C Challenge

30. Find the sum of E = [ 3 4 7 ] e equals left bracket . table with 3 rows and 1 column , row1 column 1 , 3 , row2 column 1 , 4 , row3 column 1 , 7 , end table . right bracket  and the additive inverse of G = [ − 2 0 5 ] . g equals left bracket . table with 3 rows and 1 column , row1 column 1 , negative 2 , row2 column 1 , 0 , row3 column 1 , 5 , end table . right bracket .
31. Prove that matrix addition is commutative for 2 × 2 2 times 2  matrices.
32. Prove that matrix addition is associative for 2 × 2 2 times 2  matrices.

Standardized Test Prep

SAT/ACT

33. What is the sum [ 5 7 3 − 1 0 − 4 ] + [ − 7 4 2 1 − 2 − 3 ] ? table with 1 row and 3 columns , row1 column 1 , . matrix with 2 rows and 3 columns , row1 column 1 , 5 , column 2 7 , column 3 3 , row2 column 1 , negative 1 , column 2 0 , column 3 negative 4 , end matrix , column 2 plus , column 3 . matrix with 2 rows and 3 columns , row1 column 1 , negative 7 , column 2 4 , column 3 2 , row2 column 1 , 1 , column 2 negative 2 , column 3 negative 3 , end matrix , end table . question mark
    1. The matrices cannot be added.
    2. [ − 2 11 5 0 − 2 − 7 ] . matrix with 2 rows and 3 columns , row1 column 1 , negative 2 , column 2 11 , column 3 5 , row2 column 1 , 0 , column 2 negative 2 , column 3 negative 7 , end matrix
    3. [ 12 3 1 − 2 2 − 1 ] . matrix with 2 rows and 3 columns , row1 column 1 , 12 , column 2 3 , column 3 1 , row2 column 1 , negative 2 , column 2 2 , column 3 negative 1 , end matrix
    4. [ − 35 28 6 − 1 0 12 ] . matrix with 2 rows and 3 columns , row1 column 1 , negative 35 , column 2 28 , column 3 6 , row2 column 1 , negative 1 , column 2 0 , column 3 12 , end matrix
34. Which arithmetic sequence includes the term 27?
    1. a 1 = 7 , a n = a n − 1 + 5 eh sub 1 , equals 7 comma , eh sub n , equals . eh sub n minus 1 end sub . plus 5
    2. a n = 3 + 4 ( n − 1 ) eh sub n , equals 3 plus 4 open n minus 1 close
    3. a n = 57 − 6 n eh sub n , equals 57 minus 6 n
    6. I only
    7. I and II only
    8. II and III only
    9. I, II, and III

35. Which equation is graphed below?

    

    1. ( x + 3 ) 2 + ( y − 2 ) 2 = 25 open x plus 3 close squared . plus . open y minus 2 close squared . equals 25
    2. ( x − 2 ) 2 + ( y + 3 ) 2 = 25 open x minus 2 close squared . plus . open y plus 3 close squared . equals 25
    3. ( x + 2 ) 2 + ( y − 3 ) 2 = 25 open x plus 2 close squared . plus . open y minus 3 close squared . equals 25
    4. ( x − 3 ) 2 + ( y + 2 ) 2 = 25 open x minus 3 close squared . plus . open y plus 2 close squared . equals 25

Short Response

36. For a daily airline flight to Denver, the numbers of checked pieces of luggage are normally distributed with a mean of 380 and a standard deviation of 20. What number of checked pieces of luggage is 3 standard deviations above the mean?

Mixed Review

See Lesson 11-9.

A set of data with a mean of 62 and a standard deviation of 5 is normally distributed. Find the percent of data within each interval.

37. from 57 to 67
38. greater than 52
39. from 62 to 72

See Lesson 2-3.

Find the slope and y-intercept of each line.

40. y = 2 x − 6 y equals 2 x minus 6
41. 3 y = 6 + 2 x 3 y equals 6 plus 2 x
42. − x − 2 y = 12 negative x minus 2 y equals 12
43. y = 5 x y equals 5 x

Get Ready! To prepare for Lesson 12-2, do Exercises 44–45.

See Lesson 12-1.

Find each sum.

44. [ 3 5 2 8 ] + [ 3 5 2 8 ] + [ 3 5 2 8 ] table with 1 row and 5 columns , row1 column 1 , . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 5 , row2 column 1 , 2 , column 2 8 , end matrix , column 2 plus , column 3 . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 5 , row2 column 1 , 2 , column 2 8 , end matrix , column 4 plus , column 5 . matrix with 2 rows and 2 columns , row1 column 1 , 3 , column 2 5 , row2 column 1 , 2 , column 2 8 , end matrix , end table
45. [ − 4 7 ] + [ − 4 7 ] + [ − 4 7 ] + [ − 4 7 ] + [ − 4 7 ] table with 1 row and 9 columns , row1 column 1 , . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , 7 , end matrix , column 2 plus , column 3 . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , 7 , end matrix , column 4 plus , column 5 . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , 7 , end matrix , column 6 plus , column 7 . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , 7 , end matrix , column 8 plus , column 9 . matrix with 2 rows and 1 column , row1 column 1 , negative 4 , row2 column 1 , 7 , end matrix , end table

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