Inequalities - high school - practice problems
Number of problems found: 27
- 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. - In the
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? - Three-digit numbers
How many three-digit numbers are not closer to 600 on the number axis than 400? - Open intervals
Open intervals A = (x-2; 2x-1) and B = (3x-4; 4) are given. Find the largest real number for which A ⊂ B applies.
- Inequality: 33371
Solve the quadratic inequality: -2x² + 4x + 6 - The perimeter of the rectangle
The length, l, of a rectangle is 4 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. What inequality shows the range of possible widths of the rectangle? - Inequality 12021
Solve on Z - inequality with absolute value: | x-18 | +4> 1 - Probability 7991
We have the numbers 4, 6, 9, 13, and 15. What is the probability that these will be the lengths of the sides of the triangle? (Consider only scalene triangles.) - 600 pencils
Six hundred pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
- The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - Inequality 7320
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Domains: 4845
Specify function domains: a / y = 2x-1 b / y = 5x / (2x + 1) c / y = x² / (x²-9) - Quadratic inequation
If 5x + x² > 100, then x is not - Inequalities: 4229
Find the number of all integers x that satisfy the following two inequalities: | x + 2 | = 3
- Inequality with fraction
(1 + 3x) / (x-2)> 3 - Probability 3322
We have the numbers 4, 6, 8, 10, and 12. What is the probability that with a randomly selected triangle, these will be the lengths of the sides of a scalene triangle? - Horses 2773
Horses, sheep, and ducks graze in the meadow. Sheep are more than ducks. Sheep and ducks have a total of 100 heads and legs. Ducks and sheep are three times more than horses. How many horses are there? - Lion or virgin
We toss the coin, and every throw fits a lion or a virgin with an equal probability of 1/2. Determine how much we have to make throws that, with the probability of 0.9, lions fell at least once. - Quadratic function
It is given a quadratic function y = -4x²+5x+c with an unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
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