37. Astronomy The dimensions of the elliptical orbits of three planets are given in millions of kilometers in the table. The sun is at one focus. The other focus is on the positive x-axis.
    1. Write an equation for each orbit and draw the curves on your graphing calculator. (Remember to adjust the viewing window.)
    2. Reasoning Which orbit is most circular? Justify your reasoning.

Standardized Test Prep

SAT/ACT

38. What is the standard form of the equation of the conic given by 2 x 2 + 2 y 2 + 4 x − 12 y − 22 = 0 ? 2 x squared , plus , 2 y squared , plus 4 x minus 12 y minus 22 equals 0 question mark
    1. ( x + 1 ) 2 21 − ( y − 3 ) 2 21 = 1 fraction open , x plus 1 , close squared , over 21 end fraction . minus . fraction open , y minus 3 , close squared , over 21 end fraction . equals 1
    2. ( x + 1 ) 2 21 + ( y − 3 ) 2 21 = 1 fraction open , x plus 1 , close squared , over 21 end fraction . plus . fraction open , y minus 3 , close squared , over 21 end fraction . equals 1
    3. ( x − 3 ) 2 21 + ( y + 1 ) 2 21 = 1 fraction open , x minus 3 , close squared , over 21 end fraction . plus . fraction open , y plus 1 , close squared , over 21 end fraction . equals 1
    4. ( x − 1 ) 2 7 + ( y + 3 ) 2 3 = 1 fraction open , x minus 1 , close squared , over 7 end fraction . plus . fraction open , y plus 3 , close squared , over 3 end fraction . equals 1
39. Using a calculator, what are the approximate solutions of x 2 − 7 x + 5 = 0 ? x squared , minus 7 x plus 5 equals 0 question mark
    6. − 0.65 , 7.65 negative , 0.65 , comma , 7.65
    7. − 7.65 , 0.65 negative , 7.65 , comma , 0.65
    8. − 1.14 , 6.14 negative , 1.14 , comma , 6.14
    9. 0.81, 6.19
40. What is the center of the circle with equation ( x + 3 ) 2 + ( y − 2 ) 2 = 49 ? open x plus 3 close squared . plus . open y minus 2 close squared . equals 49 question mark
    1. ( 3 , − 2 ) open 3 comma negative 2 close
    2. ( − 3 , 2 ) open negative 3 comma 2 close
    3. (3, 2)
    4. ( − 3 , − 2 ) open negative 3 comma negative 2 close

Short Response

41. How can you use the arithmetic mean to find the missing terms in the arithmetic sequence 15,□,□,□, 47, …?

Mixed Review

See Lesson 10-5.

Find the foci of each hyperbola. Draw the graph.

42. x 2 49 − y 2 36 = 1 fraction x squared , over 49 end fraction , minus , fraction y squared , over 36 end fraction , equals 1
43. 8 y 2 − 6 x 2 = 72 8 y squared , minus , 6 x squared , equals 72
44. 4 y 2 − 100 x 2 = 400 4 y squared , minus . 100 x squared . equals 400

See Lesson 8-6.

Solve each equation. Check your answers.

45. 1 3 x + 1 = 1 x 2 − 3 fraction 1 , over 3 x plus 1 end fraction . equals . fraction 1 , over x squared , minus 3 end fraction
46. 2 x + 2 = 6 x 2 − 4 fraction 2 , over x plus 2 end fraction . equals . fraction 6 , over x squared , minus 4 end fraction
47. 5 x 2 − x + 3 x − 1 = 6 fraction 5 , over x squared , minus x end fraction . plus . fraction 3 , over x minus 1 end fraction . equals 6

See Lesson 7-6.

Simplify each expression.

48. l n e l n e
49. 2 l n e 2 l n e
50. l n e 3 l n , e cubed
51. 4 l n e 2 4 l n , e squared

Get Ready! To prepare for Lesson 11-1, do Exercises 52–53.

See Lesson 1-3.

Evaluate each expression for the given value of the variable.

52. x + 5 x − x − 9 ; x = − 2 x plus 5 x minus x minus 9 semicolon x equals negative 2
53. ( n − 4 ) 2 + n ;   n = 5 open n minus 4 close squared . plus n semicolon n equals 5

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