Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = x 2 + 2x − 5
f(x) = + 1
f(x) = 0x2 − 9x + 7
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Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 2x + 3y is less than negative 3 over 2 times x minus 4part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points)part b: is the point (â’4, 6) included in the solution area for the system? justify your answer mathematically. (4 points)

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.