Examples of equations for high school - page 6 of 63
Number of problems found: 1250
- 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. - Introduced 81104
The * (asterisk) operation assigning one number to two pairs of numbers is introduced as follows: (a, b)*(c, d) = ac+bd We know that: (x,2)*(-1, v) = -1 and (2,-1)*(u, v)=5 and (u, v)*(1,1)=-2 What is (1,2)*(x, y) equal to if y=3? - Circle's 81078
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - Three-digit 81064
A three-digit number has a digit sum of 16. If we change the digits in the hundreds and tens places in this number, the number is reduced by 360. If we swap the ten's and one's digits in the original number, the number increases by 54. Find this three-dig
- Individual 81044
CZK 895 was paid for three ties. A blue tie was 18% more expensive than a gray one, and a brown one was CZK 100 more expensive than a gray one. Calculate the prices of individual ties. - Quadrilateral 81033
The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases. - Thanks 81022
Pavla is 2x older than Irena. Four years ago, Pavla was 6 times older than Irena was then. In how many years will the ages of Pavla and Irena be in the ratio of 4:3? Thanks - 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? - Five-minute 80951
Karel has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one.
- Transported 80813
Three Tatras transported 22.2 tons of sand. The second Tatra transported 20% more than the first, and the third Tatra 25% more than the second. How much did each Tatra take? - Calculate 80804
The school bought 20 tablets and 15 laptops for the students for a total of exactly €6,000. Calculate the amount of one tablet and the price of a laptop if the tablet was €50 cheaper than the laptop. - Grandmother 80795
The grandmother is 4 times older than the grandson. In 7 years, it will be only 3 times. How old is grandma? - Increases 80774
A bus travels between places A and B. If it increases its average speed by 5 km/h, the travel time will be reduced by 20 minutes. If he reduces his original speed by 4 km/h, the driving time is increased by 20 minutes. What is the average speed of the bus - 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?
- Repairing 80759
They spent three days repairing the damaged pipe, 115 m long. On the first day, they repaired a quarter of what they did on the second day, and on the third day, they repaired 20m less than on the second day. How many m of pipe did they repair on the firs - Numbers 80756
The first number is 50% of the second, the second number is 40% of the third, and the third number is 20% of the fourth. The sum of the numbers is 396. Which numbers are these?? - Determine 80714
Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the t - Determine 80662
Given the function y = x² - 4x + 3. Determine all real numbers z such that g(x) = g(-2). - Combinations 80637
If the number of elements decreases by 4, the number of combinations of the second class from these elements decreases three times. How many elements are there?
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