many meters of the walkway cleared seven volunteers for eight hours? - Loan

If you take a bank loan $ 24000 and we want to repay after the year, we have to pay the total amount $ 24696/ What is the annual interest rate on this loan? - Painters

First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together? - Moving

Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 25 km/h. How long take Tilip to catch up Vojta and how far from the house? - Pyramid roof

? of area of the roof shaped regular tetrahedral pyramid with base edge 6 m and height of 3 m is already covered with roofing. How many square meters still needs to be covered? - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Tea blend

Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k

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