Examples for 9th grade - page 24
- Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=69°. What sizes have other angles in a triangle?
- Three drivers
Three driversdriving the same direction found that they have same amounth of gasoline. The first is enough to go 6 km, 4 km second and third 3km. Gasoline they divided so all three just drove to the nearest petrol station. How many km away was a petrol sta
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
- Two valves
Water fill the pool by two valves for 16 days. After 6 days the first valve was stopped and the second valve fill pool for 12 days. How many days took to fill the pool each of the valves individually?
- Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
- Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 2184. Calculate how many books Ladislav could buy at the price of 42 and 28 euros if he don't want fill whole home library and he can buy only 63 books?
- Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
- The cone
The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
What is the average speed of the car, where half of the distance covered passed at speed 59 km/h and the other half at 119 km/h.
- Fixed expenses 2013
Since 2013, the Slovak government plans to tax more small one person businesses. Instead of fixed expences 40% will be fixed expences 40% of gross income up to 420 Eur. Calculate what percentage of fixed expences will in 2013 pays from gross income 1093 E
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 221 cm3 . Calculate the surface area of the cylinder.
3 children pulled 9 different toys from a box. Many ways can be divided toys so that each children had at least one toy?
- Triangle SAA
The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
- Fire tank
Whole fire tank was discharged once in 2 days by first out by second in $n days. Once firefighters pumped out 1/9 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
Fresh mushrooms contain 96% water, dried 12%. How many kg of fresh mushrooms is needed to collect to get 7 kg dried?
Determine the area of a trapezoid with bases 60 and 37 and height is 3 shorter than the its leg.
- Rhombus diagonal
Area of rhombus is 417. One diagonal measures 45, find length of other diagonal.