Inequalities - examples
May be the largest angle in the triangle less than 70°?
- 3-bracket 2
May be the smallest angle in the triangle greater than 20°?
- 3-bracket 3
Two angles in a triangle are 80° and 50°. Has triangle at least two equal sides?
How many intersections have circles with radius 12 dm and 17 dm, if the distance of their centers is 20 dm.
It is true (prove it) that if a> b> 0: ?
An isosceles triangle has two sides of length 9 dm and 35 dm. How long is a third side?
At party overyone clink with everyone. Together, they clink 406 times. How many people were at the party?
- Report card
Ivor hit 1× grade 5 at the beginning of the school year. How many times must now catch grade 1 to get grade 2 on report card?
Athletes standing in rows of eight. Ivan estimated that athletes are more than 120. Peter claimed that there are fewer than 130. Both are right. How many are athletes?
- Dining tables
In the dining room are tables with 4 chairs, 6 chairs, 8 chairs. How many diners must be at least to be occupy all tables (chairs) and diners are more than 50?
- Grass garden
Mr. Grass would itself be mowed garden for 5 hours. His son Michael could do it for 7 hours. They agreed that they wake up at 5 am and begins to mow together. Ms. Grass needs drive into town at 8.30. Michael says that at that time they're done with work..
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
- Lion or virgin
We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
When gas consumption, the consumer may choose one of two rates: rate A - which pays 0.35 € per 1 m3 of gas a flat monthly fee of 3.6 € (regardless of consumption) rate B - which pays 0.295 € per 1 m3 of gas a flat monthly fee of 8.3 € From what monthl
- 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.
Solve the inequation: 5k - (7k - 1)≤ 2/5 . (5-k)-2
- Mr. John
Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150.
- Cyclist vs car
Cyclist rode out of the city at 18 km/h. 1 hour 30 minutes behind him started car and caught up with the cyclist in 50 minutes. How fast was driving the car? Where (what kilometer) from the city car overtook a cyclist?