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 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 cm3, 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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