A logo consists of an equilateral triangle and a semicircle that both extend outward from different sides of a rectangle. One side of the rectangle coincides with one side of the triangle, and another side of the rectangle coincides with the diameter of the semicircle. What is the perimeter of the entire logo

The first few steps in solving the quadratic equation 9x2 + 49x = 22 ? 5x by completing the square are shown. 9x2 + 49x = 22 ? 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

An energy drink company claims that its product increases students' memory levels. to support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. the missing component in this study is a .