# Examples for 9th grade - page 47

- Function

For linear function f(x) = ax + b is f(12)=118; f(15)=132. Calculate m, if f(m) = 2005 . - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=48, b=81 and c=98. - Clocks

How long path will walk the end of the clock's minute-hand long 24 cm for 110 minutes? How long will walk in the same time hour-hand? - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Isosceles right triangle

Contents of an isosceles right triangle is 18 dm^{2.}Calculate the length of its base. - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Rhombus

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - Content area and percents

Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%. - Difference of two number

The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers. - Q of GP

Calculate quotient of geometric progression if a1=5 a a1+a2=12. - Coins

Denis and Zdeno together have 97 coins. If Denis had 4 coins less than he has now, the number of the coins would be in the ratio 14: 17. Determine the number of coins owned by Denis and Zdeno. - The car

The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B. - Centre of mass

The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p. - Outer contact of circles

Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S_{1}S_{2}S_{3}. - Shoes and slippers

Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers? - Trapezoid IV

In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD? - Diamond

Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - Rectangle

The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle. - Area of the cone

Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.

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