Quadratic Equations Problems - page 12 of 30
Number of problems found: 584
- Two-digit number puzzle
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. - Quadratic function graph
The quadratic function has the formula y = x²-2x-3. Sketch a graph of this function. Find the intersections with the axes. Find the vertex coordinates. - Quadratic function value
A quadratic function has the formula y = −2x² − 3x + 8. Calculate the function values at x = 5, x = −2, and x = 1/2. - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - A map
A map with a scale of 1:5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm². What is the actual length and width of the field? - Birthdays
In a classroom, students give candy to their classmates on their birthdays. The birthday student gives one candy to each classmate but does not receive one themselves. A total of 650 candies were given out over the course of the year. How many students ar - Quadratic - EQ2 - complex
Solve the quadratic equation: 2y²-8y + 12 = 0 - Equation root coefficient In the equation 2x² + bx-9 = 0 there is one root x1 = -3 / 2. Determine the second root and the coefficient b
- Difference of legs
In a right triangle, the hypotenuse length is 65 m, and the difference between legs is 23 m. Calculate the perimeter of this triangle. - Equation solving
Solve the equation: 5 / (x-4) - 2 / (4x-16) = - 7 - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Two groves
Two groves A and B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'? - Cylinder height radius
Calculate the height of the cylinder when r = 10 mm and S = 800 mm². Calculate the radius / r / of the cylinder when the height is 20 mm and S = 1000 mm². - Block or cuboid
The wall diagonals of the block have sizes of √29 cm, √34 cm, and √13 cm. Calculate the surface and volume of the block. - Triangle branch length
The right triangle has an area of 225 cm². One of its legs is twice the length of the other. Find the lengths of its legs. - 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
- Combination element calculation
How many elements is it possible to form twice as many second-class combinations as a fourth-class combination? - Combination element count From how many elements is it possible to create 120 second-class combinations?
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