# Examples for 9th grade - page 41

- Median

In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb. - Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle. - Concentric circles

In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord. - Garden pool

Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool? - Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - Elevator

In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the count - Prism

The volume of tetrahedral prism is 2.43 m^{3.}Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism. - Water pool

Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour? - Orchard

Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou - Lie/do not lie

The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer. - Right triangle

Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides. - Tree

How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground. - Two wine

In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine? - 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. - Garage

There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag - Trainings

The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kova - Similarity

The area of the regular 10-gon is 563 cm^{2.}The area of similar 10-gon is 606 dm^{2.}What is the coefficient of similarity. - Map scale

Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden? - Mixing

If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of. - Quadrilateral

In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm^{2,}what is the area of ABCD?

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