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College Algebra 7th Edition Robert F Blitzer - Solutions

In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.x2 - 4x - 2y = 0
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Major axis vertical with length 10; length of minor axis = 4; center: (-2, 3)
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x + 2)² 9 y² 25 1
The George Washington Bridge spans the Hudson River from New York to New Jersey. Its two towers are 3500 feet apart and rise 316 feet above the road. As shown in the figure, the cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Major axis vertical with length 20; length of minor axis = 10; center: (2, -3)
An engineer is designing headlight units for automobiles. The unit has a parabolic surface with a diameter of 12 inches and a depth of 3 inches. The situation is illustrated in the figure, where a coordinate system has been superimposed. What is the equation of the parabola in this system? Where
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (y + 2)² (x - 1)² 4 16 1
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (y-2)² (x + 1)² 36 49 1
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(x - 2)2 = 8(y - 1)
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Endpoints of major axis: (7, 9) and (7, 3)Endpoints of minor axis: (5, 6) and (9, 6)
In Exercises 34–35, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (12, 0); Directrix: x = -12
The giant satellite dish in the figure shown is in the shape of a parabolic surface. Signals strike the surface and are reflected to the focus, where the receiver is located. The diameter of the dish is 300 feet and its depth is 44 feet. How far, to the nearest foot, from the base of the dish
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(x + 2)2 = 4(y + 1)
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Endpoints of major axis: (2, 2) and (8, 2)Endpoints of minor axis: (5, 3) and (5, 1)
In Exercises 34–35, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (0, -11); Directrix: y = 11
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(x + 1)2 = -8(y + 1)
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(x + 2)2 = -8(y + 2)
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.(x - 3)2 - 4(y + 3)2 = 4
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y + 3)2 = 12(x + 1)
In Exercises 37–50, graph each ellipse and give the location of its foci. (x 3)2 (y + 1)² 3)² - + 16 9 = 1
In Exercises 37–50, graph each ellipse and give the location of its foci. (x-4)² 9 + (y + 2)² 25 1
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.(x + 3)2 - 9(y - 4)2 = 9
In Exercises 37–50, graph each ellipse and give the location of its foci.(x + 3)2 + 4(y - 2)2 = 16
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y + 4)2 = 12(x + 2)
In Exercises 37–50, graph each ellipse and give the location of its foci.(x - 3)2 + 9(y + 2)2 = 18
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.(x - 1)2 - (y - 2)2 = 3
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y + 1)2 = -8x
In Exercises 39–42, identify the conic represented by each equation without completing the square.x2 + 16y2 - 160y + 384 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. 25 + (y (x - 2)² 36 = 1
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.(y - 2)2 - (x + 3)2 = 5
In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y - 1)2 = -8x
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. 2 X 25 y² 4 1
In Exercises 39–42, identify the conic represented by each equation without completing the square.16x2 + 64x + 9y2 - 54y + 1 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x-4)²2 ² = 1 4 25
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.x2 - y2 - 2x - 4y - 4 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x + 3)² 9 + (y-2)² = 1
In Exercises 39–42, identify the conic represented by each equation without completing the square.4x2 - 9y2 - 8x + 12y - 144 = 0
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.4x2 - y2 + 32x + 6y + 39 = 0
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.x2 - 2x - 4y + 9 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x + 2)² 16 + (y - 3)² = 1
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.x2 + 6x + 8y + 1 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x - 1)² (y + 3)² 2 5 = 1
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.y2 - 2y + 12x - 35 = 0
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.9y2 - 4x2 - 18y + 24x - 63 = 0
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.y2 - 2y - 8x + 1 = 0
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.4x2 - 9y2 - 16x + 54y - 101 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x + 1)² 1)²2 (y - 3)² 2 5 = 1
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.4x2 - 9y2 + 8x - 18y - 6 = 0
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.x2 + 6x - 4y + 1 = 0
In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.x2 + 8x - 4y + 8 = 0
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. x²y² 16 9 = 1
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.4x2 - 25y2 - 32x + 164 = 0
In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.9x2 - 16y2 - 36x - 64y + 116 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci.9(x - 1)2 + 4(y + 3)2 = 36
In Exercises 49–56, identify each equation without completing the square.y2 - 4x + 2y + 21 = 0
In Exercises 49–56, identify each equation without completing the square.y2 - 4x - 4y = 0
In Exercises 37–50, graph each ellipse and give the location of its foci.36(x + 4)2 + (y + 3)2 = 36
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. X 2 9 16
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. x 25 4 1
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.9x2 + 25y2 - 36x + 50y - 164 = 0
In Exercises 49–56, identify each equation without completing the square.4x2 - 9y2 - 8x - 36y - 68 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.4x2 + 9y2 - 32x + 36y + 64 = 0
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. y² x 16 9 1
In Exercises 49–56, identify each equation without completing the square.9x2 + 25y2 - 54x - 200y + 256 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.9x2 + 16y2 - 18x + 64y - 71 = 0
In Exercises 51–56, graph each relation. Use the relation’s graph to determine its domain and range. 1² 4 x 25 1
In Exercises 49–56, identify each equation without completing the square.4x2 + 4y2 + 12x + 4y + 1 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.x2 + 4y2 + 10x - 8y + 13 = 0
In Exercises 57–60, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. 2 Jx² - y² = 4 x² + y² = 4
In Exercises 57–60, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. [x² - y² = 9 √x² + y² = 9 2
In Exercises 49–56, identify each equation without completing the square.9x2 + 4y2 - 36x + 8y + 31 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.4x2 + y2 + 16x - 6y - 39 = 0
In Exercises 49–56, identify each equation without completing the square.100x2 - 7y2 + 90y - 368 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.4x2 + 25y2 - 24x + 100y + 36 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.25x2 + 4y2 - 150x + 32y + 189 = 0
In Exercises 57–60, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. 9 = ܐ9x? + y] 9 = ܐ9x ܚ ܐy ܢ ,2
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?y2 + 6y - x + 5 = 0
In Exercises 57–60, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. 2 √4x² + y² = 4 y² - 4x² = 4
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.49x2 + 16y2 + 98x - 64y - 671 = 0
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?y2 - 2y - x - 5 = 0
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.36x2 + 9y2 - 216x = 0
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?y = -x2 + 4x - 3
In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.16x2 + 25y2 - 300y + 500 = 0
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. [x² + y² = 1 x² +9y² = 9
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?y = -x2 - 4x + 4
Moiré patterns, such as those shown in Exercises 65–66, can appear when two repetitive patterns overlap to produce a third, sometimes unintended, pattern.a. In each exercise, use the name of a conic section to describe the moiré pattern.b. Select one of the following equations that can possibly
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. S x² + y² = 25 125x² + y² = 25
An explosion is recorded by two microphones that are 1 mile apart. Microphone M1 received the sound 2 seconds before microphone M2. Assuming sound travels at 1100 feet per second, determine the possible locations of the explosion relative to the location of the microphones.
Radio towers A and B, 200 kilometers apart, are situated along the coast, with A located due west of B. Simultaneous radio signals are sent from each tower to a ship, with the signal from B received 500 microseconds before the signal from A.a. Assuming that the radio signals travel 300 meters per
An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625y2 - 400x2 = 250,000, where x and y are in yards. How far apart are the houses at their closest point? X
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?x = -4(y - 1)2 + 3
In Exercises 63–68, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. (y-2)² = x + 4 1 y = - = 2 x
Scattering experiments, in which moving particles are deflected by various forces, led to the concept of the nucleus of an atom. In 1911, the physicist Ernest Rutherford (1871–1937) discovered that when alpha particles are directed toward the nuclei of gold atoms, they are eventually deflected
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. 2 x ปล 25 9 y = 1 = = 3
In Exercises 63–68, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. [(y - 3)² = x -2 x + y = 5
In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?x = -3(y - 1)2 - 2
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. X 4 + 36 = 1 x = -2
In Exercises 63–68, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. Jx = y2 - 3 |x = y2 - 3у
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. 2 √4x² + y² = 4 2x - y = 2
In Exercises 61–66, find the solution set for each system by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. √4x² + y² = 4 x + y = 3

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