# Examples for 9th grade - page 37

- Mast

Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'. - The angle of lines

Calculate the angle of two lines y=-3x+25 and y=x-3 - Belgium vs Italy

Belgium played a match with Italy and Belgium win by 2 goals. The match fell a total 6 goals. Determine the number of goals scored by Belgium and by Italy. - ATC camp

The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple? - Digging

A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ? - Middle segment

In a triangle ABC with the side /AB/ = 24 cm is constructed middle segment /DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB. - Unknown number

Determine the unknown number, which double of its fourth square is equal the fifth its square. - Square - increased perimeter

How many times is increased perimeter of the square, where its sides increases by 150%? If the perimeter of square will increase twice, how much% increases the content area of the square? - Cyclist

Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target? - Consecutive numbers

Sum of ten consecutive numbers is 105. Determine these numbers (write first and last). - Bus and Milan

The bus started from the village at speed 60 km/h. After one kilometer, when Milan came to bus stop on a motorcycle with grandmother. When they found that bus drove away he try to catch it. At the next stop, a distance of 3km caught up bus. How quickly had - Reduce of the volume

Calculate how many % reduce the volume of the cube is we reduced length of each edge by 10%. - Diagonal - simple

Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm. - 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? - 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? - Reservoir

6 m long reservoir has a diameter of 2.2 m. What is its surface area in square meters? - Pytagoriade

Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed - Chord AB

What is the length of the chord AB if its distance from the center S of the circle k(S, 71 cm) is 27 cm? - Circle sector

Circular sector with a central angle 10 ° has area 254 cm^{2.}Calculate its radius r. - Interest p.a.

Calculate the value of interest in period of 1 year from the deposit 62000 CZK at 8 percent interest rate, after deducting 15 percent tax.

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