# Examples for secondary school students - page 33

- Rhombus

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

Solve exponential equation (in real numbers): 9^{8x-2}=9 - 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. - Coordinate

Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5^{x} - 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. - Circle chord

Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle. - 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. - Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m^{2}. Calculate the dimensions of the garden. - Sequence 3

Write the first 5 members of an arithmetic sequence: a_{4}=-35, a_{11}=-105. - The dice

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

Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5]. - Hearts

5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row? - Apples

A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples? - Hexagonal pyramid

Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid. - Triangle ABC

In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC. - Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - Algebrogram

Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.

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