# Algebra - problems - page 93

1. Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
2. KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
3. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
4. Meat loses
Meat loses 18% of its weight by smoking. How much raw meat butcher used to manufacture 35 kilos of smoked?
5. Clock's gears
In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position?
6. 3d printer
3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
7. Motorcyclist
From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle?
8. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
9. Sugars
In what ratio must two sorts of sugar, costing #390 and #315 per kg respectively, be mixed in order to produce a mixture worth #369 per kg?
10. Progression
12, 60, -300,1500 need next 2 numbers of pattern
11. New ratio
The ratio of ducks and chicken in our yard is 2 : 3. The total number of ducks and chickens together is 30. Mother gave 3 of the chickens to our neighbor. What is the new ratio now?
12. Cylinder height
Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
13. Wiring 2
Willie cut a piece of wire that was 3/8 of the total length of the wire. He cut another piece that was 9m long. The two pieces together were one half of the total length of the wire. How long was the wire before he cut it?
14. Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
15. SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
16. Two trains
From station A, the freight train traveled at a speed of 40 km/h in 9h. When he drove 15km, the fast train started from station A in the same direction at a speed of 70km/h. When will it the freight train catch up?
17. Discount price
Coat cost 150 euros after sales discount. What is the original price when the discount is 25% of the original price?
18. Barrel with water
The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
19. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
20. Mushrooms
Mushrooms lose 90% by weight drying. How many fresh mushrooms are needed for 5 kg of dried mushrooms?

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