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Daily Alg2

 Check out http://acelkeeler.wordpress.com for answers to questions as well as notes.

Tuesday/Wednesday Feb 7th - 8th

posted Feb 7, 2012, 8:44 AM by Alicegop Keeler

 The new math teacher Mr. Dull will be here starting Wednesday. To help him most effectively teach you he wants to know what you know.  You will take a practice test.  NO iPads, NO talking, NO help.  Do your best.  Show work demonstrating you are in a high school math class showing clear and well though Algebra processes. Use complete sentences. MAKE SURE YOU HAVE YOUR EDMODO SET UP AND THAT YOU HAVE TURNED IN THE FIRST FEW ASSIGNMENTS INTO EDMODO.When you have turned in your pre-test please go onto Edmodo and and for assignment #4 pre test write Mr. Dull a note about how you think you did.  This is part of your assignment, make sure you complete this.

2nd Semester!!!

posted Feb 3, 2012, 11:10 AM by Unknown user   [ updated Feb 6, 2012, 7:51 AM by Alicegop Keeler ]

W/R Feb 1-2

posted Feb 1, 2012, 11:03 AM by Unknown user

 Going over imaginary numbers and complex numbers

M/T Jan 30 Feb 1

posted Jan 30, 2012, 12:50 PM by Unknown user   [ updated Jan 30, 2012, 12:50 PM ]

R/F Jan 26-27

posted Jan 26, 2012, 11:51 AM by Alicegop Keeler

 Anything you want to have graded for the semester grade needs to be turned in this weekend. You will want to work on the worksheets for matricies that you received last time (questions and answers are on the previous daily algebra 2).#57 Algebra 2 Cumulative Questionshttp://www.quia.com/quiz/3485797.htmlYou will want to complete this with at least 50%. It might take you several attempts.  Many of the questions we have not covered but they do have directions if you submit a wrong answer, I would encourage you to look over the directions and see if you can make sense of the problem.  Many of the questions are review from Algebra 1, some are things we have done in Algebra 2 and some are completely new to you (Algebra 2).  For example we have not covered imaginary numbers (also complex numbers).  But they are not that hard, look at this website: http://www.purplemath.com/modules/complex.htm there are 3 pages, I think you might find that it is very doable. Title: 57 cumulative questionsXP: 200

T/W Jan 24-25

posted Jan 24, 2012, 10:01 AM by Alice Keeler   [ updated Jan 24, 2012, 1:00 PM by Alicegop Keeler ]

Let's do a little long division.

#47
Matrices
Title: Some matrices
Category: Alg2, classwork
Tags: matrices
XP: 150

 Name _____________________________ Date ___________________
Matrices
Complete.
1.
 1 17 -7 -6 -15 -8 8 -18 12 -5 18 -2
+
 -14 17 0 -18 -9 16 -11 11 10 12 -7 1

2.
 17 5
+
 17 -14

Complete.
3.
 16 -9 -6 20 -7 -5 -8 6
-
 10 -2 7 -6 -18 11 -14 -12

4.
 16 -6 1 -5
-
 -12 -18 -17 15

Complete.
5.
 2 -17 -19
-
 -8 13 20
-
 -10 7 -6

Complete.
6.
 9 -1 16 20
+
 7 12 -17 -9
-
 -20 -10 -4 -11

Find the product. If the product is not defined, state the reason.
7.
 1 -9 -13 -7 -1 -10 15 0 3 -5 -14 13 -20 9 -18 20

 -18 4 -20 -8 11 -1 -11 -9 18 -13 3 -15 -7 -17 0 -10

Solve for x and y.
8.
 8 11 -20 -5 6 -18 -9 -19 5 -13 13 3 0 14 -16 2

 15 2 4 3 -19 -16 -1 -7 20 14 0 9 18 8 -3 x
=
 y -480 36 -188 -90 22 99 234 636 424 24 196 -550 -432 -20 -260

Calculate the determinant of each matrix. Show your work.
9.
 -6 6 -10 9

10.
 -14 -16 11 -15

11.
 -6 6 -11 9

Calculate the determinant of each matrix. Show your work.
12.   Use the diagonals method.
 6 14 -4 8 -6 -19 -15 -13 13

13.
 -8 -7 -20 9

14.   Use the diagonals method.
 20 -14 -9 -2 -8 -20 0 4 -11

Use determinants to calculate the area. Show your work.
 15 Calculate the area of the triangle with the following points: (1, -3), (-1, -6), (3, -8)
 16 Calculate the area of the triangle with the following points: (3, 4), (1, 1), (8, 8)
 17 Calculate the area of the triangle with the following points: (-2, -2), (2, 8), (-1, 3)

Use determinants to calculate the area. Show your work.
 18 Calculate the area of the quadrilateral with the following points: (-3, 3), (-1, 7), (2, 5), (4, 2)
 19 Calculate the area of the quadrilateral with the following points: (-2, -3), (-4, 2), (-1, -1), (0, -4)
 20 Calculate the area of the quadrilateral with the following points: (4, 0), (5, 3), (9, 7), (11, 0)

Complete.
21.   Find the inverse of:
 8 10 11 1

22.   Find the inverse of:
 -6 9 -12 -2

23.   Find the inverse of:
 -12 7 5 6

Solve the matrix equation.
24.
 -9 5 9 -4
X     =
 43 53 59 -47 -46 -58

25.
 -6 6 4 5
X     +
 8 6 2 11
=
 -40 -66 -29 -22

Write the linear system as a matrix equation.
 26 -2x + 9y = 31 -6x - 8y = 58
 27 -1x - 3y = 5 4x - 5y = 65
 28 3x - 5y - 6z = 64 9x - 2y - 7z = 116 4x - 8y + 1z = 83

Use an inverse matrix to solve the linear system.
 29 -2x - 8y = 110 3x + 9y = -126
 30 1x + 5y = -33 -7x - 4y = -48

Write the augmented matrix for the linear system and then solve.
 31 -3x - 2y = 7 6x + 8y = -34
 32 -1x + 4y - 9z = -32 4x - 8y - 7z = -17 -6x + 5y - 3z = -1

Solve each system of equations using Cramer's rule.
 33 -7x + 2y + 1z = 54 -3x + 6y - 5z = -24 -9x - 1y - 5z = 72
 34 3x - 2y = -20 -7x - 6y = 4
 35 9x + 3y = 15 -4x + 2y = -10

Complete.
1.
 1 17 -7 -6 -15 -8 8 -18 12 -5 18 -2
+
 -14 17 0 -18 -9 16 -11 11 10 12 -7 1

 -13 34 -7 -24 -24 8 -3 -7 22 7 11 -1
2.
 17 5
+
 17 -14

 34 -9

Complete.
3.
 16 -9 -6 20 -7 -5 -8 6
-
 10 -2 7 -6 -18 11 -14 -12

 6 -7 -13 26 11 -16 6 18
4.
 16 -6 1 -5
-
 -12 -18 -17 15

 28 12 18 -20

Complete.
5.
 2 -17 -19
-
 -8 13 20
-
 -10 7 -6

 20 -37 -33

Complete.
6.
 9 -1 16 20
+
 7 12 -17 -9
-
 -20 -10 -4 -11

 36 21 3 22

Find the product. If the product is not defined, state the reason.
7.
 1 -9 -13 -7 -1 -10 15 0 3 -5 -14 13 -20 9 -18 20

 -18 4 -20 -8 11 -1 -11 -9 18 -13 3 -15 -7 -17 0 -10

 -302 301 40 338 178 -189 175 -127 -452 -22 -47 101 -5 -195 247 149

Solve for x and y.
8.
 8 11 -20 -5 6 -18 -9 -19 5 -13 13 3 0 14 -16 2

 15 2 4 3 -19 -16 -1 -7 20 14 0 9 18 8 -3 x
=
 y -480 36 -188 -90 22 99 234 636 424 24 196 -550 -432 -20 -260

x=-9; y=-579

Calculate the determinant of each matrix. Show your work.
9.
 -6 6 -10 9

6
10.
 -14 -16 11 -15

386
11.
 -6 6 -11 9

12

Calculate the determinant of each matrix. Show your work.
12.   Use the diagonals method.
 6 14 -4 8 -6 -19 -15 -13 13

-468 + 3990 + 416 - -360 - 1482 - 1456, or 1360
13.
 -8 -7 -20 9

-212
14.   Use the diagonals method.
 20 -14 -9 -2 -8 -20 0 4 -11

1760 + 0 + 72 - 0 - -1600 - -308, or 3740

Use determinants to calculate the area. Show your work.
 15 Calculate the area of the triangle with the following points: (1, -3), (-1, -6), (3, -8) (+/-): (2 - 12 + 26) / 2 = 16 / 2 = 8
 16 Calculate the area of the triangle with the following points: (3, 4), (1, 1), (8, 8) (+/-): (-21 + 28 + 0) / 2 = 7 / 2 = 3 1/2
 17 Calculate the area of the triangle with the following points: (-2, -2), (2, 8), (-1, 3) (+/-): (-10 + 6 + 14) / 2 = 10 / 2 = 5

Use determinants to calculate the area. Show your work.
 18 Calculate the area of the quadrilateral with the following points: (-3, 3), (-1, 7), (2, 5), (4, 2) Triangle 1: (+/-): (-6 + 9 - 19) / 2 = -16 / 2 = 8 Triangle 2: (+/-): (-8 + 10 - 21) / 2 = -19 / 2 = 9 1/2 Answer = Triangle 1 + Triangle 2 = 17 1/2
 19 Calculate the area of the quadrilateral with the following points: (-2, -3), (-4, 2), (-1, -1), (0, -4) Triangle 1: (+/-): (-6 - 9 + 6) / 2 = -9 / 2 = 4 1/2 Triangle 2: (+/-): (0 - 4 - 1) / 2 = -5 / 2 = 2 1/2 Answer = Triangle 1 + Triangle 2 = 7
 20 Calculate the area of the quadrilateral with the following points: (4, 0), (5, 3), (9, 7), (11, 0) Triangle 1: (+/-): (-16 - 0 + 8) / 2 = -8 / 2 = 4 Triangle 2: (+/-): (-77 - 0 + 28) / 2 = -49 / 2 = 24 1/2 Answer = Triangle 1 + Triangle 2 = 28 1/2

Complete.
21.   Find the inverse of:
 8 10 11 1

 -1/102 5/51 11/102 -4/51
22.   Find the inverse of:
 -6 9 -12 -2

 -1/60 -3/40 1/10 -1/20
23.   Find the inverse of:
 -12 7 5 6

 -6/107 7/107 5/107 12/107

Solve the matrix equation.
24.
 -9 5 9 -4
X     =
 43 53 59 -47 -46 -58

 -7 -2 -6 -4 7 1
25.
 -6 6 4 5
X     +
 8 6 2 11
=
 -40 -66 -29 -22

 1 3 -7 -9

Write the linear system as a matrix equation.
26.   -2x + 9y = 31
-6x - 8y = 58

 -2 9 -6 -8

 x y
=
 31 58
27.   -1x - 3y = 5
4x - 5y = 65

 -1 -3 4 -5

 x y
=
 5 65
28.   3x - 5y - 6z = 64
9x - 2y - 7z = 116
4x - 8y + 1z = 83

 3 -5 -6 9 -2 -7 4 -8 1

 x y z
=
 64 116 83

Use an inverse matrix to solve the linear system.
29.   -2x - 8y = 110
3x + 9y = -126

 -2 -8 3 9

 x y
=
 110 -126

Inverse of the A=
 1 1/2 1 1/3 -1/2 -1/3

x=-3, y=-13

30.   1x + 5y = -33
-7x - 4y = -48

 1 5 -7 -4

 x y
=
 -33 -48

Inverse of the A=
 -4/31 -5/31 7/31 1/31

x=12, y=-9

Write the augmented matrix for the linear system and then solve.
31.   -3x - 2y = 7
6x + 8y = -34

 -3 -2 | 7 6 8 | -34

x=1, y=-5

32.   -1x + 4y - 9z = -32
4x - 8y - 7z = -17
-6x + 5y - 3z = -1

 -1 4 -9 | -32 4 -8 -7 | -17 -6 5 -3 | -1

x=-3, y=-2, z=3

Solve each system of equations using Cramer's rule.
33.   -7x + 2y + 1z = 54
-3x + 6y - 5z = -24
-9x - 1y - 5z = 72

x =
 54 2 1 -24 6 -5 72 -1 -5

362
=
 -3258 362
y =
 -7 54 1 -3 -24 -5 -9 72 -5

362
=
 -2172 362
z =
 -7 2 54 -3 6 -24 -9 -1 72

362
=
 1086 362
x=-9, y=-6, z=3
34.   3x - 2y = -20
-7x - 6y = 4

x =
 -20 -2 4 -6

-32
=
 128 -32
y =
 3 -20 -7 4

-32
=
 -128 -32
x=-4, y=4
35.   9x + 3y = 15
-4x + 2y = -10

x =
 15 3 -10 2

30
=
 60 30
y =
 9 15 -4 -10

30
=
 -30 30
x=2, y=-1

Here is some more practice problems.  These below we can use for in class practice or extra practice.

 Name _____________________________ Date ___________________
Matrices
Complete.
1.
 8 -2 -16 10 -19 -3 3 -15 -6 12 20 -18
+
 -20 -10 17 -15 6 19 -2 -17 -1 -11 10 16

2.
 12 -7 10 6 9 -10
+
 -12 -10 -16 15 -13 17

Complete.
3.
 -11 -10
-
 -4 -9

4.
 -7 14 1 -6 -20 8 -3 10 -15 9 13 6
-
 14 -8 10 3 -13 11 -7 -18 -20 -4 -9 -17

Complete.
5.
 18 5 19 16 10 12 -20 1 -6 -13 0 -5
+
 15 16 -6 -19 18 6 -7 -10 2 -5 13 -2
+
 -14 16 -6 1 7 15 -12 4 -8 2 -20 12

Complete.
6.
 14 -6 -2 -15 -20 7
+
 -6 1 -19 -8 6 13
+
 18 -1 19 20 -18 9

Find the product. If the product is not defined, state the reason.
7.
 0 10 -20 4

 10 -7 9 17

Solve for x and y.
8.
 8 2 -7 x 4 -15 19 11 -18 -13 14 -17 1 -11 -6 -14

 20 -15 -7 1 7 16 -17 -4 13 -9 0 -8 9 4 14 -11
=
 164 11 36 -43 y -427 381 -209 -422 -132 109 109 -261 -193 -16 247

Calculate the determinant of each matrix. Show your work.
9.
 -3 -19 7 11

10.
 -7 18 -10 15

11.
 -15 -14 -17 -5

Calculate the determinant of each matrix. Show your work.
12.  Expand along row 3.
 -18 -3 2 0 5 -14 1 10 -7

13.
 8 1 13 -12

14.  Use the diagonals method.
 -4 18 4 5 -2 9 16 -7 20

Use determinants to calculate the area. Show your work.
 15 Calculate the area of the triangle with the following points:(2, -1), (-3, -5), (-1, -6)
 16 Calculate the area of the triangle with the following points:(-5, 0), (-8, -3), (-2, 5)
 17 Calculate the area of the triangle with the following points:(5, 2), (2, -1), (1, -4)

Use determinants to calculate the area. Show your work.
 18 Calculate the area of the quadrilateral with the following points:(-5, -1), (-4, 2), (1, 4), (4, -4)
 19 Calculate the area of the quadrilateral with the following points:(-2, -5), (1, -1), (4, -2), (5, -4)
 20 Calculate the area of the quadrilateral with the following points:(-2, 2), (-2, 5), (1, 4), (5, -1)

Complete.
21.  Find the inverse of:
 5 3 -10 -4

22.  Find the inverse of:
 8 -10 -7 6

23.  Find the inverse of:
 9 6 5 -5

Solve the matrix equation.
24.
 12 -11 7 1
X    +
 5 -11 3 4
=
 -138 118 -73 57

25.
 6 12 5 -11
X    =
 -120 90 110 -72

Write the system of linear equations represented by each matrix equation.
26.
 -1 6 3 -4 -8 -9 -7 5 -2

 x y z
=
 23 37 91

27.
 -1 4 -8 -6 5 -7 2 9 -3

 x y z
=
 -65 -30 -86

Use the inverse of the linear system to solve for x, y, and z.
28.  8x + 6y - 1z = -99
-3x - 9y + 2z = 93
-7x + 4y + 5z = -9
A-1  =
 53/343 34/343 -3/343 -1/343 -33/343 13/343 75/343 74/343 54/343

29.  -9x + 3y + 5z = 35
-1x + 2y - 8z = 64
6x - 4y - 7z = 16
A-1  =
 -46/209 1/209 -34/209 -5/19 3/19 -7/19 -8/209 -18/209 -15/209

Write the augmented matrix for the linear system and then solve.
 30 7x - 9y - 6z = 12-5x - 4y - 1z = -29-3x + 8y + 2z = 19
 31 1x - 8y - 6z = 21-4x - 9y + 5z = 42-2x - 7y + 3z = 32

Solve each system of equations using Cramer's rule.
 32 -1x + 7y - 4z = -66x - 8y + 3z = -35x - 9y - 2z = 18
 33 -3x - 8y = -41-7x + 1y = -76
 34 -2x - 4y = 149x - 6y = 153

Complete.
1.
 8 -2 -16 10 -19 -3 3 -15 -6 12 20 -18
+
 -20 -10 17 -15 6 19 -2 -17 -1 -11 10 16

 -12 -12 1 -5 -13 16 1 -32 -7 1 30 -2
2.
 12 -7 10 6 9 -10
+
 -12 -10 -16 15 -13 17

 0 -17 -6 21 -4 7

Complete.
3.
 -11 -10
-
 -4 -9

 -7 -1
4.
 -7 14 1 -6 -20 8 -3 10 -15 9 13 6
-
 14 -8 10 3 -13 11 -7 -18 -20 -4 -9 -17

 -21 22 -9 -9 -7 -3 4 28 5 13 22 23

Complete.
5.
 18 5 19 16 10 12 -20 1 -6 -13 0 -5
+
 15 16 -6 -19 18 6 -7 -10 2 -5 13 -2
+
 -14 16 -6 1 7 15 -12 4 -8 2 -20 12

 19 37 7 -2 35 33 -39 -5 -12 -16 -7 5

Complete.
6.
 14 -6 -2 -15 -20 7
+
 -6 1 -19 -8 6 13
+
 18 -1 19 20 -18 9

 62 -6 -2 33 -68 95

Find the product. If the product is not defined, state the reason.
7.
 0 10 -20 4

 10 -7 9 17

 90 170 -164 208

Solve for x and y.
8.
 8 2 -7 x 4 -15 19 11 -18 -13 14 -17 1 -11 -6 -14

 20 -15 -7 1 7 16 -17 -4 13 -9 0 -8 9 4 14 -11
=
 164 11 36 -43 y -427 381 -209 -422 -132 109 109 -261 -193 -16 247

x=9; y=321

Calculate the determinant of each matrix. Show your work.
9.
 -3 -19 7 11

100
10.
 -7 18 -10 15

75
11.
 -15 -14 -17 -5

-163

Calculate the determinant of each matrix. Show your work.
12.  Expand along row 3.
 -18 -3 2 0 5 -14 1 10 -7

32 - 2520 + 630 = -1858
13.
 8 1 13 -12

-109
14.  Use the diagonals method.
 -4 18 4 5 -2 9 16 -7 20

160 + 2592 + -140 - -128 - 252 - 1800, or 688

Use determinants to calculate the area. Show your work.
 15 Calculate the area of the triangle with the following points:(2, -1), (-3, -5), (-1, -6)(+/-): (2 - 2 + 13) / 2 = 13 / 2 = 6 1/2
 16 Calculate the area of the triangle with the following points:(-5, 0), (-8, -3), (-2, 5)(+/-): (40 - 0 - 46) / 2 = -6 / 2 = 3
 17 Calculate the area of the triangle with the following points:(5, 2), (2, -1), (1, -4)(+/-): (15 - 2 - 7) / 2 = 6 / 2 = 3

Use determinants to calculate the area. Show your work.
 18 Calculate the area of the quadrilateral with the following points:(-5, -1), (-4, 2), (1, 4), (4, -4)Triangle 1: (+/-): (10 - 5 - 18) / 2 = -13 / 2 = 6 1/2Triangle 2: (+/-): (-20 - 24 - 19) / 2 = -63 / 2 = 31 1/2Answer = Triangle 1 + Triangle 2 = 38
 19 Calculate the area of the quadrilateral with the following points:(-2, -5), (1, -1), (4, -2), (5, -4)Triangle 1: (+/-): (-2 - 15 + 2) / 2 = -15 / 2 = 7 1/2Triangle 2: (+/-): (-15 - 24 + 24) / 2 = -15 / 2 = 7 1/2Answer = Triangle 1 + Triangle 2 = 15
 20 Calculate the area of the quadrilateral with the following points:(-2, 2), (-2, 5), (1, 4), (5, -1)Triangle 1: (+/-): (-2 + 6 - 13) / 2 = -9 / 2 = 4 1/2Triangle 2: (+/-): (-10 - 3 - 10) / 2 = -23 / 2 = 11 1/2Answer = Triangle 1 + Triangle 2 = 16

Complete.
21.  Find the inverse of:
 5 3 -10 -4

 -2/5 -3/10 1 1/2
22.  Find the inverse of:
 8 -10 -7 6

 -3/11 -5/11 -7/22 -4/11
23.  Find the inverse of:
 9 6 5 -5

 1/15 2/25 1/15 -3/25

Solve the matrix equation.
24.
 12 -11 7 1
X    +
 5 -11 3 4
=
 -138 118 -73 57

 -11 8 1 -3
25.
 6 12 5 -11
X    =
 -120 90 110 -72

 0 1 -10 7

Write the system of linear equations represented by each matrix equation.
26.
 -1 6 3 -4 -8 -9 -7 5 -2

 x y z
=
 23 37 91

-1x + 6y + 3z = 23
-4x - 8y - 9z = 37
-7x + 5y - 2z = 91

27.
 -1 4 -8 -6 5 -7 2 9 -3

 x y z
=
 -65 -30 -86

-1x + 4y - 8z = -65
-6x + 5y - 7z = -30
2x + 9y - 3z = -86

Use the inverse of the linear system to solve for x, y, and z.
28.  8x + 6y - 1z = -99
-3x - 9y + 2z = 93
-7x + 4y + 5z = -9
A-1  =
 53/343 34/343 -3/343 -1/343 -33/343 13/343 75/343 74/343 54/343

x=-6, y=-9, z=-3
29.  -9x + 3y + 5z = 35
-1x + 2y - 8z = 64
6x - 4y - 7z = 16
A-1  =
 -46/209 1/209 -34/209 -5/19 3/19 -7/19 -8/209 -18/209 -15/209

x=-10, y=-5, z=-8

Write the augmented matrix for the linear system and then solve.
30.  7x - 9y - 6z = 12
-5x - 4y - 1z = -29
-3x + 8y + 2z = 19

 7 -9 -6 | 12 -5 -4 -1 | -29 -3 8 2 | 19

x=3, y=5, z=-6

31.  1x - 8y - 6z = 21
-4x - 9y + 5z = 42
-2x - 7y + 3z = 32

 1 -8 -6 | 21 -4 -9 5 | 42 -2 -7 3 | 32

x=1, y=-4, z=2

Solve each system of equations using Cramer's rule.
32.  -1x + 7y - 4z = -6
6x - 8y + 3z = -3
5x - 9y - 2z = 18

x =
 -6 7 -4 -3 -8 3 18 -9 -2

202
=
 -606202
y =
 -1 -6 -4 6 -3 3 5 18 -2

202
=
 -606202
z =
 -1 7 -6 6 -8 -3 5 -9 18

202
=
 -606202
x=-3, y=-3, z=-3
33.  -3x - 8y = -41
-7x + 1y = -76

x =
 -41 -8 -76 1

-59
=
 -649-59
y =
 -3 -41 -7 -76

-59
=
 -59-59
x=11, y=1
34.  -2x - 4y = 14
9x - 6y = 153

x =
 14 -4 153 -6

48
=
 52848
y =
 -2 14 9 153

48
=
 -43248
x=11, y=-9

F/F Jan 20-23

posted Jan 20, 2012, 1:00 PM by Alicegop Keeler   [ updated Jan 20, 2012, 1:14 PM ]

 We will do stuff together.  GET STUFF TURNED IN!!!!!!!!Long Division

W/R Jan 18-19

posted Jan 17, 2012, 9:40 PM by Alicegop Keeler   [ updated Jan 17, 2012, 9:42 PM ]

Warm Up - Do a 3x3 matrix determinant.
(Note, 5th period you might want to look at the daily from last time.  I posted a bunch of examples)

#47 Continue working on #47 worksheet.  Working with Polynomials.
Answers are below so you MUST show work samples too!

#48 Take this practice quiz. Need to get at least 20% (keep taking it until you do!!!)
http://www.quia.com/quiz/3461693.html

As always... Post to your WordPress!!!!!!!

#47 worksheets
Calculate the determinant of each matrix. Show your work.

1.Expand along column 3.
 19 -1 1 -18 -6 -11 9 16 15

2.Expand along column 2.
 -1 17 -12 2 20 0 8 -5 -4

3.Expand along column 1.
 6 14 -5 -12 -6 -7 19 -9 16

4.Expand along row 2.
 -19 -4 16 13 -13 -10 20 -6 -2

5.Expand along row 2.
 -13 -2 14 8 -14 -7 13 -5 19

6.Expand along column 3.
 -18 -20 13 17 14 9 -4 -5 3

7.Expand along row 3.
 -3 13 15 -16 20 -18 -8 -19 14

8.Expand along column 3.
 4 -6 1 -14 9 -8 -17 -11 12

9.Expand along column 3.
 15 -20 5 -4 -19 -10 14 -9 7

10.Expand along column 1.
 4 -13 -4 -2 -1 1 18 17 11

11.Expand along row 3.
 -4 -12 4 17 -17 18 20 -2 -15

12.Expand along column 1.
 18 16 6 2 7 3 -6 -1 -3

13.Expand along row 2.
 -16 16 12 -10 -7 -4 0 -17 -20

14.Expand along column 3.
 -18 -5 -16 13 5 -8 17 10 -6

15.Expand along row 3.
 1 9 -3 15 -17 -20 -9 6 -15

16.Expand along row 2.
 -15 20 -20 -4 15 4 8 5 -16

17.Expand along row 1.
 -11 19 -20 3 11 -8 -1 -15 -6

18.Expand along column 1.
 10 15 12 1 -7 -18 2 13 -12

19.Expand along column 3.
 12 -16 -10 16 20 -8 19 -19 5

20.Expand along row 2.
 -11 15 10 -14 20 -13 4 -3 -20

21.Expand along column 1.
 16 -1 17 13 -10 15 2 -16 5

 Name _____________________________ Date ___________________
Matrices
Calculate the determinant of each matrix. Show your work.

1.Expand along column 3.
 19 -1 1 -18 -6 -11 9 16 15

-234 + 3443 - 1980 = 1229
2.Expand along column 2.
 -1 17 -12 2 20 0 8 -5 -4

2256
3.Expand along column 1.
 6 14 -5 -12 -6 -7 19 -9 16

-954 + 2148 - 2432 = -1238
4.Expand along row 2.
 -19 -4 16 13 -13 -10 20 -6 -2

-1352 + 3666 + 1940 = 4254
5.Expand along row 2.
 -13 -2 14 8 -14 -7 13 -5 19

-256 + 6006 + 637 = 6387
6.Expand along column 3.
 -18 -20 13 17 14 9 -4 -5 3

-377 - 90 + 264 = -203
7.Expand along row 3.
 -3 13 15 -16 20 -18 -8 -19 14

4272 + 5586 + 2072 = 11930
8.Expand along column 3.
 4 -6 1 -14 9 -8 -17 -11 12

307 - 1168 - 576 = -1437
9.Expand along column 3.
 15 -20 5 -4 -19 -10 14 -9 7

1510 + 1450 - 2555 = 405
10.Expand along column 1.
 4 -13 -4 -2 -1 1 18 17 11

-112 - 150 - 306 = -568
11.Expand along row 3.
 -4 -12 4 17 -17 18 20 -2 -15

-2960 - 280 - 4080 = -7320
12.Expand along column 1.
 18 16 6 2 7 3 -6 -1 -3

-324 + 84 - 36 = -276
13.Expand along row 2.
 -16 16 12 -10 -7 -4 0 -17 -20

-1160 - 2240 + 1088 = -2312
14.Expand along column 3.
 -18 -5 -16 13 5 -8 17 10 -6

-720 - 760 + 150 = -1330
15.Expand along row 3.
 1 9 -3 15 -17 -20 -9 6 -15

2079 - 150 + 2280 = 4209
16.Expand along row 2.
 -15 20 -20 -4 15 4 8 5 -16

-880 + 6000 + 940 = 6060
17.Expand along row 1.
 -11 19 -20 3 11 -8 -1 -15 -6

2046 + 494 + 680 = 3220
18.Expand along column 1.
 10 15 12 1 -7 -18 2 13 -12

3180 + 336 - 372 = 3144
19.Expand along column 3.
 12 -16 -10 16 20 -8 19 -19 5

6840 + 608 + 2480 = 9928
20.Expand along row 2.
 -11 15 10 -14 20 -13 4 -3 -20

-3780 + 3600 - 351 = -531
21.Expand along column 1.
 16 -1 17 13 -10 15 2 -16 5

3040 - 3471 + 310 = -121

Polynomials
Multiply.

 1 (-12x6 + 6x3 + 12x2) (9x + 5)
 2 (-5x2 + 3x + 2) (5x2 + 3x + 5)
 3 (2x6 + 12x3 - 12x) (-4x + 4)
 4 (8x2 + 3x - 4) (12x2 + 9x + 11)
 5 (8x2 + 3x + 2) (9x2 - 9x - 2)
 6 (12) (3x2 - 2x - 11)
 7 (9x - 12) (8x + 3)
 8 (-11x5 - 2x3 - 9) (-2x2 - 11x - 8)
 9 (7x7 - 4x4 + 6x) (6x2 + 3x + 6) (-4x2 + 6x + 11)
 10 (-10x + 4) (8x2 - 12x + 9)
 11 (2x4 - 6x2) (-12x + 9) (-6x2 - 10x - 5)
 12 (8x + 8) (-6x - 7)
 13 (11x2 - 7x + 12) (12x + 4)
 14 (10) (4x2 + 10x + 4)
 15 (-2x7 - 10x6 - 12x3) (-7x2 - 12x - 6) (6x - 10)
 16 (-11x2 + 6x + 8) (9x - 2)
 17 (4x + 7) (9x + 3)
 18 (-9x6 + 6x5 - 11x4) (-7x - 2) (-4x - 7)
 19 (8x + 8) (2x3 - 8x2 + 8x - 11)
 20 (9x7 + 9x4 - 5) (-8x3 + 6x2 + 2x - 7) (-7x - 11)

 Name _____________________________ Date ___________________
Polynomials
Multiply.

1.(-12x6 + 6x3 + 12x2) (9x + 5)

 -108x7 - 60x6 + 54x4 + 138x3 +
 60x2
2.(-5x2 + 3x + 2) (5x2 + 3x + 5)

 -25x4 - 6x2 + 21x + 10
3.(2x6 + 12x3 - 12x) (-4x + 4)

 -8x7 + 8x6 - 48x4 + 48x3 +
 48x2 - 48x
4.(8x2 + 3x - 4) (12x2 + 9x + 11)

 96x4 + 108x3 + 67x2 - 3x -
 44
5.(8x2 + 3x + 2) (9x2 - 9x - 2)

 72x4 - 45x3 - 25x2 - 24x -
 4
6.(12) (3x2 - 2x - 11)

 36x2 - 24x - 132
7.(9x - 12) (8x + 3)

 72x2 - 69x - 36
8.(-11x5 - 2x3 - 9) (-2x2 - 11x - 8)

 22x7 + 121x6 + 92x5 + 22x4 +
 16x3 + 18x2 + 99x + 72
9.(7x7 - 4x4 + 6x) (6x2 + 3x + 6) (-4x2 + 6x + 11)

 -168x11 + 168x10 + 420x9 + 579x8 +
 366x7 - 240x6 - 420x5 - 120x4 +
 360x3 + 414x2 + 396x
10.(-10x + 4) (8x2 - 12x + 9)

 -80x3 + 152x2 - 138x + 36
11.(2x4 - 6x2) (-12x + 9) (-6x2 - 10x - 5)

 144x7 + 132x6 - 492x5 - 486x4 +
 180x3 + 270x2
12.(8x + 8) (-6x - 7)

 -48x2 - 104x - 56
13.(11x2 - 7x + 12) (12x + 4)

 132x3 - 40x2 + 116x + 48
14.(10) (4x2 + 10x + 4)

 40x2 + 100x + 40
15.(-2x7 - 10x6 - 12x3) (-7x2 - 12x - 6) (6x - 10)

 84x10 + 424x9 - 148x8 - 960x7 -
 96x6 + 24x5 - 1008x4 - 720x3
16.(-11x2 + 6x + 8) (9x - 2)

 -99x3 + 76x2 + 60x - 16
17.(4x + 7) (9x + 3)

 36x2 + 75x + 21
18.(-9x6 + 6x5 - 11x4) (-7x - 2) (-4x - 7)

 -252x8 - 345x7 - 92x6 - 543x5 -
 154x4
19.(8x + 8) (2x3 - 8x2 + 8x - 11)

 16x4 - 48x3 - 24x - 88
20.(9x7 + 9x4 - 5) (-8x3 + 6x2 + 2x - 7) (-7x - 11)

 504x11 + 414x10 - 720x9 + 747x8 +
 1107x7 - 720x6 + 243x5 + 413x4 -
 230x3 + 400x2 - 135x - 385

F/T Jan 13-17

posted Jan 12, 2012, 8:52 AM by Alicegop Keeler   [ updated Jan 17, 2012, 8:30 AM by Alice Keeler ]

Warm Up - Practice graphing systems of inequalities.
**Go through this Presentation, work with a partner would be great. Post evidence you followed along on your WP blog**

Graphing Linear Systems

#47 Determinant of 3x3 matrix and polynomials
Take notes on this video.  Probably you will need to watch it more than once.
On my desk are worksheets with the 3x3 determinants.  Please ask the sub to give you one. Do not just take it off my desk.
SHOW WORK ON PAPER or on iPad
Include your WORK when you turn into the wordpress blog post you make.
The answers are below so you need to have WORK shown in order to get credit.
You will not get to the 2nd page of polynomials, hold on to it for next time.
Title: 3x3 determinants and polynomials
XP: 100
Category: Alg2, Classwork
Tags: matrix, determinant

Notice the minus on the b. This means you change the sign.

3x3 matrix notes

From example #3

This is for next time also, but if you finish the matrix problems you can try this.
#48 Take this practice quiz. Need to get at least 20%
http://www.quia.com/quiz/3461693.html

#47 worksheets
Calculate the determinant of each matrix. Show your work.

1.   Expand along column 3.
 19 -1 1 -18 -6 -11 9 16 15

2.   Expand along column 2.
 -1 17 -12 2 20 0 8 -5 -4

3.   Expand along column 1.
 6 14 -5 -12 -6 -7 19 -9 16

4.   Expand along row 2.
 -19 -4 16 13 -13 -10 20 -6 -2

5.   Expand along row 2.
 -13 -2 14 8 -14 -7 13 -5 19

6.   Expand along column 3.
 -18 -20 13 17 14 9 -4 -5 3

7.   Expand along row 3.
 -3 13 15 -16 20 -18 -8 -19 14

8.   Expand along column 3.
 4 -6 1 -14 9 -8 -17 -11 12

9.   Expand along column 3.
 15 -20 5 -4 -19 -10 14 -9 7

10.   Expand along column 1.
 4 -13 -4 -2 -1 1 18 17 11

11.   Expand along row 3.
 -4 -12 4 17 -17 18 20 -2 -15

12.   Expand along column 1.
 18 16 6 2 7 3 -6 -1 -3

13.   Expand along row 2.
 -16 16 12 -10 -7 -4 0 -17 -20

14.   Expand along column 3.
 -18 -5 -16 13 5 -8 17 10 -6

15.   Expand along row 3.
 1 9 -3 15 -17 -20 -9 6 -15

16.   Expand along row 2.
 -15 20 -20 -4 15 4 8 5 -16

17.   Expand along row 1.
 -11 19 -20 3 11 -8 -1 -15 -6

18.   Expand along column 1.
 10 15 12 1 -7 -18 2 13 -12

19.   Expand along column 3.
 12 -16 -10 16 20 -8 19 -19 5

20.   Expand along row 2.
 -11 15 10 -14 20 -13 4 -3 -20

21.   Expand along column 1.
 16 -1 17 13 -10 15 2 -16 5

 Name _____________________________ Date ___________________
Matrices
Calculate the determinant of each matrix. Show your work.

1.   Expand along column 3.
 19 -1 1 -18 -6 -11 9 16 15

-234 + 3443 - 1980 = 1229
2.   Expand along column 2.
 -1 17 -12 2 20 0 8 -5 -4

2256
3.   Expand along column 1.
 6 14 -5 -12 -6 -7 19 -9 16

-954 + 2148 - 2432 = -1238
4.   Expand along row 2.
 -19 -4 16 13 -13 -10 20 -6 -2

-1352 + 3666 + 1940 = 4254
5.   Expand along row 2.
 -13 -2 14 8 -14 -7 13 -5 19

-256 + 6006 + 637 = 6387
6.   Expand along column 3.
 -18 -20 13 17 14 9 -4 -5 3

-377 - 90 + 264 = -203
7.   Expand along row 3.
 -3 13 15 -16 20 -18 -8 -19 14

4272 + 5586 + 2072 = 11930
8.   Expand along column 3.
 4 -6 1 -14 9 -8 -17 -11 12

307 - 1168 - 576 = -1437
9.   Expand along column 3.
 15 -20 5 -4 -19 -10 14 -9 7

1510 + 1450 - 2555 = 405
10.   Expand along column 1.
 4 -13 -4 -2 -1 1 18 17 11

-112 - 150 - 306 = -568
11.   Expand along row 3.
 -4 -12 4 17 -17 18 20 -2 -15

-2960 - 280 - 4080 = -7320
12.   Expand along column 1.
 18 16 6 2 7 3 -6 -1 -3

-324 + 84 - 36 = -276
13.   Expand along row 2.
 -16 16 12 -10 -7 -4 0 -17 -20

-1160 - 2240 + 1088 = -2312
14.   Expand along column 3.
 -18 -5 -16 13 5 -8 17 10 -6

-720 - 760 + 150 = -1330
15.   Expand along row 3.
 1 9 -3 15 -17 -20 -9 6 -15

2079 - 150 + 2280 = 4209
16.   Expand along row 2.
 -15 20 -20 -4 15 4 8 5 -16

-880 + 6000 + 940 = 6060
17.   Expand along row 1.
 -11 19 -20 3 11 -8 -1 -15 -6

2046 + 494 + 680 = 3220
18.   Expand along column 1.
 10 15 12 1 -7 -18 2 13 -12

3180 + 336 - 372 = 3144
19.   Expand along column 3.
 12 -16 -10 16 20 -8 19 -19 5

6840 + 608 + 2480 = 9928
20.   Expand along row 2.
 -11 15 10 -14 20 -13 4 -3 -20

-3780 + 3600 - 351 = -531
21.   Expand along column 1.
 16 -1 17 13 -10 15 2 -16 5

3040 - 3471 + 310 = -121

Polynomials
Multiply.

 1 (-12x6 + 6x3 + 12x2) (9x + 5)
 2 (-5x2 + 3x + 2) (5x2 + 3x + 5)
 3 (2x6 + 12x3 - 12x) (-4x + 4)
 4 (8x2 + 3x - 4) (12x2 + 9x + 11)
 5 (8x2 + 3x + 2) (9x2 - 9x - 2)
 6 (12) (3x2 - 2x - 11)
 7 (9x - 12) (8x + 3)
 8 (-11x5 - 2x3 - 9) (-2x2 - 11x - 8)
 9 (7x7 - 4x4 + 6x) (6x2 + 3x + 6) (-4x2 + 6x + 11)
 10 (-10x + 4) (8x2 - 12x + 9)
 11 (2x4 - 6x2) (-12x + 9) (-6x2 - 10x - 5)
 12 (8x + 8) (-6x - 7)
 13 (11x2 - 7x + 12) (12x + 4)
 14 (10) (4x2 + 10x + 4)
 15 (-2x7 - 10x6 - 12x3) (-7x2 - 12x - 6) (6x - 10)
 16 (-11x2 + 6x + 8) (9x - 2)
 17 (4x + 7) (9x + 3)
 18 (-9x6 + 6x5 - 11x4) (-7x - 2) (-4x - 7)
 19 (8x + 8) (2x3 - 8x2 + 8x - 11)
 20 (9x7 + 9x4 - 5) (-8x3 + 6x2 + 2x - 7) (-7x - 11)

 Name _____________________________ Date ___________________
Polynomials
Multiply.

1.   (-12x6 + 6x3 + 12x2) (9x + 5)

 -108x7 - 60x6 + 54x4 + 138x3 +
 60x2
2.   (-5x2 + 3x + 2) (5x2 + 3x + 5)

 -25x4 - 6x2 + 21x + 10
3.   (2x6 + 12x3 - 12x) (-4x + 4)

 -8x7 + 8x6 - 48x4 + 48x3 +
 48x2 - 48x
4.   (8x2 + 3x - 4) (12x2 + 9x + 11)

 96x4 + 108x3 + 67x2 - 3x -
 44
5.   (8x2 + 3x + 2) (9x2 - 9x - 2)

 72x4 - 45x3 - 25x2 - 24x -
 4
6.   (12) (3x2 - 2x - 11)

 36x2 - 24x - 132
7.   (9x - 12) (8x + 3)

 72x2 - 69x - 36
8.   (-11x5 - 2x3 - 9) (-2x2 - 11x - 8)

 22x7 + 121x6 + 92x5 + 22x4 +
 16x3 + 18x2 + 99x + 72
9.   (7x7 - 4x4 + 6x) (6x2 + 3x + 6) (-4x2 + 6x + 11)

 -168x11 + 168x10 + 420x9 + 579x8 +
 366x7 - 240x6 - 420x5 - 120x4 +
 360x3 + 414x2 + 396x
10.   (-10x + 4) (8x2 - 12x + 9)

 -80x3 + 152x2 - 138x + 36
11.   (2x4 - 6x2) (-12x + 9) (-6x2 - 10x - 5)

 144x7 + 132x6 - 492x5 - 486x4 +
 180x3 + 270x2
12.   (8x + 8) (-6x - 7)

 -48x2 - 104x - 56
13.   (11x2 - 7x + 12) (12x + 4)

 132x3 - 40x2 + 116x + 48
14.   (10) (4x2 + 10x + 4)

 40x2 + 100x + 40
15.   (-2x7 - 10x6 - 12x3) (-7x2 - 12x - 6) (6x - 10)

 84x10 + 424x9 - 148x8 - 960x7 -
 96x6 + 24x5 - 1008x4 - 720x3
16.   (-11x2 + 6x + 8) (9x - 2)

 -99x3 + 76x2 + 60x - 16
17.   (4x + 7) (9x + 3)

 36x2 + 75x + 21
18.   (-9x6 + 6x5 - 11x4) (-7x - 2) (-4x - 7)

 -252x8 - 345x7 - 92x6 - 543x5 -
 154x4
19.   (8x + 8) (2x3 - 8x2 + 8x - 11)

 16x4 - 48x3 - 24x - 88
20.   (9x7 + 9x4 - 5) (-8x3 + 6x2 + 2x - 7) (-7x - 11)

 504x11 + 414x10 - 720x9 + 747x8 +
 1107x7 - 720x6 + 243x5 + 413x4 -
 230x3 + 400x2 - 135x - 385

W/R Jan 11-12

posted Jan 11, 2012, 7:41 AM by Alicegop Keeler   [ updated Jan 12, 2012, 8:51 AM ]

#46 Graph the following systems of equations using your graphing calculator.  Take screen shots.  Post the equations, the graphs and the SOLUTION to your wordpress blog.
Title: Graphing Systems XP: 100 Tags: graphing, systems

#46 worksheet
Linear Equations
Graph each system of equations and state its solution.
1.
 y = x + 5

-9y = -57 - 15x

2.  4y = 2 + 2x
 y = 2 x + 8

Graph each system of equations and state its solution.
3.
y =
 52
x  -
 312

5x - 2y = 31

4.  5x - 3y = -11
 3x - 4y4
=
 -114

Solve each system of equations using the substitution method.
 5 10x - y = -558x + 19y = -539
 6 14x - 3y = -3223x - y = -79

Solve each system of equations using the substitution method.
7.
y =
 -1715
x  -
 1565

12x - y = -481

 8 2x - 3y = -43-9y = -104 - x

Solve each system of equations using the elimination method.
 9 17x + 19y = 30912x + 19y = 369
 10 4x + 7y = 187x - 3y = 306

Solve each system of equations using the elimination method.
11.
 16x + 17y8
=  -165

 80 = -4 y + 2 x

 12 38x = -1906 + 36y10x - 9y = -485

Solve each system of equations using any method.
 13 14x + 15y = 11217x - 18y = 643
 14 16x + 13y = -4382x + y = -46

Solve each system of equations using any method.
15.
y =
 136
x  -
 452

 16x + 17y2
=  205

16.  -9y = 492 - 12x
y =
 -43
x  +
 443

Solve each system by graphing. Find the vertices of the graph.
 17 5y    55x - y    195x - 6y    39
 18 3x - y    -63x + 2y    -156x + y    -12
 19 x - 4y    203x - y    -64x - 5y    3

Solve each system by graphing. Find the vertices of the graph.
 20 4x - 5y    -23x - 3y    -4x + 2y    13y    9
 21 x + y    105x - 3y    -222x + y    03x - 7y    0
 22 2x + y    115x + y    04x - 5y    293x - 4y    0

Solve each system by graphing. Find the vertices of the graph.
 23 3x - 2y    125x - 2y    205x - y    419x - 7y    53
 24 x - 4y    -74x - y    324x - y    17x + y    3
 25 5x - 3y    315y    -355x + 2y    21

Find the minimum and maximum values of the objective quantity.
 26 3x - 2y    207x - 10y    365x + 2y    -20f(x,y) = -12x - 3y + 22
 27 11x - 5y    867x - 9y    14x + y    2f(x,y) = 2x - 8y
 28 5x    155x - 3y    273y    -27f(x,y) = -3x - 5y

Find the minimum and maximum values of the objective quantity.
 29 5x - 6y    15x - y = 32x    03y    -15f(x,y) = -12x + 6y
 30 2x - y    54x + 3y    553x + 2y    411x - 4y    -8f(x,y) = -7x - 11y
 31 6x + 7y    582x + 3y    4x + 5y    26x    30f(x,y) = -8x - 12y

Find the minimum and maximum values of the objective quantity.
 32 3x - 2y    132y    -163x    3f(x,y) = 5x + 6y
 33 13x - 2y    2311x - 8y    51x - y    311x - 3y    9f(x,y) = 4x - 2y
 34 4x - 5y    -162x - y    -2x - 2y    -42x - y    -2f(x,y) = -x - 12y - 14

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