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 cm3. 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?
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.
Solve equation: 4(a-3)=3(2a-5)
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 cm2 of the bottom of the sheet.
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 cm2 (with circle base), its surface area is 20 cm2. 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.
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