# Expression of a variable from formula - problems - page 23

1. Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
2. Pupils
There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many are boys in the class? c) Find the ratio of boys and girls in the class. Wr
3. Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
4. Pravoúhly trojúhelník
Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
5. Population growth
How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
6. Isosceles triangle
The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
7. Twelve
Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by expressi
8. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
9. Klara
Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?
10. Rain
It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
11. Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
12. AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
13. Two cyclists 2
At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,.
14. Collection of stamps
Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
They brought in d two kilos and t three kilos of bread to the store. By the end of the day, 14 two-kg bread were sold. How many kilos of bread remained in the store by the next day?
16. Cube
The sum of all cube edges is 30cm. Find the surface area of the cube.
17. On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
18. Two resistors
Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
19. Circle described
The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
20. Exponential warm
Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degre

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