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Published on February 19, 2025
The area of the unknown rectangle (A4) is calculated to be 6 square meters by using the given areas of the other rectangles and the relationships between their dimensions.
The sum of three angles around a point, 2x, x, and x, equals 360 degrees, leading to the solution x = 90 degrees.
To find the unknown interior angle x, the exterior angle theorem was used, setting up and solving an equation to find x = 40 degrees.
The problem involves finding the equation of a circle given a point on the circle, the radius, and the fact that the center of the circle lies on a given line. Two possible circles satisfy the conditions, each with a different center, and the equations for both circles are derived.
The solution finds the trace lines of a plane by setting one coordinate to zero and solving for the other two coordinates in terms of the remaining parameter. This results in parametric equations for the trace lines in the xy, xz, and yz planes.
The solution finds the equation of a line g' that is the reflection of line g across line s. It involves finding the intersection point of g and s, projecting a direction vector of g onto a normal vector of s, and then calculating the direction vector of g'. Finally, the equation of g' is determined using the intersection point and the direction vector of g'.
The unknown angle is 50 degrees.
To find x, the exterior angle theorem is used, along with the knowledge that a right angle is 90 degrees, to solve for x, which equals 45 degrees.
The unknown angle in a triangle, formed by two slanted lines and a vertical line, with two given angles of 80 degrees each, is calculated to be 20 degrees using the triangle angle sum property.
To find x, supplementary angles 5x and 4x are used, along with the fact that the sum of the interior angles of a quadrilateral is 360 degrees. Solving the equation 9x = 180 yields x = 20.
The area of the region defined by the inequalities y ≥ x, y > -x + 1, and y < 10 is 90.25 square units.