Quadratic equation + planimetrics - practice problems - page 2 of 11
Number of problems found: 220
- Determine 82394
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t, - Determine 81988
Determine s5 of the geometric sequence if: a1 + a2 = 10 and a4 - a2 = 120 - Perpendicular 81837
Two neighboring cottagers have cottages under the forest by the stream. They decided to build a bridge over the stream at a place far from the two huts. The distance between the cottages is 230 m; one cottage is 120 m from the stream, and the other is 85 - Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence.
- Determine 81587
Determine the type of polygon if the number of all diagonals is 90. (Write down the number of its pages.) - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Determine 80662
Given the function y = x² - 4x + 3. Determine all real numbers z such that g(x) = g(-2). - Two conductors
Two conductors have resistance Rs=5 ohms when connected in series and Rp=1.2 ohms when connected in parallel. Calculate the value of the resistors. - Equation 80525
Write the equation of the parabola that passes through the points: A[1,1] B[3,-1] C[1,2]
- Sequence 80450
How many terms does the sequence have if a1=4, Sn=589, d=3, n=? - FX parabola
Determine the equation of the parabola going through the following co-ordinates (1;2), (-1;-2), and (2;7) - Parabolic 79764
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - Rectangle 78924
The length of the rectangle is 1 cm more than its width. Its content is 4 cm². What is its width?
- Quadrilateral 78874
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime - Calculate 78714
Calculate the size of the base and side of an isosceles triangle if the side is 1 cm longer than the base and the height to the base is 2 cm shorter than the side. - Arithmetic mean - parabola
Find the value of k so that k² + 2k – 3 is the arithmetic mean between k² + 4k + 5 and k² – 6k + 10. - Find all
Find all right-angled triangles whose side lengths form an arithmetic sequence. - A yard
Yevgen is fencing in a yard that is 30 meters longer than it is wide. The yard will have an area of 1000 m². Find its width and length.
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