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

#### Number of problems found: 37

- Non linear eqs

Solve the system of non-linear equations: 3x^{2}-3x-y=-2 -6x^{2}-x-y=-7 - 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? - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle. - Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Gardens

The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens? - 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? - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - Land areas

Two land areas is 244 m^{2}. The first parcel is 40 m^{2}less than twice of the second one. What have acreage of each parcel? - Time gone

Square of Richard age equals the age of his mother. When he will be two times older than his mom will be 7/2 times older than he. How old is Richard and his mom? - Two lands

The common area of the two neighboring lands is 964 m^{2}. The second land is 77 m^{2}smaller than twice the size of the first land. Find the areas of each land. - Two gardens

The total area of the two gardens is 864 m^{2}. The first garden is 60 m^{2}smaller than three times the second garden. What is the area of each garden? - Parabola 3

Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ? - Geometric sequence

In the geometric sequence is a_{4}= 20 a_{9}= -160. Calculate the first member a_{1}and quotient q. - Geometric sequence 3

In geometric sequence is a_{8}= 312500; a_{11}= 39062500; s_{n}=1953124. Calculate the first item a_{1}, quotient q and n - number of members by their sum s_n. - Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ? - Quadratic function

Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4) - Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m^{2}. Calculate the dimensions of the garden. - The sum

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

The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?

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