Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)? x squared over 16 minus y squared over 4 equals 1
x squared over 12 minus y squared over 4 equals 1
y squared over 16 minus x squared over 4 equals 1
y squared over 12 minus x squared over 4 equals 1

Which of the following are accepted without proof in a logical system? check all that apply.

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part 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 (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Given the equation −4  = 12, solve for x and identify if it is an extraneous solution.