# Examples for 9th grade - page 42

- 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. - Midpoint of segment

Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B? - Cutting circles

From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste? - 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. - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - 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. - 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? - Three digits number

From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there? - 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? - Traffic collision

When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village. - Right triangle

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

It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the. - Diamond

Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area. - 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. - Tent

Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m. - Road - permille

5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises? - Three friends

Three friends squirrels together went to collect hazelnuts. Zrzecka he found more than twice Pizizubka and Ouska even three times more than Pizizubka. On the way home they talked while eating and was cracking her nuts. Pizizubka eaten half of all nuts whi - The dice

What is the probability of events that if we throw a dice is rolled less than 6? - Rectangle and circle

The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.

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