Quadratic Equations Problems - page 6 of 30
Number of problems found: 584
- Sequence term count
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) - Tennis ball parabola
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? - Find k
Find k so that the terms k-3, k+1, and 4k-2 form a geometric sequence. Show your solution. - Rectangle - diagonal
A rectangle whose one side measures 35 m and the other is 7 m shorter than the diagonal of the rectangle. Calculate its area in m² (square meters). - Rectangle - area and width The length of the rectangle is 1 cm more than its width. Its area is 4 cm². What is its width?
- Quadrilateral circle radius
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 - A construction 2
A construction company will be penalized for its bridge construction delays. The penalty is set at 4,000 for the first day and shall be subjected to a 1,000 increase for each succeeding day. The company can afford a maximum payment of 165,000 for a penalt - Isosceles triangle sides
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. - The product 9
The product of the third and second terms of the arithmetic progression is 3000. If the common difference is 10, find the first term. - 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. - Regular polygons
Two regular polygons, x and y, are such that the number of sides of x is three more than the number of the sides of y. If the sum of the exterior angles of x and y is 117°, how many sides have x? - Solve 12
Solve the following quadratic equation: 3/2-(2x-1)²=5/4 - Intersection of Q2 with line
The equation of a curve C is y=2x² - 8x +9, and the equation of a line L is x + y=3. (1) Find the x-coordinates of the points of intersection of L and C. (ii) show that one of these points is also the - A speedboat
A speedboat goes 900 km against a current of 25 km/hr. Its trip took 10 minutes longer than it would have taken to travel with the current. What is the speedboat's speed in still water? - A cuboid 2
A cuboid with a depth of 4 cm but a length and width of x cm is cut out from one corner of the original cuboid as shown (the original cuboid has dimensions of 10x8x4 cm). The remaining shape has a volume of 199 cm³. Calculate the value of x. - A boy 2
A boy dropped a coin from the top of the dry well and heard a sound 6 seconds later. Considering this as a free-fall object, how deep is the well? The speed of sound in air is approximately 343 m/s. - The length 11
The length of a rectangle is four times its width. If the area is 100 m², what is the length of the rectangle?
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