System of equations + square (second power, quadratic) - math problems
Number of problems found: 37
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-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.
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 m2. The first parcel is 40 m2 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 m2. The second land is 77 m2 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 m2. The first garden is 60 m2 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 a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
- Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
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)
The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. 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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