C Challenge

Geometry Each matrix represents the vertices of a transformed polygon. Write a matrix to represent the vertices of the image before each transformation.

39. [ − 3 0.5 − 5 0 3 3 ] ; . matrix with 2 rows and 3 columns , row1 column 1 , negative 3 , column 2 0.5 , column 3 negative 5 , row2 column 1 , 0 , column 2 3 , column 3 3 , end matrix . semicolon  dilation of 2
40. [ 3 4.5 5 3.5 3 1.5 2 4 ] ; . matrix with 2 rows and 4 columns , row1 column 1 , 3 , column 2 4.5 , column 3 5 , column 4 3.5 , row2 column 1 , 3 , column 2 1.5 , column 3 2 , column 4 4 , end matrix . semicolon  rotation of 90 ° 90 degrees
41. Writing Explain why a reflection of a matrix of points from a function table across the line y = x y equals x  is equivalent to finding the inverse of the function.

Standardized Test Prep

SAT/ACT

42. What are the coordinates of X(5, 1), Y ( − 5 , − 3 ) , y open negative 5 comma negative 3 close comma  and Z ( − 1 , 3 ) z open negative 1 comma 3 close  reflected across the line y = x ? y equals x question mark
    1. X ' ( − 5 , − 1 ) , Y ' ( 5 , 3 ) , Z ' ( 1 , − 3 ) x apostrophe open negative 5 comma negative 1 close comma y apostrophe open 5 comma 3 close comma z apostrophe open 1 comma negative 3 close
    2. X ' ( 1 , 5 ) , Y ' ( − 3 , − 5 ) , Z ' ( 3 , − 1 ) x apostrophe open 1 comma 5 close comma y apostrophe open negative 3 comma negative 5 close comma z apostrophe open 3 comma negative 1 close
    3. X ' ( − 1 , − 5 ) , Y ' ( 3 , 5 ) , Z ' ( − 3 , 1 ) x apostrophe open negative 1 comma negative 5 close comma y apostrophe open 3 comma 5 close comma z apostrophe open negative 3 comma 1 close
    4. X ' ( 5 , 1 ) , Y ' ( − 5 , − 3 ) , Z ' ( − 1 , 3 ) x apostrophe open 5 comma 1 close comma y apostrophe open negative 5 comma negative 3 close comma z apostrophe open negative 1 comma 3 close
43. Given p = [ 4 3 − 2 − 1 0 5 ] p equals . matrix with 2 rows and 3 columns , row1 column 1 , 4 , column 2 3 , column 3 negative 2 , row2 column 1 , negative 1 , column 2 0 , column 3 5 , end matrix  and Q = [ 3 − 2 − 5 − 1 − 2 − 1 ] , q equals . matrix with 2 rows and 3 columns , row1 column 1 , 3 , column 2 negative 2 , column 3 negative 5 , row2 column 1 , negative 1 , column 2 negative 2 , column 3 negative 1 , end matrix . comma  what is 2 P − 3 Q ? 2 p minus 3 q question mark
    6. [ 1 − 5 3 0 − 2 6 ] . matrix with 2 rows and 3 columns , row1 column 1 , 1 , column 2 negative 5 , column 3 3 , row2 column 1 , 0 , column 2 negative 2 , column 3 6 , end matrix
    7. [ 17 0 19 − 5 6 7 ] . matrix with 2 rows and 3 columns , row1 column 1 , 17 , column 2 0 , column 3 19 , row2 column 1 , negative 5 , column 2 6 , column 3 7 , end matrix
    8. [ − 1 12 11 1 6 13 ] . matrix with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 12 , column 3 11 , row2 column 1 , 1 , column 2 6 , column 3 13 , end matrix
    9. [ 1 5 3 0 2 6 ] . matrix with 2 rows and 3 columns , row1 column 1 , 1 , column 2 5 , column 3 3 , row2 column 1 , 0 , column 2 2 , column 3 6 , end matrix
44. What is the solution to the matrix equation [ 3 − 1 − 1 2 ] [ a b ] = [ 7 − 9 ] ? . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 negative 1 , row2 column 1 , negative 1 , column 2 2 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , eh , row2 column 1 , b , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 7 , row2 column 1 , negative 9 , end matrix . question mark
    1. a = 7 , b = − 9 eh equals 7 comma b equals negative 9
    2. a = 2 , b = 1 eh equals 2 comma b equals 1
    3. a = 7 3 , b = 9 2 eh equals , 7 thirds , comma b equals , 9 halves
    4. a = 1 , b = − 4 eh equals 1 comma b equals negative 4
45. What is the determinant of [ − 5 4 − 9 7 ] ? . matrix with 2 rows and 2 columns , row1 column 1 , negative 5 , column 2 4 , row2 column 1 , negative 9 , column 2 7 , end matrix . question mark
    6. − 71 negative 71
    7. 1
    8. − 3 negative 3
    9. 71

Short Response

46. The results of a college entrance exam are shown below. What is the probability that a student's score on the verbal section is from 401 to 514?

Mixed Review

See Lesson 12-4.

Solve each system of equations. Check your answers.

47. { 3 x + 2 y = 5 − x + y = − 5 left brace . table with 2 rows and 2 columns , row1 column 1 , 3 x plus 2 y equals , column 2 5 , row2 column 1 , negative x plus y equals , column 2 negative 5 , end table
48. { x + 4 y + 3 z = 3 2 x − 5 y − z = 5 3 x + 2 y − 2 z = − 3 left brace . table with 3 rows and 2 columns , row1 column 1 , x plus 4 y plus 3 z equals , column 2 3 , row2 column 1 , 2 x minus 5 y minus z equals , column 2 5 , row3 column 1 , 3 x plus 2 y minus 2 z equals , column 2 negative 3 , end table
49. { x + y + z = − 1 y + 3 z = − 5 x + z = − 2 left brace . table with 3 rows and 2 columns , row1 column 1 , x plus y plus z equals , column 2 negative 1 , row2 column 1 , y plus 3 z equals , column 2 negative 5 , row3 column 1 , x plus z equals , column 2 negative 2 , end table

Get Ready! To prepare for Lesson 12-6, do Exercises 50–52.

See Lesson 12-2.

Find each product.

50. 0.8 [ 20 15 ] 0.8 . matrix with 2 rows and 1 column , row1 column 1 , 20 , row2 column 1 , 15 , end matrix
51. [ 1 − 2 ] [ 2 − 5 ] . matrix with 1 row and 2 columns , row1 column 1 , 1 , column 2 negative 2 , end matrix . matrix with 2 rows and 1 column , row1 column 1 , 2 , row2 column 1 , negative 5 , end matrix
52. [ − 3 − 5 ] [ − 4 − 2 ] . matrix with 1 row and 2 columns , row1 column 1 , negative 3 , column 2 negative 5 , end matrix . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , negative 2 , end matrix

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