# Grade - examples - page 114

- Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - Heating plant

Workers dump imported coke at heating plant. On the first day used half of the amount, the second day three quarters the rest and on the third day left 120 tons. How much coke they dump at heating plant? - Cookies

In the box were total of 200 cookies. These products have sugar and chocolate topping. Chocolate topping is used on 157 cookies. Sugar topping is used on 100 cakes. How many of these cookies has two frosting? - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Tiles

How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles? - Cube diagonals

Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Cube

Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm^{2.} - Log

Calculate value of expression log |3 +7i +5i^{2}| . - Truncated cone

A truncated cone has a base radius 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - Debt

Joe and Caryl have a debt of $100,500. Joe makes $90,000 per year, and Caryl makes $35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries? - Book

Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book? - Meat

Half a kilogram of pork and three-quarters of a kilogram of beef cost total 5.1 USD. One quarter of a kilogram of beef and 1 kilogram of pork cost 4.9 USD. Determine the price of 1 kg of each type of meat. - Shoes and slippers

Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers? - Drainage channel

The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel. - Vector - basic operations

There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w. - Roman numerals 2-

Subtract up the number writtens in Roman numerals. Write the results as a roman numbers. - Railway wagon

The railway wagon holds 75 m^{3}load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons? - Percentage and rectangle

About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%? - Numeric question

It is possible negative irrational number? - Water reservoir

The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.

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