# Examples for 9th grade - page 51

- Obtuse angle

The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Rhombus

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - Three men

Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old? - Square circles

Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm. - Laths

There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide - Tray

Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm. - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - The city

In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)? - Sputnik

The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round? - Welders

Welder do the job for six hours, the second one for 8 hours. How long do the job third welder if all together can do job in 2 hours? - The creek

Workers cleaned the creek within 3 days. The first day cleanse one-fifth the length of the creek, the next day 40% of the length of the stream and the third day 8 km length of the creek. How long is a creek? - Annual income

The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean. - James

James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether? - Square ABCD

Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4]. - Juice box 2

Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the - Saw

Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute. - Equation

How many real roots has equation ? ? - Surveyor

Calculate the area of what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm? - Sisters

Sisters Zuzka Lenka and Vierka has save for a new bike. Zuzka save € 90, Lenka save € 90 and Vierka save € 82. Missing 30% gave them their mother. What is the price of the bike? - Clock face

clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.

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