System of equations + real numbers - practice problems
Number of problems found: 10
- Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - The sum 15
The sum of the real numbers x and y is 24. Their difference is 12. What is the value of xy? - Sum and product
The sum of the real numbers x and y is 12. Their difference is 8. What is the value of xy? - Forestry workers
56 laborers have employed planted trees in the forest. For 8 hour work, a day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others if they work 10 hours a day? - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18 - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately? - Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than the second one. How many minutes is filled with the first pump? - Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
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