Quadratic Equations Problems - page 10 of 30
Number of problems found: 584
- Perpendicular legs PT
In a right triangle, one leg is 5 cm longer than the other leg. The hypotenuse is 150 mm. Calculate the lengths of the legs. - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - 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? - Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, the second 4, and keep the third, we get the geometric series. Find AP and GP members. - The cylinder
In a rotating cylinder, it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Rotary cylinder
In the rotary cylinder, it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - 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 - Hard cone problem
The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone. - Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence. - The pool
The cube-shaped pool has 140 cubic meters of water. Determine the bottom's dimensions if the water's depth is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom? - The product of the roots Find the product and the sum of the roots of x² + 3x - 9 = 0
- 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? - Rectangles - integers
How many different rectangles with integer side lengths have an area S = 60 cm²? - Staircase
On a staircase 3.6 meters high, the number of steps would increase by three if the height of one step decreased by 4 cm. How high are the stairs? - Please
Please determine the solvability conditions of the equation, solve the equation and perform the test: x divided by x squared minus 2x plus1 the whole minus x + 3 divided by x squared minus one is equal to 0: x/(x²-2x+1) - (x+3)/( x²-1) = 0 - Quadratic inequality solving
Solve the quadratic inequality: -2x² + 4x + 6 - The tangent line
Find the tangent line of the ellipse 9x² + 16y² = 144 with slope k = -1. - Tangents to ellipse Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1].
- 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. - Area and perimeter of rectangle
The rectangle area is 3000 cm2, and one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
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