# Examples for 7th grade (seventh) - page 34

1. Angles The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C?
2. Saw Imagine that the saw blade with diameter 40 cm has one tooth colored with a different color. How long is path describing by the tip of the tooth after 15 minutes, if the blade is rotated 13365 times?
3. Distance runner Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route?
4. Determine the number Determine the number x that ?.
5. Rectangles - sides One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
6. Area of RT 2 Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm.
7. Two numbers The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
8. Diplomas Suzanne helped write out diplomas. Issuance its first took 3 minutes, each next 2.3 minutes. How much time it will take to write out n=16 diplomas (including the first), write out this pace?
9. Cottages The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three?
10. 9-gon Sum of interiol angles of 9-gon is:
11. The store The store received the same number of cans of peas and corn. The first day sold 10 cans of peas and 166 cans ofcorn so that left 5 times more peas than corn cans. How many cans of each kind were in the store?
12. Concrete pillar How many m³ of concrete is needed for the construction of the pillar shape of a regular tetrahedral prism, when a = 60 cm and the height of the pillar is 2 meters?
13. Cube 7 Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
14. Nectar Nectar collected by bees contains 70% water. From the nectar of the some process produces honey which contains 19% water. How many kg of nectar bees need to collect to make 1 kg of honey?
15. Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
16. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
17. Car consumption The car has consumption 4 l/100 km. How much money will it cost ride 4 km in long if diesel price is 1.53 USD/l?
18. Is right triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
19. Children Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh?
20. Cube 3 How many times will increase the volume of a cube if we double the length of its edge?

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