Equation + square - practice problems - page 8 of 21
Number of problems found: 414
- 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. - Circumference 26651
A rectangle with sides of lengths a, b (cm) has a circumference of 100 cm. The dependence of its area P (in cm2) on the number a can be expressed by the quadratic function P = sa + ta². Find the coefficients s, t. - 1 page
One page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book? - Intersections 25141
The quadratic function has the formula y = x²-2x-3. Sketch a graph of this function. Find the intersections with the axes. Find the vertex coordinates. - Calculate 25111
The quadratic function has the formula y = -2x²-3x + 8. Calculate the function value in points 5, -2, and ½.
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - The circumference
The circumference and width of the rectangle are in a ratio of 5:1. Its area is 216cm². What is its length? - Percentage increase
What is the annual percentage increase in the city when the population has tripled in 20 years? - 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. - A map
A map with a scale of 1:5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
- Birthdays
In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give it himself. A total of 650 candies were distributed in the class per year. How many students are in - Quadratic 21643
Solve the quadratic equation: 2y²-8y + 12 = 0 - Coefficient 21623
In the equation 2x² + bx-9 = 0 there is one root x1 = -3 / 2. Determine the second root and the coefficient b - Magnification 21383
When we increased the circle's radius by 2 cm, its area increased by 40π cm². Determine the radius of the circle before magnification. - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
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