Answer the following below. show your solution.

Using Euler's Formula for Polyhedra, how many edges should a solid figure with * 6 vertices, and 8 faces have to make it a polyhedron? O 8 O 10 O 12 O 14Which of the following statements is true about the equation x2 - 2x + y? - 2y -14 = 0? O a. The radius is 16 O b. The center is at (1, 1) c. The radius is 32 O d. The center is at (-1, -1)What is the length of the latus rectum of a parabola with general equation x2 - 6x - 8y + 49 = 0? O a. 8 O b. 4 O c. 2 O d. 6Which is true? * There are two standard equation of the ellipse. 2 2 (a) The standard equation of the ellipse is :iz + {2 = 1 has the transverse axis as the x- axis and the conjugate axis as the y-axis. 2 yZ kb) The standard equation of the ellipse is :7 + E = 1 has the transverse axis as the y- axis and the conjugate axis as the x-axis. O a. Statement (a) is true and (b) is false. 0 b. Statement (a) is false and (b) is true. 0 a. Bath statements are true. 0 d. Both statements are false. What is the equation of the hyperbola with Foci at (5. O) and (5. O), and conjugate axis of length 8? x'_ b__ 9 16 ' 25 16 Find the surface area of a square pyramid given that its base area is 196 square * inches and the height of each of its triangular faces is 16 inches. Base area= 196 11.: 0000 7. What is the center and radius 0f the circle? x2+y2+8x4y=11 a. Center (4, -2}; r= 3 b. Center (-4, -2); r= 9 0. Center (4, -2); r=9 cl. Center (-4, 2); r= 3 One section of a suspension bridge hangs between two towers that are 50 feet * above the surface and 400 feet apart, as shown in the figure below. A cable strung between the tops of the two towers is in the shape of a parabola with its vertex 10 feet above the surface. With axes drawn as indicated in the figure. what is the equation of the parabola