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All Textbook Solutions for College Algebra

For the following exercises, find the determinant. |8415|For the following exercises, find the determinant. |1034|For the following exercises, find the determinant. |1020010|For the following exercises, find the determinant. |100.250.1|For the following exercises, find the determinant. |6384|For the following exercises, find the determinant. |233.14,000|For the following exercises, find the determinant. |1.10.67.20.5|For the following exercises, find the determinant. |100010003|For the following exercises, find the determinant. |140023003|For the following exercises, find the determinant. 17. |101010100|For the following exercises, find the determinant. |231341561|For the following exercises, find the determinant. |214428283|For the following exercises, find the determinant. |612435191|For the following exercises, find the determinant. 21. |511231363|For the following exercises, find the determinant. |1.1214004.10.42.5|For the following exercises, find the determinant. |21.63.11.1389.302|For the following exercises, find the determinant. | 1 2 1 3 1 4 1 5 1 6 1 700 1 8|For the following exercises, solve the system of linear equations using Cramer’s Rule. 2x3y=14x+5y=9 For the following exercises, solve the system of linear equations using Cramer’s Rule. 5x4y=24x+7y=6 For the following exercises, solve the system of linear equations using Cramer’s Rule. 6x3y=28x+9y=1 For the following exercises, solve the system of linear equations using Cramer’s Rule. 2x+6y=125x2y=13 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x+3y=232xy=1 For the following exercises, solve the system of linear equations using Cramer’s Rule. 10x6y=25x+8y=1 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x3y=32x+6y=4 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x5y=73x+9y=0 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x+10y=1803x5y=105 For the following exercises, solve the system of linear equations using Cramer’s Rule. 8x2y=34x+6y=4 For the following exercises, solve the system of linear equations using Cramer’s Rule. x+2y4z=17x+3y+5z=262x6y+7z=6 For the following exercises, solve the system of linear equations using Cramer’s Rule. 5x+2y4z=474x3yz=943x3y+2z=94 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x+5yz=72x9y+2z=85y+7z=21 For the following exercises, solve the system of linear equations using Cramer’s Rule. 38. 4x3y+4z=105x2z=23x+2y5z=9 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x2y+3z=66x+y=22x+7y+8z=24 For the following exercises, solve the system of linear equations using Cramer’s Rule. 5x+2yz=17x8y+3z=1.56x12y+z=7 For the following exercises, solve the system of linear equations using Cramer’s Rule. 13x17y+16z=7311x+15y+17z=6146x+10y30z=18 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x3y8z=72x9y+5z=0.55x6y5z=2 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x6y+8z=102x+3y4z=5x+y+z=1 For the following exercises, solve the system of linear equations using Cramer’s Rule. 4x6y+8z=102x+3y4z=512x+18y24z=30 For the following exercises, use the determinant function on a graphing utility. |1089021010300243|For the following exercises, use the determinant function on a graphing utility. |1021091330210112|For the following exercises, use the determinant function on a graphing utility. | 1 2 1 7 4 0 1 2 100 5 0 0 2 2,000 0 0 0 2|For the following exercises, use the determinant function on a graphing utility. |1000230045607890|For the following exercise, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution. 49. Two numbers add up to 56. One number is 20 less than the other.For the following exercise, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution. 50. Two numbers add up to 104. If you add two times the first number plus two times the second number, your total is 208 For the following exercise, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution. 51. Three numbers add up to 106. The first number is 3 less than the second number. The third number is 4 more than the first number.For the following exercise, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution. 52. Three numbers add to 216. The sum of the first two numbers is 112. The third number is 8 less than the first two numbers combined.For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 53. You invest $10,000 into two accounts, which receive 8% interest and 5% interest. At the end of a year, you had $10,710 in your combined accounts. How much was invested in each account?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 54. You invest $80,000 into two accounts, $22,000 in one account, and $58,000 in the other account. At the end of one year, assuming simple interest, you have earned $2,470 in interest. The second account receives half a percent less than twice the interest on the first account. What are the interest rates for your accounts?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 55. A movie theater needs to know how many adult tickets and children tickets were sold out of the 1,200 total tickets. If children's tickets are $5.95, adult tickets are $11.15, and the total amount of revenue was $12,756, how many children's tickets and adult tickets were sold?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 56. A concert venue sells single tickets for $40 each and couple's tickets for $65. If the total revenue was $18,090 and the 321 tickets were sold, how many single tickets and how many couple's tickets were sold?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 57. You decide to paint your kitchen green. You create the color of paint by mixing yellow and blue paints. You cannot remember how many gallons of each color went into your mix, but you know there were 10 gal total. Additionally, you kept your receipt, and know the total amount spent was $29.50. If each gallon of yellow costs $2.59, and each gallon of blue costs $3.19, how many gallons of each color go into your green mix?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 58. You sold two types of scarves at a farmers' market and would like to know which one was more popular. The total number of scarves sold was 56, the yellow scarf cost $10, and the purple scarf cost $11. If you had total revenue of $583, how many yellow scarves and how many purple scarves were sold?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 59. Your garden produced two types of tomatoes, one green and one red. The red weigh 10 oz., and the green weigh 4 oz. You have 30 tomatoes, and a total weight of 13 1b, 14 oz. How many of each type of tomato do you have?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 60. At a market, the three most popular vegetables make up 53% of vegetable sales. Corn has 4% higher sales than broccoli, which has 5% more sales than onions. What percentage does each vegetable have in the market share?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 61. At the same market, the three most popular fruits make up 37% of the total fruit sold. Strawberries sell twice as much as oranges, and kiwis sell one more percentage point than oranges. For each fruit, find the percentage of total fruit sold.For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 62. Three bands performed at a concert venue. The first band charged $15 per ticket, the second band charged $45 per ticket, and the final band charged $22 per ticket. There were 510 tickets sold, for a total of $12,700. If the first band had 40 more audience members than the second band, how many tickets were sold for each band?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 63. A movie theatre sold tickets to three movies. The tickets to the first movie were $5, the tickets to the second movie were $11, and the third movie was $12. 100 tickets were sold to the first movie. The total number of tickets sold was 642, for a total revenue of $6,774. How many tickets for each movie were sold?For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 64. Men aged 20 - 29, 30 - 39, and 40-49 made up 78% of the population at a prison last year. This year, the same age groups made up 82.08% of the population. The 20 - 29 age group increased by 20%, the 30 - 39 age group increased by 2%, and the 40 - 49 age group decreased to 34 of their previous population. Originally, the 30-39 age group had 2% more prisoners than the 20—29 age group. Determine the prison population percentage for each age group last year.For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 65. At a women's prison down the road, the total number of inmates aged 20 - 49 totaled 5,525. This year, the 20 - 29 age group increased by 10%, the 30 - 39 age group decreased by 20%, and the 40 - 49 age group doubled. There are now 6,040 prisoners. Originally, there were 500 more in the 30-39 age group than the 20-29 age group. Determine the prison population for each age group last year.For the following exercises, use this scenario: A health-conscious company decides to make a trail mix Out Of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in Table 1. 66. For the special "low-carb" trail mix, there are 1,000 pieces of mix. The total number of carbohydrates is 425 g, and the total amount of fat is 570.2 g. If there are 200 more pieces of cashews than cranberries, how many of each item is in the trail mix?For the following exercises, use this scenario: A health-conscious company decides to make a trail mix Out Of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in Table 1. 67. For the "hiking" mix, there are 1,000 pieces in the mix, containing 390.8 g of fat, and 165 g of protein. If there is the same amount of almonds as cashews, how many of each item is in the trail mix?For the following exercises, use this scenario: A health-conscious company decides to make a trail mix Out Of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in Table 1. 68.For the "energy-booster" mix, there are 1,000 pieces in the mix, containing 145 g of protein and 625 g of carbohydrates. If the number of almonds and cashews summed together is equivalent to the amount of cranberries, how many of each item is in the trail mix?For the following exercise, determine whether the ordered pair is a solution to the system of equations. 3xy=4 x+4y=3 and (1,1)For the following exercise, determine whether the ordered pair is a solution to the system of equations. 2. 6x2y=24 3x+3y=18 and (9,15)For the following exercises, use substitution to solve the system of equations. 10x+5y=5 3x2y=12 For the following exercises, use substitution to solve the system of equations. 47x+15y=4370 56x13y=23 For the following exercises, use substitution to solve the system of equations. 5x+6y=14 4x+8y=8 For the following exercises, use addition to solve the system of equations. 3x+2y=7 2x+4y=6 For the following exercises, use addition to solve the system of equations. 3x+4y=2 9x+12y=3 For the following exercises, use addition to solve the system of equations. 8x+4y=2 6x5y=0.7 For the following exercises, write a system of equations to solve each problem. Solve the system of equations. 9. A factory has a cost of production C(x)=150x+15,000 and a revenue function R(x)=200x . What is the break-even point?For the following exercises, write a system of equations to solve each problem. Solve the system of equations. 10. A performer charges C(x)=50x+10,000 , where x is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?For the following exercises, solve the system of three equations using substitution or addition. 0.5x0.5y=100.2y+0.2x=40.1x+0.1z=2 For the following exercises, solve the system of three equations using substitution or addition. 12. 5x+3yz=53x2y+4z=134x+3y+5z=22 For the following exercises, solve the system of three equations using substitution or addition. x+y+z=12x+2y+2z=13x+3y=2 For the following exercises, solve the system of three equations using substitution or addition. 2x3y+z=1x+y+z=44x+2y3z=33 For the following exercises, solve the system of three equations using substitution or addition. 3x+2yz=10xy+2z=7x+3y+z=2 For the following exercises, solve the system of three equations using substitution or addition. 3x+4z=11x2y=54yz=10 For the following exercises, solve the system of three equations using substitution or addition. 2x3y+z=02x+4y3z=06x2yz=0 For the following exercises, solve the system of three equations using substitution or addition. 6x4y2z=23x+2y5z=46y7z=5 For the following exercises, perform the given matrix operations. 19. Three odd numbers sum up to 61. The smaller is one-third the larger and the middle number is 16 less than the larger. What are the three numbers?For the following exercises, write a system of equations to solve problem. Solve the system of equations. 20. A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type was sold?For the following exercises, solve the system of nonlinear equations. y=x27y=5x13 For the following exercises, solve the system of nonlinear equations. y=x24y=5x+10 For the following exercises, solve the system of nonlinear equations. x2+y2=16y=x8 For the following exercises, solve the system of nonlinear equations. x2+y2=25y=x2+5 For the following exercises, solve the system of nonlinear equations. x2+y2=4yx2=3 For the following exercises, graph the inequality. yx21 For the following exercises, graph the system of inequalities. 14x2+y24 For the following exercises, graph the system of inequalities. x2+y2+2x3yx23 For the following exercise, graph the system of inequalities. x22x+y24x4yx+4 For the following exercises, graph the system of inequalities. x2+y21y2x For the following exercises decompose into partial fractions. 2x+6x2+3x+2 For the following exercises decompose into partial fractions. 32. 10x+24x2+4x+1 For the following exercises decompose into partial fractions. 7x+20x2+10x+25 For the following exercises decompose into partial fractions. x18x212x+36 For the following exercises decompose into partial fractions. x2+36x+70x3125 For the following exercises decompose into partial fractions. 5x2+6x2x3+27 For the following exercises decompose into partial fractions. x34x2+3x+11(x22)2 For the following exercises decompose into partial fractions. 4x42x3+22x26x+48x(x2+4)2 For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 39. -4A For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 40. 10D6E For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 41. B+C For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 42. AB For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 43. BA For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 44. BC For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 45. CB For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 46. DE For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 47. ED For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 48. EC For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 49. CE For the following exercises, perform the requested operations on the given matrices. A=[4213],B=[6731124],C=[61114720],D=[1491057285],E=[7143213019] 50. A3 For the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution. [10 3012000|750]For the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution. [10501 2000|943]For the following exercises, write the augmented matrix from the system of linear equations. 2x+2y+z=72x8y+5z=019x10y+22z=3 For the following exercises, write the augmented matrix from the system of linear equations. 4x+2y3z=1412x+3y+z=1009x6y+2z=31 For the following exercises, write the augmented matrix from the system of linear equations. x+3z=12x+4y=0y+2z=7 For the following exercises, solve the system of linear equations using Gaussian elimination. 3x4y=7-6x+8y=14 For the following exercises, solve the system of linear equations using Gaussian elimination. 3x4y=16x+8y=6 For the following exercises, solve the system of linear equations using Gaussian elimination. 1.1x2.3y=6.25.2x4.1y=4.3 For the following exercises, solve the system of linear equations using Gaussian elimination. 2x+3y+2z=14x6y4z=210x+15y+10z=0 For the following exercises, solve the system of linear equations using Gaussian elimination. x+2y4z=83y+8z=47x+y+2z=1 For the following exercises, find the inverse of the matrix. [0.21.41.20.4]For the following exercises, find the inverse of the matrix. [ 1 2 1 2 1 4 3 4]For the following exercises, find the inverse of the matrix. [1296132432]For the following exercises, find the inverse of the matrix. [213123321]For the following exercises, find the solutions by computing the inverse of the matrix 0.3x0.1y=100.1x+0.3y=14 For the following exercises, find the solutions by computing the inverse of the matrix 0.4x0.2y=0.60.1x+0.05y=0.3 For the following exercises, find the solutions by computing the inverse of the matrix 4x+3y3z=4.35x4yz=6.1x+z=0.7 For the following exercises, find the solutions by computing the inverse of the matrix 2x3y+2z=3x+2y+4z=52y+5z=3 For the following exercises, write a system of equations to solve each problem. Solve the system of equations. 69. Students were asked to bring their favorite fruit to class. 90% of the fruits consisted of banana, apple, and oranges. If oranges were half as popular as bananas and apples were 5% more popular than bananas, what are the percentages of each individual fruit?For the following exercises, write a system of equations to solve each problem. Solve the system of equations. 70. A sorority held a bake sale to raise money and sold brownies and chocolate chip cookies. They priced the brownies at $2 and the chocolate chip cookies at $1. They raised $250 and sold 175 items. How many brownies and how many cookies were sold?For the following exercises, find the determinant. 71. [100000]For the following exercises, find the determinant. 72. [0.20.60.71.1]For the following exercises, find the determinant. 73. [143023003]For the following exercises, find the determinant. 74. [200020002]For the following exercises, use Cramer’s rule to solve the linear systems of equations. 75. 4x2y=235x10y=35 For the following exercises, use Cramer’s rule to solve the linear systems of equations. 76. 0.2x0.1y=00.3x+0.3y=2.5 For the following exercises, use Cramer’s Rule to solve the linear systems of equations. 77. 0.5x+0.1y=0.30.25x+0.05y=0.15 For the following exercises, use Cramer’s rule to solve the linear systems of equations. 78. x+6y+3z=42x+y+2z=33x2y+z=0 For the following exercises, use Cramer’s rule to solve the linear systems of equations. 4x3y+5z=527x9y3z=32x5y5z=52 For the following exercises, use Cramer’s rule to solve the linear systems of equations. 310x15y310z=150110x110y12z=95025x12y35z=15 Is the following ordered pair a solution to the system of equations? 5xy=12 x+4y=9with(3,3)For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 12x13y=4 32xy=0 ]For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 12x4y=4 2x+16y=2 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 4. 5xy=1 10x+2y=2 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 4x6y2z=110 x7y+5z=14 3x+6y9z=65 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 6. x+z=20 x+y+z=20 x+2y+z=10 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 5x4y3z=0 2x+y+2z=0 x6y7z=0 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. y=x2+2x3 y=x1 For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. 9. y2+x2=25 y22x2=1 For the following exercises, graph the following inequalities. 10. yx2+9 For the following exercises, graph the following inequalities. x2+y24 yx2+1 For the following exercises, write the partial fraction decomposition. 8x30x210x+25 For the following exercises, write the partial fraction decomposition. 13x+2(3x+1)2 For the following exercises, write the partial fraction decomposition. x4x3+2x1x(x2+1)2 For the following exercises, perform the given matrix operations. 5[4923]+12[61248]For the following exercises, perform the given matrix operations. [1472951204][34 1 5 3 10 ]For the following exercises, perform the given matrix operations. [ 1 2 1 3 1 4 1 5 ]1 For the following exercises, perform the given matrix operations det|004004,000|For the following exercises, perform the given matrix operations. det| 1 2 1 20 1 20 1 20 1 20|For the following exercises, perform the given matrix operations. 20. If det(A)=6 , what would be the determinant if you switched rows 1 and 3, multiplied the second row by 12, and took the inverse?For the following exercises, perform the given matrix operations. 21. Rewrite the system of linear equations as an augmented matrix. 14x2y+13z=1402x+3y6z=1x5y+12z=11 For the following exercises, perform the given matrix operations. 22. Rewrite the augmented matrix as a system of linear equations. [103249612|1258]For the following exercises, solve the system of nonlinear equations. x6y=42x12y=0 For the following exercises, use Gaussian elimination to solve the systems of equations. 2x+y+z=3x2y+3z=6xyz=6 For the following exercises, use the inverse of a matrix to solve the systems of equation 4x5y=50x+2y=80 For the following exercises, use the inverse of a matrix to solve the systems of equations. 1100x3100y+120z=493100x7100y1100z=139100x9100y9100z=99 For the following exercises, use Cramer’s Rule to solve the systems of equations. 200x300y=2400x+715y=4 For the following exercises, use Cramer’s Rule to solve the systems of equations. 28. 0.1x+0.1y0.1z=1.20.1x0.2y+0.4z=1.20.5x0.3y+0.8z=5.9 For the following exercises, solve using a system of linear equations. 29. A factory producing cell phones has the following cost and revenue functions: C(x)=x2+75x+2,688 and R(x)=x2+160x . What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.For the following exercises, solve using a system of linear equations. 30. A small fair charges $1.50 for students, $1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of $1,050. How many of each type of ticket was sold?What is the standard form equation of the ellipse that has vertices (0,4) and foci (0+15)What is the standard form equation of the ellipse that has vertices (3,3)and(5,3) and foci (123,3) and (1+23,3) ?Graph the ellipse given by the equation x236+y24=1 . Identify and label the center, vertices, co-vertices, and foci.Graph the ellipse given by the equation 49x2+16y2=784 . Rewrite the equation in standard form. Then identify and label the center, vertices, co-vertices, and foci.Graph the ellipse given by the equation (x4)236+(y2)220=1 . Identify and label the center, vertices, co-vertices, and foci.Express the equation of the ellipse given in standard form. Identify the center, vertices, co-vertices, and foci of the ellipse. 4x2+y224x+2y+21=0 Suppose a whispering chamber is 480 feet long and 320 feet wide. a. What is the standard form of the equation of the ellipse representing the room? Hint: assume a horizontal ellipse, and le the center of the morn he the point (0,0) . b. If two people are standing at the foci of this morn and can hear each other whisper, how far apart are the people? Round to the nearest fool.Define an ellipse in terms of its foci.Where must the foci of an ellipse lie?What special case of the ellipse do we have when the major and minor axis are of the same length?For the special case mentioned in the previous question, what would be true about the foci of that ellipse?What can be said about the symmetry of the graph of an ellipse with center at the origin and foci along the y-axis?For the following exercises, determine whether the given equations represent ellipses. If yes. write in standard form. 6. 2x2+y=4 For the following exercises, determine whether the given equations represent ellipses. If yes, write in standard form. 7. 4x2+9y2=36 For the following exercises, determine whether the given equations represent ellipses. If yes, write in standard form. 8. 4x2y2=4 For the following exercises, determine whether the given equations represent ellipses. If yes, write in standard form. 9. 4x2+9y2=1 For the following exercises, determine whether the given equations represent ellipses. If yes write in standard form. 10. 4x28x+9y272y+112=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 11. x24+y249=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 12. x2100+y264=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 13. x2+9y2=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 14. 4x2+16y2=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 15. (x2)249+(y4)225=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 16. (x2)281+(y+1)216=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 17. (x+5)24+(y7)29=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 18. (x7)249+(y7)249=1 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 19. 4x28x+9y272y+112=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 20. 9x254x+9y254y+81=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 21. 4x224x+36y2360y+864=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 22. 4x2+24x+16y2128y+228=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 23. 4x2+40x+25y2100y+110=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 24. x2+2x+100y21000y+2401=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 25. 4x2+24x+25y2+200y+336=0 For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci. 26. 9x2+72x+16y2+16y+4=0 ALGEBRAIC For the following exercises, find the foci for the given ellipses. 27. (x+3)225+(y+1)236=1 For the following exercises, find the foci for the given ellipses. 28. (x+1)2100+(y2)24=1 For the following exercises, find the foci for the given ellipses. 29. x2+y2=1 For the following exercises, find the foci for the given ellipses. 30. x2+4y2+4x+8y=1 For the following exercises, find the foci for the given ellipses. 31. 10x2+y2+200x=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 32. x225+y236=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 33. x216+y29=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 34. 4x2+9y2=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 35. 81x2+49y2=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 36. (x2)264+(y4)216=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 37. (x+3)29+(y3)29=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 38. x22+(y+1)25=1 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 39. 4x28x+16y232y44=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 40. x28x+25y2100y+91=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 41. x2+8x+4y240y+112=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 42. 64x2+128x+9y272y368=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 43. 16x2+64x+4y28y+4=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 44. 100x2+1000x+y210y+2425=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 45. 4x2+16x+4y2+16y+16=0 For the following exercises, graph the given ellipses, noting center, vertices, and foci. 46. Center at the origin, symmetric with respect to the x and y-axes, focus at (4,0) , and point on graph (0,3) .For the following exercises, graph the given ellipses, noting center, vertices, and foci. 47. Center at the origin, symmetric with respect to the x- and y-axes, focus at (0,2) , and point on graph (5,0) .For the following exercises, use the given information about the graph of each ellipse to determine its equation. 48. Center at the origin, symmetric with respect to the x- and y-axes, focus at (3,0) , and major axis is twice as long as minor axis.For the following exercises, use the given information about the graph of each ellipse to determine its equation. 49. Center (4,2) ; vertex (9,2) ; one focus: (4+26,2) .For the following exercises, use the given information about the graph of each ellipse to determine its equation. 50. Center (3,5) ; vertex (3,11) ; one focus: (3,5+42) 51. Center (3,4) vertex (1,4) ; one focus (3+23,4)For the following exercises, graph the given ellipses, nothing center, vertices and foci. 51. Center (3,4) ; vertex (1,4) ; one focus (3+23,4)For the following exercises, given the graph of the ellipse, determine its equation. 52.For the following exercises, given the graph of the ellipse, determine its equation.For the following exercises, given the graph of the ellipse, determine its equation.For the following exercises, given the graph of the ellipse, determine its equation.For the following exercises, given the graph of the ellipse, determine its equation.For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area =ab 57. (x3)29+(y3)216=1 For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area =ab 58. (x+6)216+(y6)236=1 For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area =ab 59. (x+1)24+(y2)25=1 For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area =ab 60. 4x28x+9y272y+112=0 For the following exercises, find the area of the ellipse. The area of an ellipse is given by the formula Area =ab 61. 9x254x+9y254y+81=0 Find the equation of the ellipse that will just fit inside a box that is 8 units wide and 4 units high.Find the equation of the ellipse that will just fit inside a box that is four times as wide as it is high. Express in terms of h, the height.An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse, and use that to find the height to the nearest 0.01 foot of the arch at a distance of 4 feet from the center.An arch has the shape of a semi-ellipse. The arch has a height of 12 feet and a span of 40 feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is 6 feet. Round to the nearest hundredth.A bridge is to be built in the shape of a semielliptical arch and is to have a span of 120 feet. The height of the arch at a distance of 40 feet from the center is to be 8 feet. Find the height of the arch at its center.A person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other focus because all the sound waves that reach the ceiling are reflected to the other person. If a whispering gallery has a length of 120 feet, and the foci are located 30 feet from the center, find the height of the ceiling at the center.A person is standing 8 feet from the nearest wall in a whispering gallery. If that person is at one focus, and the other focus is 80 feet away, what is the length and height at the center of the gallery?Identify the vertices and foci of the hyperbola with equation x29y225=1 .What is the standard form equation of the hyperbola that has vertices (0,2) and foci (0,25) ?What is the standard form equation of the hyperbola that has vertices (1,2)and(1,8) and foci (1,10)and(1,16) ?Graph the hyperbola given by the equation x2144y281=1. Identify and Label the vertices, co-vertices, foci, and asymptotes.Graph the hyperbola given by the standard form of an equation (y+4)2100(x3)264=1 . Identify and label the center,vertices, co-vertices, foci, and asymptotes.A design for a cooling tower project is shown in Figure 12. Find the equation of the hyperbola that models the sides of the cooling tower. Assume that the center of the hyperbola - indicated by the intersection of dashed perpendicular lines in the figure - is the origin of the coordinate plane. Round final values to four decimal places.Define a hyperbola in terms of its foci.What can we conclude about a hyperbola if its asymptotes intersect at the origin?What must be true of the foci of a hyperbola?If the transverse axis of a hyperbola is vertical, what do we know about the graph?Where must the center of hyperbola be relative to its foci?For the following exercises, determine whether the following equations represent hyperbolas. If so, write in standard form. 6. 3y2+2x=6 For the following exercises, determine whether the following equations represent hyperbolas. If so, write in standard form. 7. x236y29=1 For the following exercises, determine whether the following equations represent hyperbolas. If so, write in standard form. 8. 5y2+4x2=6x For the following exercises, determine whether the following equations represent hyperbolas. If so, write in standard form. 9. 25x216y2=400 For the following exercises, determine whether the following equations represent hyperbolas. If so, write in standard form. 10. 9x2+18x+y2+4y14=0 For the followung exericses, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write eqations of asymptotes. 11. x225y236=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 12. x2100y29=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 13. y24x281=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 14. 9y24x2=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 15. (x1)29(y2)216=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 16. (y6)236(x+1)216=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 17. (x2)249(y+7)249=1 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 18. 4x28x9y272y+112=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 19. 9x254x+9y254y+81=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 20. 4x224x36y2360y+864=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 21. 4x2+24x+16y2128y+156=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 22. 4x2+40x+25y2100y+100=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 23. x2+2x100y21000y+2401=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 24. 9x2+72x+16y2+16y+4=0 For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. 25. 4x2+24x25y2+200y464=0 For the following exercises, find the equations of the asymptotes for each hyperbola. 26. y232x232=1 For the following exercises, find the equations of the asymptotes for each hyperbola. 27. (x3)252(y+4)222=1 For the following exercises, find the equations of the asymptotes for each hyperbola. 28. (y3)232(x+5)262=1 For the following exercises, find the equations of the asymptotes for each hyperbola. 29. 9x218x16y2+32y151=0 For the following exercises, find the equations of the asymptotes for each hyperbola. 30. 16y2+96y4x2+16x+112=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 31. x249y216=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 32. x264y24=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 33. y29x225=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 34. 81x29y2=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 36. (y+5)29(x4)225=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 36. (x2)28(y+3)227=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 37. (y3)29(x3)29=1 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 38. 4x28x+16y232y52=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 39. x28x25y2100y109=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 40. x2+8x+4y240y+88=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 41. 64x2+128x9y272y656=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 42. 16x2+64x4y28y4=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 43. 100x2+1000x+y210y2575=0 For the following exercise, sketch a graph of the hyperbola, labelling vertices and foci. 44. 4x2+16x4y2+16y+16=0 For the following exercise, given information about the graph of the hyperbola, find its equation. 45. Vertices at (3,0) and (3,0) and one focus at (5,0) .For the following exercise, given information about the graph of the hyperbola, find its equation. 46.Vertices at (0,6)and(0,-6) and one focus at (0,8) .For the following exercise, given information about the graph of the hyperbola, find its equation. 47. Vertices at (1,1)and(11,1) and one focus at (12,1) .For the following exercise, given information about the graph of the hyperbola, find its equation. 48. Center: (0,0) ; vertex: (0,13) ; one focus: (0,313) .

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