Square (second power, quadratic) + reason - practice problems - page 4 of 7
Number of problems found: 126
- Equation 6738
Solve the given equation in the set N: 1 - x + x² - x³ + x4 - x5 +…. + = 1/3 - Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with the same circumference so that these circumferences are as small as possible. - Two rectangles
I cut out two rectangles with 54 cm² and 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together, I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your - Prove
Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
- Electrified 6472
The electrified carpet was rectangular, 16 square meters in area, and no two points on it were more than 7 meters apart. What different circuits can carpets that meet these conditions have? - Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - In the
Workers will pave a 1-meter-wide sidewalk in the garden with tiles around the block-shaped pool. The dimensions of the bottom of the pool are 8.5 meters and 6 meters. The height of the pool walls is 2 meters. How many m² of pavement will be laid with tile - The coil
How many ropes (the diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has dimensions: The inner diameter is 400mm. The outside diameter is 800mm. The length of the coil is 470mm. - Determine 5893
Determine the largest integer n for which the square table n×n can be filled with natural numbers from 1 to n² (n squared) so that at least one square power of the integer is written in each of its 3×3 square parts.
- ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Isosceles from square
How many isosceles triangles form in a square when we mark all diagonals? - Horizontally 5480
Let's have a 4x6 grid, i.e., with 5x7 grid points. Can each grid point be colored white or blue so that each point has an even number of white neighbors? At the same time, those points that are connected by one line of the grid are considered to be neighb - Squares 5479
Draw two stone squares. They have a total of 34 stones. What edges do the squares have? - Circumscribed 5465
Inside the rectangle ABCD, the points E and F lie so that the line segments EA, ED, EF, FB, and FC are congruent. Side AB is 22 cm long, and the circle circumscribed by triangle AFD has a radius of 10 cm. Determine the length of side BC.
- Occupies 5461
What is the land area in reality if 1 cm² occupies on a 1:20000 scale map? - Asymmetric 5407
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121) - MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M, and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBC - Three-digit 5312
Find the smallest four-digit number abcd such that the difference (ab)²− (cd)² is a three-digit number written in three identical digits. - Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at a ratio of 5:6. Find the triangle area.
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