Quadratic equation + geometry - practice problems - page 3 of 6
Number of problems found: 113
- Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - 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 - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Shell area cy
The cylinder has a shell area of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
- The cylinder
The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder. - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Dimensions 20553
The surface of the block is 558 cm², and its dimensions are in the ratio of 5:3:2. Calculate the volume. - Calculate 19443
Calculate the height of the cylinder when r = 10 mm and S = 800 mm². Calculate the radius / r / of the cylinder when the height is 20 mm and S = 1000 mm². - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block.
- Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14, and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not? - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - 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. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23
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