# Examples for 9th grade - page 47

- Count of triangles

Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points. - Cube 7

Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm. - Rectangle - sides 3

If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we incr - Three siblings

Three siblings have birthday in one day-today. Together they have 35 years today. The youngest is three years younger than middle and the oldest is 5 years older than middle. How old is each? - Sportsman

A trained athlete is able to exhale after a deep breath still 500 ml of air. At normal inhalation and exhalation is breathing 500 ml of air. Within one minute, one breath and exhaled 14 times. What part of breathing air per day is one exhalation? - Angles of a triangle

In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle. - Quadrant

In what quadrant is a -1165° angle? - Freight train

The train carries 525 tons of limestone in 29 wagons. Wagons are 15 tonne and 20 tons. How many is 15 ton and how many is 20 ton wagons? - Smallest internal angle

Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8 - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - The farmer

The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004? - Two numbers

The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number. - Product

The product of two consecutive odd numbers is 8463. What are this numbers? - Pine

How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut pine trees constitute 94% of all trees left." - Pyramid in cube

In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid. - Line segment

For the line segment whose endpoints are L[-10, -14] and M[-13, -4], find the x and y value for the point located 3 over 4 the distance from L to M. - Holidays

Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany. - Passenger car and truck

From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck? - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3,}a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Mean

if the mean of the set of data 5, 17, 19, 14, 15, 17, 7, 11, 16, 19, 5, 5, 10, 8, 13, 14, 4, 2, 17, 11, x is -91.74, what is the value of x?

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