# Examples for 9th grade - page 7

- Katy MO

Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY? - Octahedron - sum

On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also. - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir - Cubes

Cube, which consists of 27 small cubes with edge 3 dm has volume: - Sale

If the product twice price cut by 20%, what percentage was price cut in total? - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm. - Lathe

From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - Wiring

Conduit has a cross section 49^{2}mm. Maybe put it into 5 conductors with a cross section S2 $mm^{2}? - Chords

How many 6-tones chords (chord = at the same time sounding different tones) is possible to play within 10 tones? - Phone numbers

How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - Commitee

A class consists of 5 males and 18 females. How many committees of 4 are possible if the committee must consist of 3 males and 1 females? - Climb in percentage

The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Clock

How many times a day hands on a clock overlap? - Friends in cinema

5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter? - Two tributaries

Two tributaries of the pool fill it in 10 hours. One of the tributaries would fill 15 hours. How long would fill the first tributary? - Painters

Five painters painting the fence for eight days. How many days over will take work if paint the fence only four decorators? - Estate

Semicircle estate must be fence. The straight section has 44 meters long fence. How many meters of fence should buy? - Square grid

Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm^{2}and circumference 12 cm and that their sides is in square grid. - Lie/do not lie

The function is given by the rule f(x) = -x-12. Determine whether point D[-4; 2] lies on this function. Solve graphically or numerically and give reasons for the your answer.

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