Expression of a variable from formula - examples - page 18

1. Area of iso-trap
Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
2. Surface of cubes
Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
3. 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?
4. 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.
5. Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
6. Equation of circle
find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
7. Equation of circle 2
Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
8. Simplify
Simplify the following problem and express as a decimal: 5.68-[5-(2.69+5.65-3.89) /0.5]
9. Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
10. 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
11. 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
12. Trapezium bases
Find the trapezium height if a = 8 cm and c = 4 cm if its content 21 square centimeters.
13. Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
14. A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
15. 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
16. Bicycle gears
The toothed wheel on the bicycle pedal has 40 teeth, the wheel on the rear wheel has only 16 teeth. How many times does the rear wheel turn if the pedals rotate 50 times?
17. Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
18. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
19. Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
20. A square
A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.

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