Examples for 9th grade - page 26

Gauss
Help little C.F. Gauss sum all the integers from 1 to 340.
Angles ratio
In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
SAS triangle
The triangle has two sides long 7 and 19 and included angle 144°11'59″. Calculate area of this triangle.
Journey
The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla
Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
Forth and back
Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
Bomber
Bomber flies 5 km at 1400 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s^2.
Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
Aircraft
The aircraft has in a fuel tank 100 hl of aviation fuel and flight consumes 4.3 liters of fuel. Identify the function, which expresses the dependence of the volume of fuel in tank on the track distance plane flew by. How many hectolites of fuel is still i
Work
First paver pave pavement for 33 hours. Second for 24 hours. Started first paver and after 5 hours, join the second. How long will they finish pavement?
Two runners
Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute
Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
Rectangle
The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
Reciprocal
What is the reciprocal of the sum of the reciprocals of 7 and 2?
Horizontal Cylindrical Segment
How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
Car
The driver of a car is to get to 378 km distant city. From atlas found that 99 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 117 km/h. Calculate how many hours it will ta
Interest
Calculate how much you earn for 7 years 14000 deposit if the interest rate is 1.8% and the interest period is a quarter.
Racer
The first racer run at a speed 12 m/s and is 470 meters before the finish and ahead 22 meters before second competitor. At what speed must run the second racer to catch first racer at the finish line?
Elections
In elections candidate 8 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes.

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