# System of equations + square (second power, quadratic) - practice problems

#### Number of problems found: 59

- The ratio 7

The ratio of the sides of two squares 4:5 if the sum of their areas is 180 cm² Find the sides of the two squares. - The satellite

The satellite orbiting the Earth at an altitude of 800 km has a speed of 7.46 km/s. For how long would it have to move from the start to the orbit to reach this speed if it evenly accelerated its motion in a straight line? What is the acceleration of sate - Louis

Louis wants to carpet the rectangular floor of his basement. The basement has an area of 5,120 square feet. The width of the basement is 4/5 its length. What is the length of Louis's basement? - Truncated pyramid

The truncated regular quadrilateral pyramid has a volume of 74 cm^{3}, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base. - The block

The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block. - Long hot dog

In Kostelec above Black Forest, they made a record-long hot dog. When slowly moved it to the square, one of the spectators decided to measure its length: the size of his footprint is 28 cm; he measured 20 feet in travel direction, counted 5 feet against t - Outside point

The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4? - The sum

The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - 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. - Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - 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] - Find the 13

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 the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents 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? - 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 at the same time had a content of 40cm² and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the - 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.

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