# Quadratic Equations Problems

#### Number of problems found: 464

- 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 3 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 has x? - Solve 12

Solve 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. It took 10 minutes longer for his trip than it would have taken it 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. Calculate the value of x. - A boy 2

A boy dropped a coin from top of the dry well and a sound was heard by him 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? - Determine 73454

The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - Unknown 72884

The square root of an unknown number equals the square of 2. What is the unknown number? - Hypotenuse 72524

We know the height of the hypotenuse h = 4cm and the hypotenuse c = 19cm in a right triangle. How to calculate the segments of legs - sections on the hypotenuse c1, c2 - One side 2

One side of the rectangle is 3 times larger, and the other is 4 cm smaller than the side of the square. Find the area of the square if more than the area of the rectangle by 10 cm². - An equivalent

An equivalent triangle has the same perimeter of a rectangle whose sides are b and h (b > h). Considering that the area of the triangle is 3 times the area of the rectangle. What is the value of b/h? - Calculate 70804

The garden has the shape of a right triangle and is fenced with a fence length of 364m. The shorter slope of the triangle is 26 m long. Calculate the area of this garden. - Variations 70724

If we increase the number of elements by 2, the number of variations of the second class without repetition increases by 22. How many elements do we have initially? - Combinations 70714

If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have? - Quadrilateral 70294

The edge lengths of a quadrilateral prism are in the ratio a: b: c = 2: 4: 5. The surface of the prism is 57 cm². Calculate the volume. - Consecutive 69904

The three numbers that make three consecutive members of an arithmetic sequence have a sum of 60 and a product of 7500. Find these numbers. - Vertically 65984

We threw the stone vertically upwards at a speed of v = 15m. s-1. How long will it be at a) 10 m, b) 12 m?

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