Reason + quadratic equation - practice problems
Number of problems found: 69
- Palidrom
A number consists of two digits whose product is 24. When 18 is subtracted from the number, the digits change their places. Find the number. - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Participants 80965
After the meeting, all participants shook hands with each other - a total of 105 times. How many people were there at the meeting? - Increases 80772 The product of two numbers we know. If we increase the first factor by 2 and decrease the second factor by two, the product increases by 4. How much does the product change if we decrease the first factor by 3 and increase the second factor by 3?
- Parabolic 79764
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Variations 70724
If we increase the number of elements by 2, the number of variations of the second class without repetition increases by 22. How many elements do we have initially? - Combinations 70714 If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have?
- AP - consecutive members
In the arithmetic sequence, a1 = 4.8, d = 0.4. How many consecutive members, starting with the first, need to be added so that the sum is greater than 170?
- Two workers
One worker makes a part 4 hours and the second 9 hours later than they would make the same part together. How long does it take for each worker to make the part himself? - Tourists
Tourists hire a guide. Everyone will pay the same amount. If there are two fewer of them, they will pay 14 crowns more, and if there are three more, they will pay 14 crowns less. How many tourists are there and how much have the guides paid? - Two grandmothers
Two grandmothers went to the market to sell eggs, and they had 100. When they sold all the eggs, they made the same money. The first grandmother said to the second, "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmother replied - Pagans
Jano and Michael ate pagans. Jano ate three more than Michael. The product of their counts (numbers) is 180. How many pagans did each of them eat? - Kohlrabies
The price of one kohlrabi increased by € 0.40. The number of kohlrabies a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
- Points in space
There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How long is its longest side? - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - Determine 25341
In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number. - The tourist
The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. However, after a 4 km walk, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re
Ten contestants in the competition answer five questions, one per round. Anyone who answers correctly will receive as many points as the number of competitors who answered incorrectly in that round. After the contest, one of the contestants said: We got 1Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
