9th grade (14y) + quadratic equation - examples
The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
- Find two
Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
- 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.
If water flows into the pool by two inlets, fill the whole for 12 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
- 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.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
- Right triangle
Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre.
- R triangle
Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg.
- Rhombus and inscribed
Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals.
- 2nd class variations
From how many elements you can create 6480 variations of the second class?
Right triangle has hypotenuse c = 15 cm. How large sections cuts height hc=7 cm on the hypotenuse c?
From station 130 km away started passenger train and after 2.8 hours after the express train, which travels 24 km an hour more. Express train finish journey 14 minutes early. Calculate the average speed of this two trains.
- RT - hypotenuse and altitude
Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments?
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
Cinema auditorium is built for 1740 people. The first row is planned for 29 seats and each next gradually 2 more. How many rows of seats will have auditorium?
In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
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