# Equation + quadratic equation - problems

1. 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,.
2. Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
3. Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
4. Substitution method
Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
5. Diagonals of a rhombus 2
One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
6. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
7. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
8. Root
The root of the equation ? is: ?
9. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
10. Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
11. MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
12. R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
13. Rectangle SS
Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle.
14. Trains
From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains.
15. Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump?
16. Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
17. RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
18. Circle
Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
19. Coins
Harvey had saved up a number of 2-euro coins. He stored coins in a single layer in a square. Left 6 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
20. Circle
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.

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