System of equations + square (second power, quadratic) - practice problems
Number of problems found: 111
- Inverse matrix
Find out the inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3] - Difference 3113
The difference between the two numbers is 82. The first number is eight, less than the square of the second number. Specify these numbers. - Quadratic function
Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4) - Equation 80525
Write the equation of the parabola that passes through the points: A[1,1] B[3,-1] C[1,2] - Garden
The garden has a rectangular shape, a circumference of 130 m, and an area of 800.25 m². Calculate the dimensions of the garden. - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - Parabola 3
Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. f: y=x²+bx+c - Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle. - Parametric equation
Point A [6; -2]. Point B = [-3; 1] Write the parametric equation of the line BA so that t belongs to the closed interval < 0;3 > - Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q. - 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 - 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. The square and rectangle have the same area. Calculate the length of the sides of a square and a rectangle. - Parabola
Find the equation of a parabola that contains the points at A[10; -5], B[18; -7], C[20; 0]. (use y = ax²+bx+c) - Rectangular field
One dimension of the rectangular field is 56 m greater than the second dimension. If each side of the rectangle increases by 10 m increases, the surface field is 1480 m². Find dimensions of the field. - Intersection 81611
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Determine 70894
The two numbers are in a 3:4 ratio. Their product is 108. Determine the larger of them. - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - 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] - Two girl's numbers
Dagmar and Julka had numbers. Dagmar's number was equal to the square root of Julka's number. The sum of Dagmar's and Julka's numbers equals 84. Find what number Dagmar and Julka had.
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