# Grade - examples - page 210

1. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
2. How many 2 How many three lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed
3. Father and son Father and son weigh together 108kg. The father weighs 2.6 times more than his son. How much does weight my father and son count?
4. Cows and calves There are 168 cows and calves in the cowshed. Cows are in nine stalls and calves in four stalls. Same count cows are in every cow stall and three more in each calf stall than in a cow stall. What is the capacity of the stalls for cows and what for calves?
5. Hyperbola equation Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
6. Doses A child is to receive a dose of 0.5 teaspoon of cough medicine every 12 hours. if the bottle contains 60 doses, how many days will the medicine last?
7. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
8. Shopping center The shopping center buys from the manufacturer bikes at a purchase price of 180 €. It sells them for a sale price of 250 €. However, in the advertising for the sale of these goods, the shopping center spent 20% of the selling price of all bicycles in stock
9. Equations - simple Solve system of linear equations: x-2y=6 3x+2y=4 A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
11. Train speed Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
12. A car A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
13. Winery The wine processing plant sold 8/15 of its total wine production to the domestic market, 2/7 to the foreign the rest of the wine. How many percents are still in stock?
14. Simplify 3 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
15. Area of a triangle What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3?
16. Supplementary angles One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
17. Discount sale At Christmas Sale after a 20% discount cosmetic package was priced at a price of 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount?
18. Non linear eqs Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
19. Poplar How tall is a poplar by the river, if we know that 1/5 of its total height is a trunk, 1/10th of the height is the root and 35m from the trunk to the top of the poplar?
20. The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.

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