# Expression of a variable from formula - problems - page 16

1. Diagonals
Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
2. Red balls
In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
3. Two machines
Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?
4. Quotient
Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
5. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
6. Coach
Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?
7. Hotel
The hotel has a p floors each floor has i rooms from which the third are single and the others are double. Represents the number of beds in hotel.
8. Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
9. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
10. Q of GP
Calculate quotient of geometric progression if a1=5 a a1+a2=12.
11. Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
12. Parallelogram
Calculate the missing side of a parallelogram, if you know the perimeter o and one side: a) o = 7.2 cm; b = 1.8 cm b) o = 5.4 cm; a = 1.9 cm
13. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
14. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8
15. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
16. Difference AP 4
Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
17. Volume and area
What is the volume of a cube which has area of 361 cm2?
18. Combinations
If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
19. Boys and girls
There are 28 girls in the hall. 5/7 of all children are boys. How many children and how many boys are there?
20. Trapezium
The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.

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