Square (second power, quadratic) + system of equations - practice problems - page 3 of 6
Number of problems found: 111
- Line intersect segment
Decide whether the line p : x + 2 y - 7 = 0 intersects the line segment given by points A[1, 1] and B[5, 3] - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0 - In the
In the rectangle ABCD, the distance of its center from line AB is 3 cm greater than from line BC. The circumference of the rectangle is 52 cm. Calculate the area of the rectangle. Express the result in cm².
- The circumference
The circumference and width of the rectangle are in a ratio of 5:1. Its area is 216cm². What is its length? - 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 gardens
The total area of the two gardens is 864 m². The first garden is 60 m² smaller than three times the second garden. What is the area of each garden? - Czechoslovakia 17233
Slovakia has an area 38% smaller than the Czech Republic. Original Czechoslovakia had an area of 128,000 square kilometers. What are the areas of both states? - Two patches
Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches simultaneously had an area of 40cm² and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the sec
- Rectangular garden
The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters. - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23 - Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second, differ by 19272 cm². Calculate the edge length of both cubes. - Rectangular 8136
Divide a square garden with a perimeter of 124 m into two rectangular gardens, with the fence of one garden 10 m longer than the fence of the other. What dimensions will these rectangular gardens be? - Determine 8134
The perimeter of the rectangle, which can be divided into three squares, is 168 cm. Determine the lengths of its sides.
- Dimensions 8044
In the given rectangle, the length is 12 m greater than the width. We get a square if we reduce the length by 10 m and increase the width by 2 m. The area of the original rectangle is 300 m² more than the area of the square. Determine the dimensions of th - Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Divisors 7779
Two numbers are guessing. The second number is five times greater than the first number, and the square of the first number is equal to 3/5 of the second number. Find the sum of the two numbers and all its divisors. - Rectangle 7768
The base of a cuboid is a rectangle. The ratio of its length to width is 3:2. The length of the rectangle of the base is in the ratio of 4:5 to the height of the block. The sum of the lengths of all the edges of the block is 2.8m. Find: a) the surface of
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