# Units - examples - page 98

1. Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
3. Regular prism
The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
4. Inlet minus outlet
Water flows into the tank through two pipes and flows out of the third pipe spontaneously. The pipe A itself would fill the tank in 3 hours, the pipe B itself would fille in 4 hours, and the pipe C itself would flow out in 12 hours. How long will the tank.
5. The Stolen Money
A man walks into a store and steals a \$100 bill. 5 minutes later, he returns to the store and buys stuff worth \$70. He pays with the bill that he had stolen, so the owner of the store returns him \$30. How many dollars did the store owner lose?
6. Discount sale
After the discount, the computer costs 9600, - CZK. How much did it cost when the price was reduced: a) by half b) by a third c) by one fifth and then by 160 CZK
Lucy, Tereza, and Petra decided to compile the compulsory reading records together. It would take 30 days for Lucia alone, 36 for Tereza and 45 for Petra. How long will take make records if they will work together?
8. Mushrooms
Fresh mushrooms contain 88% water, dried 14% water. How many kilograms of fresh mushrooms should be collected to get 3 kg of dried?
9. Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
10. Slant height
The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
11. Two buses
The first bus runs 15 minutes the second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet?
12. Rhombus 29
One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
13. Inscribed
Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
14. Iron ball
The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
15. Granules
Katy had two dogs. The first one ate a pack of granules a week and the other two times longer. Katka bought them two bags of granules. How long does it last for both dogs?
16. Bulbs
There are 875 identical light bulbs in the sports hall lightning for 2 hours. How long does it lightning 100 this light bulbs?
17. Prism 4 sides
Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
18. Products
15 products are 48 € more expensive than 12 products. How many euros will it cost five same products?
19. The factory
The factory z can complete an order in 12 days, factory p in 18 days. For how many days does an order completed when the first two days work only the factory z and then both factories?
20. Pravoúhly trojúhelník
Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.

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