# Algebra - examples

- Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. - Hollow sphere

The volume of the hollow ball is 3432 cm^{3.}What is its internal radius when the wall thickness is 3 cm? - Forest nursery

In the forest nursery after winter, they found that 1/10 stems died out of them. For them, they land 193 new spruces. How many spruces are in the forest nursery? - Tailor

From the rest of the cloth tailor could cut off either 3 m in men's suits without vest or 3.6 m with vest. What shortest possible length could the rest of the cloth have? How many suits a) without a vest b) with vest could make the tailor from the re - Circle and rectangle

A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle. - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - Guess a fraction

Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form) - VCP equation

Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0 - Crown coins

Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns? - Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees. - Trees - orchard

The 3/5 trees are apple trees and 1/3 of the trees are cherries. The remaining 5 trees are pear trees. How many trees are in the orchard. - Eq1

Solve equation: 4(a-3)=3(2a-5) - Pagans

Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm^{2}of the bottom of the sheet. - Diameter

What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm? - Fifth of the number

The fifth of the number is by 24 less than that number. What is the number? - Father and son

Father is 48 years old, son 23. When will be the father twice older than a son? - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2.}Calculate the deviation of the side of this cone from the plane of the base. - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Grandfather

The grandfather is three years older than an grandmother. The average age of the grandmother, the grandfather and their seven grandchildren is 28 years. The grandchildren have a total of 105 years. Calculate how old is grandfather. - LCD 2

The least common denominator of 2/5, 1/2, and 3/4

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