# Quadratic equation + system of equations - math problems

#### Number of problems found: 78

- Intersections 3

Find the intersections of the circles x^{2}+ y^{2}+ 6 x - 10 y + 9 = 0 and x^{2}+ y^{2}+ 18 x + 4 y + 21 = 0 - Rectangle

The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides. - Four integers

Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two. - 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. - Circle

The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm^{2}and the side length is 13 cm. - R triangle

Calculate the right triangle area whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Two pipes

One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately? - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Two grandmothers

Two grandmothers went to sell eggs at the market, and they had a total of 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmot - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Kohlrabies

The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros. - Area and perimeter of rectangle

The content area of the rectangle is 3000 cm^{2}, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle. - Golden ratio

Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line. - Rotary cylinder

In the rotary cylinder it is given: surface S = 96 cm^{2}and volume V = 192 cm cubic. Calculate its radius and height. - Pumps

The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? - AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area? - Sequences AP + GP

The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members. - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - 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?

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