# Examples for 9th grade - page 43

- 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. - Canister

Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg? - 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? - 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. - Right triangle

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

Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area. - 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. - Tetrahedral prism - rhomboid base

Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm. - 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. - Rhombus

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

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

Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm. - 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? - Machines 2

2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products? - Chord MN

Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle. - Trees

Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ? - Rectangle

The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.

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