# Examples for 9th grade - page 16

- Isosceles trapezoid

Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm. - Inflow - outflow

The tank will fill by inflow for 93 minutes and empties by outflow for 104 minutes. How long take to fill tank if it is also opened the inflow and outflow? - Exp

If ?, then n is: - Rectangle

In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling. - Tangents

To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre. - Water inlets

Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after? - 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 - Mushrooms

For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day? - Rotary cylinder

The rotating cylinder has a surface area 69.08 cm^{2.}The area of the shell is 62.8 cm^{2.}What is the diameter of the cylinder? - The camp

At the end of the camp a 9 friends exchanged addresses. Any friend gave remaining 8 friends his card. How many addresses they exchanged? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Cylinder

The cylinder surface is 139 dm^{2,}its height is equal to the radius of the base. Calculate height of this cylinder. - Divisors

Find all divisors of number 418. How many are them? - Three-digit numbers

How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)? - Distance

Wha is the distance between the origin and the point (23; -7)? - 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? - Water tank

Water tank shape cuboid has a width of 3.3 m and length twice larger. How high will reach water if water flow into 15 liters of water per second during 23 minutes? - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm^{2.}What scale is the city plan? - 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?

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