# Examples for 9th grade - page 30

- Quadratic equation

Solve quadratic equation: 2x^{2}-58x+396=0 - Two cars

From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what. - Trapezoid

Area of trapezoid is 135 cm^{2.}Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation... - Chicken

I threw three chicken for a handful of grains and I noticed that it eat in a ratio of 8:7:6 and two of them grabbed 156 grains. How many grains have fought that chicken? - Racer

The first racer run at a speed 20 m/s and is 750 meters before the finish and ahead 79 meters before second competitor. At what speed must run the second racer to catch first racer at the finish line? - Cross-country competition

Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B? - Mountain railway

Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track. - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2.}Determine the side length of the original square. - Building

The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building? - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Divisors

Find all divisors of number 493. How many are them? - 30-60-90

The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg? - Circle sector

Circular sector with a central angle 80 ° has area 1257 cm^{2.}Calculate its radius r. - Flowerbed 2

Around the square flower bed in a park is sidewalk 2 m wide. The area of this sidewalk is 243 m^{2.}What is the area of the flowerbed? - RT and ratio

Right triangle whose cathetus are in a ratio 7:14 has hypotenuse 78 m long. How long are cathetus? - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Cone and cube

About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r? - Cube and water

How many liters of water can fit into a cube with an edge length of 0.11 m? - Water

On the lawn which has area 914 m^{2}rained 3 mm of water. How many liters of water rained? - Field with vegetables

Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?

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