# Examples for 9th grade - page 99

- Ladder

Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder? - Pavement

Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m. - Cube cut

The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '. - A candle

A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How m - Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm^{2}. Determine the radius r of the sphere from which the spherical cap was cut. - Cancel fractions

Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! - 2 pipes

2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone? - Driver

The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s? - Associative law multiplication

In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first) - Sheep and cows

There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm? - An angle

An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x. - Assembly parts

Nine machines produce 1,800 parts on nine machines. How many hours will it produce 2 100 parts on seven such machines? - On a farm

On a farm, there are 90 rabbits, 700 sheep, 300 cattle and 500 pigs. What percentage of the total number of animals are rabbits? - Average height

The average height of all pupils is 162 cm. The class teacher's height is 178 cm. The average height of all (teacher and all pupils) is 163 cm. Calculate the number of pupils in the class. - Carrot seed

Carrot seed germination is 85%, weight 1000 carrots seeds are 2.4g. How many seeds are likely to germinate if we sow 8g of seeds? - Special watch

Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°? - Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z. - Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm. - Three people

Three people start doing a work at a same time. The first worked only 2 hours. The second ended 3 hours before the end. On an individual basis, it would take the first time to do the work 10 hours, second 12 hours and 15 hours third. How many hours did it. - Three points

Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?

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