Directions: Please help with the following visual questions.

For the multiple choice ones you can simply show the answer to save time however please provide WORK for my understanding for the non-multiple choice questions!

Note: THIS ISNT FOR AN ASSIGNMENT BUT MERELY FOR MY OWN UNDERSTANDING AND COMPREHENSION! PLEASE BE ORGINAL! THIS IS FOR PRACTICE.

Which of the following is the equation of the circle with center C and a point P on the circle, as shown in the graph? P 5 4- 3 2 r = 10 -6 -5 -4 -3 -2 1 0 2 3 4 5 6 -1 -2 -3 C -4 -5 6 O(x - 4)2 + () + 5)2 = 10 O (x + 2)2 + (y-3)2 = 10 O (x - 2)2 + () + 3)2 = 100 O (x + 4)2 + (y-5)2 = 100A railroad's track can be determined using the following graph. 10 -10 -8 8 7 6 5 4 -3 -2 12345 6 10 Several different roadways are in the same region as the railroad. Part A: A highway's path can be found using the equation 2x + 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. Part B: A turnpike's route is determined by the equation y - -x. Prove algebraically how many intersections there will be between the railroad and the tumpike, showing all necessary work. An ice cube is freezing in such a way that the side length s, in inches, is s() = 2+6. where f is in hours. The surface area of the ice cube is the function A(s) = 682. Part A: Write an equation that gives the volume at I hours after freezing begins. Part B: Find the surface area as a function of time, using composition, and determine its range. Part C: After how many hours will the surface area equal 384 square inches? Show all necessary calculations.Which of the following equations would correspond to a conic section formed when a plane intersects a cone perpendicular to the base? Ox2 + 2 -32 Ox - By 52 Which conic section is formed in the image shown? Circle O Parabola O Ellipse Hyperbola To form a circle, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? The plane is at an angle that is neither parallel nor perpendicular to the base of the cone. The plane must be at a 45" angle to the base of the cone. The plane may be perpendicular to the base of the cone. The plane is parallel to the base of the cone. Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone? O Circle Parabola One line Two linesThe graphs of f (x) = x3 + x2 - Gx and g(x) = ex -3 - 1 have which of the following features in common? O Range Ox-intercept Oy-intercept O End behavior Which graph represents two functions that are decreasing on all points across the domain that is common to both functions? O h(=) 3(z) -5 4 4 2 1 2A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 16 mm halfway across a horizontal distance of SCI mm. Part A: Write the equation 01 the parabola in standard form that models the spider's jump. Show your work. [4 points) Part B: Identify the focus, direotrix, and axis of symmetry of the parabola. {5 points] Which equation represents the graph of the circle? O(x -32+ 6+ 57 - 16 Ow+3/ + (+ 5 -4 O( + 3/+ ly-57 -4 Ow+3/+1-57 - 16 Which is the equation of the circle that has a diameter with endpoints located at (-2, 0) and (8, 6)? Oux - 22 +4-37 - 25 O(x-27 +(-2) - 100 O(x - 67 + 6-67 - 100 O(x . 2) + y - 26 Addison and Kelsey are running on a path modeled by x? + y - 12x - By - 309 =0, where the distance is in meters. What is the maximum distance between the runners at any given time? 38 meters 35 meters 20 meters 19 metersA right triangle is shown in the graph. y (ac, y) (a, b) b Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (a, b) and a point on the circle at (x, y). Show all necessary math work. Part B: If (a, b) = (5, -2) and c = 10, determine the domain and range of the circle. Part C: Is the point (10, 2) inside the border of the circle if (a, b) = (5, -2) and c = 10? Explain using mathematical evidence.What is the interval in which both f (x) and g(x) are positive? 10 f(x) -10 -9 -8 -7 6 -5 4 -3 -2 -10 2 4 5 6 7 8 9 10 g() O (-1, 00) O (2, 00) O (3, 00) O (-00, 2) u (2, co )Which is the standard equation of the parabola in the graph? -9- Directrix 7 -6- -5 4 Focus Axis P = 2 -5 -4 -3 2 -1 0 2 3 4 5 6 B -1- -2 Ox2 = 8(y - 3) Ox2 = -8(y + 3) O ( + 3)2 = -8x O (y - 3)2 = 8x The path of a skateboarder can be modeled by the equation (x - 3)