System of equations + line - practice problems - page 2 of 3
Number of problems found: 47
- 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] - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - In the
In the rectangle ABCD, the distance of its center from line AB is 3 cm greater than from line BC. The circumference of the rectangle is 52 cm. Calculate the area of the rectangle. Express the result in cm². - Coordinates
Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
- Trapezoid 20873
In the trapezoid ABCD (AB II CD) is α = 57 °, γ = 4β. Calculate the size of all interior angles. - Motion
The two bodies move in the same direction evenly in a straight line, at speeds of 5 cm/s and 10 cm/s. The movement of the first body started 2 seconds earlier than the movement of the second body, from a point located at a distance of 20 cm from the start - Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Three points 4
The line passed through three points - see table: x y -6 4 -4 3 -2 2 Write line equation in y=mx+b form. - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23
- Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angle size. - Describe 6648
Images of three numbers are marked on the number line: 0, m, 3m-1. The marked pieces are the same length. a) express the ratio m:(3m-1) b) mark and describe the image of the number 1 on the number line. - Intersection 6374
Determine the intersection of the two lines p and q if. : p: 3y + 2x-5 = 0 q: 4x + 7y-11 = 0 - Coordinates of the vertices
Calculate the coordinates of the vertices of a triangle if the equations of its sides are 7x-4y-1 = 0 x-2y + 7 = 0 2x + y + 4 = 0 - Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
- Simultaneously 5610
Two cyclists rode towards each other simultaneously from opposite ends of the 28km long route. Each covered the entire route at a constant speed, the fastest being at the finish line 35 minutes earlier. On the route, the cyclists passed each other after 1 - Intersection 5413
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - Line segment
Cut a line segment of 15 cm into two line segments so that their lengths are in a ratio of 2:1. What length will each have? - Equations 5070
Solve in RxRxR a system of 3 linear equations with three unknowns: 1/2 x + 3/4 y = 6z 2x-z = 10 1/2 2z + x = 2y + 7 note : / is a fraction line - Linear function
What is the equation of linear function passing through points: a) A (0,3), B (3,0) b) A (-2,-6), B (3,4)
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