# Examples for 8th grade - page 93

1. Remainder A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
2. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
3. Embankment Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
4. Unknown number 17 Milada said, I am thinking of a number such that I evaluate expression x1/3, the value of the expression would be 5. Which number Milada thinking?
5. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?
6. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
7. Unknown numbers The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
8. Clubhouse There were only chairs and table in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs w
9. Five pumps The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps?
10. Rhombus construction Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
11. Competitors In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
12. 6 terms Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
13. Fence and scale The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
14. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
15. Diamond diagonals Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
16. Soaps Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
17. Trapezium bases Find the trapezium height if a = 8 cm and c = 4 cm if its content 21 square centimeters.
18. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
19. Trapezoid ABCD ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD.
20. Paul earned Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t

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