Quadratic equation + expression of a variable from the formula - practice problems - page 5 of 13
Number of problems found: 256
- Determine 25341
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. - Calculate 25111
The quadratic function has the formula y = -2x²-3x + 8. Calculate the function value in points 5, -2, and ½. - 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. - 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 cm square. What is the actual length and width of the field? - 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: 21313
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 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'?
- Dimensions 20553
The surface of the block is 558 cm², and its dimensions are in the ratio of 5:3:2. Calculate the volume. - Calculate 19443
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 √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Branches 18533
The right triangle has an area of 225 cm². One of its branches is twice the size of the other. Find the lengths of its hangers. - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
- Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - Rectangle field
The field has a shape of a rectangle, having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m? - Determine 12331
An annulus with an area S = 4.2 square meters has an inner radius r = 2.25 m. Determine the outer radius of the annulus. - Flowerbed
We enlarged the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius. - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths.
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