# Examples for 9th grade - page 54

- Gardens

I have a garden in the shape of a square with a side length of 0.02 kilometers. Neighbor has a large garden as well and one side of the garden we share. I'd bought from a neighbor garden that my area of my garden increased to 5 ares. a/ By how many acres I - Gp - 80

Sum of the first four members of a geometric progression is 80. Determine they if we know that the fourth member is nine times greater than the second. - Fog

The car started in fog at speed 30 km/h. After a 12-minute drive, the fog dissipated and the driver drove next 12 minutes distance 17 km. On the last 17 km long again the driving conditions deteriorated and the driver drove the speed of 51 km/h. a) Calcu - Inscribed circle

XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm. - Car

Car goes some distance in 3 hours and 20 minutes. If it increase speed by 10 km/h, i goes this distance in 2.5 hours. Calculate the distance. - Three figures - numbers

The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures. - Percentage and rectangle

About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%? - Trapezium

The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm^{2.}Calculate the length of the base and the height of the trapezoid. - 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. - Float boya

A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m - Quatrefoil

Calculate area of the quatrefoil which is inscribed in a square with side 6 cm. - Diagonals in diamons/rhombus

Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal. - Two pipes

One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately? - Brigade

On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week? - Eight blocks

Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four - Addends

Number 118 divide into two addends, so first addend is 69 greater than 75% of the second addend. - Forces

Determine the resultant of two perpendicular forces F_{1}= 560 N and second force of 25% smaller. - Diamond ABCD

In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Cube containers

Two containers shaped of cube with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube? - Sweets

3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations

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