# Examples for secondary school students - page 58

- Tricolors

From the colors - red, blue, green, black and white, create all possible tricolors. - Medians of isosceles triangle

The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians? - AS - sequence

What are the first ten members of the sequence if a11=22, d=2. - Adam and Ben

When Ben is so many years old to Adam today, Adam will be 23 years old. When Adam was as old as Ben, Ben was two years old. How old is today Ben and Adam? - Rectangle

Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width. - Quadratic function 2

Which of the points belong function f:y= 2x^{2}- 3x + 1 : A(-2, 15) B (3,10) C (1,4) - Tokens

In the non-transparent bags are red, white, yellow, blue tokens. We 3times pull one tokens and again returned it, write down all possibilities. - Vegan shop

To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts. - Determine AP

Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71 - Elimination method

Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15 - Potatoes bags

I have three bags with 21 kg potatoes. The first bag is 5.5 kg more than in the second bag and the third is 0.5 kg more than in the second bag. Determine how many kgs of potatoes is in each bag. - Geometric seq

Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient. - 925 USD

Four classmates saved an annual total 925 USD. The second save twice as the first, third 35 USD more than the second and fourth 10 USD less than the first. How USD save each of them? - Dividing money

Imrich, Daniel and Dezider shared an unknown amount in the ratio 1:2:4, where Dezider received 750 euros more than Imrich and Daniel got half as much as Dezider. Determine an unknown amount of money and determine the amounth that got Imrich, Daniel and De - Red balls

In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%? - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4. - Three friends

Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor. - Find the area

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.

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