Chapter 3 Worksheets.pdf
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NAME
CLASS
DATE
Practice Masters Level A
3.1
Solving Systems by Graphing or Substitution
Graph and classify each system. Then find the solution from the graph. 1.
冦
y ⴝ ⴚx ⴙ 2 y ⴝ 2x ⴚ 1
2.
y ⴝ ⴚx ⴙ 6 1 yⴝ xⴙ2 3
冦
y
4
4
4
2
2
2
⫺4 ⫺2
冦
冦
xⴙyⴝ0 3x ⴙ y ⴝ 6
y
y
4.
3.
2
4
x
⫺4 ⫺2
2
4
x
⫺4 ⫺2
⫺2
⫺2
⫺2
⫺4
⫺4
⫺4
2x ⴙ 4y ⴝ 12 xⴙyⴝ2
5.
冦
yⴝx y ⴝ 5x ⴙ 0
6.
冦
4
2
2
2
4
x
⫺4 ⫺2
2
4
x
⫺4 ⫺2
2
4
⫺2
⫺2
⫺2
⫺4
⫺4
⫺4
x
Use substitution to solve each system of equations. Check your solution.
yⴝxⴙ3
7.
冦 10x ⴙ 2y ⴝ 18
8.
10.
x ⴚ 3y ⴝ 0 3x ⴚ 2y ⴝ ⴚ7
11.
46
冦
xⴝyⴚ8
冦 4x ⴚ y ⴝ ⴚ2 冦
2x ⴚ y ⴝ ⴚ12 ⴚ2x ⴚ 4y ⴝ 2
Practice Masters Levels A, B, and C
9.
12.
2x ⴙ y ⴝ 7
冦 3x ⴙ 2y ⴝ 10 冦
x ⴚ 6y ⴝ ⴚ18 ⴚ3x ⴙ 2y ⴝ 6
Algebra 2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4
2
x
y
4
⫺4 ⫺2
4
y ⴝ ⴚ2x ⴙ 1 y ⴝ ⴚ2x ⴙ 5
y
y
2
Answers Lesson 3.1 Level A 1.
4.
(ⴚ2, 4), independent y
(1, 1), independent
4
y 2 4 ⫺4 2
⫺4
x
⫺2
2
4
⫺2
x
⫺2
2
⫺4
4
⫺4
5.
(0, 0), independent y
2.
(3, 3), independent 4
y 2 4 ⫺4
x
⫺2
2
4
⫺2 ⫺4
x
⫺2
2
4
⫺2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
⫺4
6.
no solution, inconsistent y
3.
(3, ⴚ3), independent
4
y 4 ⫺4
2
⫺4
2
4
⫺2
x
⫺2
x
⫺2
2
⫺4
4
⫺2 ⫺4
Algebra 2
7.
(1, 4)
8.
(2, 10)
9.
(4, ⴚ1),
10.
(ⴚ3, ⴚ1)
11.
(ⴚ5, 2)
12.
(0, 3)
Practice Masters Levels A, B, and C
305
NAME
CLASS
DATE
Practice Masters Level A
3.2
Solving Systems by Elimination
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Use elimination to solve each system of equations. Check your solution.
2x ⴙ y ⴝ 41 2x ⴙ 5y ⴝ 13
1.
冦
3.
冦 2x ⴙ y ⴝ 10
5.
冦 3x ⴚ y ⴝ ⴚ11
7.
冦 ⴚ6x ⴙ 3y ⴝ ⴚ6
9.
冦 16x ⴙ 8y ⴝ ⴚ16
x ⴚ 2y ⴝ 5
x ⴙ 3y ⴝ 3
3x ⴚ 2y ⴝ 4
4x ⴙ 2y ⴝ ⴚ4
4.
冦 ⴚ4x ⴙ 5y ⴝ ⴚ23
6.
冦 7c ⴙ 3d ⴝ 12
8.
冦 ⴚ3x ⴙ 3y ⴝ 39
8x ⴙ 3y ⴝ 7
7c ⴙ 3d ⴝ 25
ⴚ5x ⴚ 2y ⴝ 44
ⴚ3x ⴚ y ⴝ ⴚ1
冦 4x ⴙ 8y ⴝ ⴚ2
12.
冦
1 2 ⴚ3x ⴙ 2y ⴝ 0
14.
冦
11x ⴙ 12y ⴝ 112 11x ⴙ 12y ⴝ 324
16.
3x ⴚ 4y ⴝ 16 2x ⴙ 5y ⴝ 3
冦
13.
冦
6x ⴚ 5y ⴝ
冦
冦
10.
11.
15.
3x ⴙ 4y ⴝ 3 ⴚ3x ⴚ 2y ⴝ ⴚ9
2.
Algebra 2
2x ⴚ 5y ⴝ
8 7
1 7x ⴙ y ⴝ ⴚ2 2
1 x ⴙ 2y ⴝ 4 3 ⴚ4x ⴚ y ⴝ 21
冦
9x ⴚ 18y ⴝ 45 18x ⴙ 9y ⴝ 90
Practice Masters Levels A, B, and C
49
Answers Lesson 3.1 Level B 1.
(ⴚ3, ⴚ7), independent
8.
no solution
9.
(ⴚ0.1, 0.4)
10.
125 feet wide, 500 feet long
11.
75 mL acid solution 25 mL pure acid
12.
8.5 pounds of pecans 5.5 pounds of almonds
y 10 8 6 4 2 ⫺10
⫺6 ⫺4 ⫺2 ⫺2
4 6 8 10
x
Lesson 3.1 Level C
⫺6 ⫺8 ⫺10
2.
(6, 0), independent y 10 8 6
1.
(1.73, ⴚ1.73)
2.
(ⴚ0.68, 3.07)
3.
(1, ⴚ2, ⴚ4)
4.
冢12, 41, ⴚ27 8 冣
5.
(2, ⴚ1, 1)
6.
(ⴚ7, 5, ⴚ2.5)
2
3.
2 4 6
10
x
7.
plane air speed is 280 mph wind speed is 40 mph
8.
6 mL chlorine solution
no solution, inconsistent y
9.
1
$444.44 at 11% $4555.56 at 6.5%
x 2
4 5
⫺2 ⫺3 ⫺4 ⫺5
4.
(ⴚ1, 11)
5.
(12, ⴚ4)
6.
all real numbers
7.
冢2, 3 冣
306
1 3
13 mL pure water
5 4 3
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
2 3
Copyright © by Holt, Rinehart and Winston. All rights reserved.
⫺10 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 ⫺6 ⫺8 ⫺10
1 2
Practice Masters Levels A, B, and C
10.
rate of boat
25d 48
rate of current
mph 7d 48
mph
Lesson 3.2 Level A 1.
(24, ⴚ7)
2.
(5, ⴚ3)
3.
(5, 0)
Algebra 2
Answers 4.
(2, ⴚ3)
5.
(ⴚ3, 2)
6.
no solution
7.
(0, ⴚ2)
8.
(ⴚ10, 3)
9.
infinite number of solutions
10.
11.
12.
13.
冣
(4, ⴚ1)
冢
ⴚ11 ⴚ1 , 42 3
冣
ⴚ1 ⴚ1
冢3, 2冣 (ⴚ6, 3)
15.
no solution (5, 0)
Lesson 3.2 Level B 1.
(10, 6)
2.
(ⴚ12, 1)
3.
(ⴚ1, ⴚ12) 1 ⴚ1 , 6 8
4.
冢
5.
(5, 6)
6.
infinitely many solutions
7.
no solution
8.
(ⴚ358, 269)
9.
冢4, 2 冣 7
Algebra 2
(20, ⴚ16)
11.
冢2, ⴚ3冣
12.
冢2, 2 冣
13.
(ⴚ6, ⴚ2)
14.
no solution
1
1 ⴚ7
Lesson 3.2 Level C
14.
16. Copyright © by Holt, Rinehart and Winston. All rights reserved.
冢
1 ⴚ1 , 2 2
10.
冣
1.
no solution
2.
(4, ⴚ12)
3.
infinitely many solutions
4.
(2a ⴙ b, ⴚ3a ⴚ2b)
5.
(0.05, ⴚ0.08)
6.
冢
7.
9 skilled, 15 unskilled
8.
300 large, 240 small
9.
$3695.65 at 19% $1304.35 at 7.5%
5c ⴙ 2d 4c ⴙ 3d , 7 ⴚ7
冣
Lesson 3.3 Level A y
1. 5 4 3 2 1
x
⫺5 ⫺4 ⫺3 ⫺2
1 2 3 4 5 ⫺2 ⫺3 ⫺4 ⫺5
Practice Masters Levels A, B, and C
307
NAME
CLASS
DATE
Practice Masters Level A
3.3
Linear Inequalities In Two Variables
Graph each linear inequality. 1.
yⱖx
2.
y ⬍ 2x ⴙ 4
y
yⱕ
y ⬎ ⴚx y
y
4
4
4
2
2
2
⫺4 ⫺2
4.
3.
2
4
x
⫺4 ⫺2
2
4
x
⫺4 ⫺2
⫺2
⫺2
⫺2
⫺4
⫺4
⫺4
ⴚ1 xⴙ2 2
5.
3x ⴙ y ⴚ 5 ⬎ 0
6.
4
4
2
2
2
4
x
⫺4 ⫺2
2
4
x
⫺4 ⫺2
2
4
⫺2
⫺2
⫺2
⫺4
⫺4
⫺4
7.
For a fund raiser, The Honor Society is selling two sizes of candy bars. They earn a profit of $1.00 on small candy bars, s, and $2.00 on large candy bars, l.
a.
Write an inequality that represents a profit of at least $300.
x Copyright © by Holt, Rinehart and Winston. All rights reserved.
2
x
y
4
⫺4 ⫺2
4
y ⬍ ⴚ2
y
y
2
ᐉ 400 300
b. c.
Graph the inequality on the coordinate grid to the right. Find three ordered pairs that represent achieving the goal of making a $300 profit.
200 100 50
52
Practice Masters Levels A, B, and C
100 150 200
s
Algebra 2
Answers 4.
(2, ⴚ3)
5.
(ⴚ3, 2)
6.
no solution
7.
(0, ⴚ2)
8.
(ⴚ10, 3)
9.
infinite number of solutions
10.
11.
12.
13.
冣
(4, ⴚ1)
冢
ⴚ11 ⴚ1 , 42 3
冣
ⴚ1 ⴚ1
冢3, 2冣 (ⴚ6, 3)
15.
no solution (5, 0)
Lesson 3.2 Level B 1.
(10, 6)
2.
(ⴚ12, 1)
3.
(ⴚ1, ⴚ12) 1 ⴚ1 , 6 8
4.
冢
5.
(5, 6)
6.
infinitely many solutions
7.
no solution
8.
(ⴚ358, 269)
9.
冢4, 2 冣 7
Algebra 2
(20, ⴚ16)
11.
冢2, ⴚ3冣
12.
冢2, 2 冣
13.
(ⴚ6, ⴚ2)
14.
no solution
1
1 ⴚ7
Lesson 3.2 Level C
14.
16. Copyright © by Holt, Rinehart and Winston. All rights reserved.
冢
1 ⴚ1 , 2 2
10.
冣
1.
no solution
2.
(4, ⴚ12)
3.
infinitely many solutions
4.
(2a ⴙ b, ⴚ3a ⴚ2b)
5.
(0.05, ⴚ0.08)
6.
冢
7.
9 skilled, 15 unskilled
8.
300 large, 240 small
9.
$3695.65 at 19% $1304.35 at 7.5%
5c ⴙ 2d 4c ⴙ 3d , 7 ⴚ7
冣
Lesson 3.3 Level A y
1. 5 4 3 2 1
x
⫺5 ⫺4 ⫺3 ⫺2
1 2 3 4 5 ⫺2 ⫺3 ⫺4 ⫺5
Practice Masters Levels A, B, and C
307
Answers y
2.
y
6.
5 4
5 4 3 2 1
2 1 ⫺5 ⫺4 ⫺3
x
⫺1 ⫺1 ⫺2 ⫺3 ⫺4 ⫺5
7. a.
5 4 3 2 1
x 2 3 4 5
0
y c.
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
1 2 3 4
⫺2 ⫺3 ⫺4 ⫺5
50
100
150
200
250
s
answers may vary, sample answers: (134, 500), (1000, 1), (1, 577)
Lesson 3.3 Level B
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5 4 3 2 1
y
1. 5 4
y
2 1
5 4 3 2 1 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
ᐉ
500 450 400 350 300 250 200 150 100 50
⫺2 ⫺3 ⫺4 ⫺5
5.
1.0s ⴙ 2.0l ⱖ 300
b.
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
4.
1 2 3 4 5
⫺3 ⫺4 ⫺5
y
3.
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
1 2 3 4 5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
x 1
3 4 5
x 1 2 3 4 5
⫺2 ⫺3 ⫺4 ⫺5
⫺2 ⫺3 ⫺4 ⫺5
308
Practice Masters Levels A, B, and C
Algebra 2
NAME
CLASS
DATE
Practice Masters Level A
3.4
Systems of Linear Inequalities
Graph each system of linear inequalities. 1.
y ⱕ 3x ⴙ 1
冦 y ⱖ ⴚx
2.
y ⬎ 4x ⴚ 2
冦 y ⬎ 3x ⴚ 1
y
3.
y ⱕ 2x
冦 y ⱖ ⴚx ⴙ 2
y
y
4
4
4
2
2
2
⫺4 ⫺2
2
4
x
⫺4 ⫺2
2
4
x
⫺4 ⫺2
2
⫺2
⫺2
⫺2
⫺4
⫺4
⫺4
4
x
Write the system of inequalities whose solution is graphed. y
4.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4 3 2 1 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
(0, ⴚ1)⫺2
y
5.
(1, 2) (2, 0) 1 2 3 4 5
x
5
5 4
2 1
2 1
(0, 0)
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
1
⫺2 ⫺3
7.
x 3 4 5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
(0, 2) (54 , ⴚ1 2)
x
2 3 4 5
⫺2
(12 , ⫺5 2)
(0, ⴚ3) ⫺5
y
6.
(0, ⫺3)⫺3
⫺5
Graph the system of linear inequalities. y ⱕ ⴚ4x ⴙ 6 y ⬍ 3x ⴚ 1 y ⱖ ⴚ2x ⴚ 3
冦
y 4 4
8
12
16
x
⫺4 ⫺8 ⫺12 ⫺16
Algebra 2
Practice Masters Levels A, B, and C
55
Answers y
2.
c.
D ⱕ ⴚ1.1Pⴙ5.27 ᐉ
5 4 3 2 1 ⫺5 ⫺4 ⫺3
10 8 4 2
x
⫺1 ⫺1 ⫺2 ⫺3 ⫺4 ⫺5
1 2 3 4 5
⫺10 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 ⫺6 ⫺8 ⫺10
2 4
8 10
p
y
3.
⫺4y/5 ⬎ 3
5 4 3 2 1
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
d.
ᐉ 8 6 4 2
x 1 2 3 4 5
⫺2 ⫺3
⫺10 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 ⫺6 ⫺8 ⫺10
⫺5
4. a.
S ⱕ ⴚ1.57Pⴙ8.3
D ⴝ ⱕ ⴚ1.5Lⴙ5.8
2 4
8 10
p
ᐉ
Lesson 3.4 Level A
⫺10 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 ⫺6 ⫺8 ⫺10
b.
y
1. 2 4 6 8 10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
10 8 6 4 2
5 4 3 2 1
p
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
S ⱕ ⴚ2.14Lⴙ5.8
1 2 3 4 5
⫺3 ⫺4 ⫺5
ᐉ 10
⫺10 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 ⫺6 ⫺8 ⫺10
310
y
2.
6 4 2 2 4 6 8 10
p
Practice Masters Levels A, B, and C
5 4 3 2 1 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
x 1 2 3 4 5
⫺2
Algebra 2
Answers y
3.
y
2.
5 4 3 2 1
5 4 3 2 1
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
1 2
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
4 5
⫺3 ⫺4 ⫺5
⫺3 ⫺4 ⫺5
y ⬍ ⴚ2x ⴙ 4 y ⬎ 3x ⴚ 1
4.
冦
5.
冦y ⱖ x ⴚ 3
6.
5 4 3 1 ⫺5 ⫺4 ⫺3
y ⬍ 2x ⴚ 3 y ⱖ ⴚ2x ⴙ 2 y
7. 4
x
⫺4
4
8
12
16
4.
5. Copyright © by Holt, Rinehart and Winston. All rights reserved.
y
3.
y ⱕ ⴚ5x
冦
⫺12 ⫺16
6.
Lesson 3.4 Level B y
1.
1
3 4 5
y ⱖ ⴚ2x ⴙ 3
冦 y ⱖ 2x ⴚ 3
y ⬍ 4x ⴚ 2 1 y⬎ xⴚ2 2
冦
冦
y ⱕ 2x 3 y ⱖ xⴚ3 2 yⱕ0 y 5
x
1
x
1 2 3 4 5 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1 ⫺3 ⫺4 ⫺5
Algebra 2
x
⫺1 ⫺1 ⫺2 ⫺3 ⫺4 ⫺5
7.
5 4 3 2 1 ⫺5 ⫺4 ⫺3 ⫺2
x
1 2
4 5
⫺2 ⫺3 ⫺4 ⫺5
Practice Masters Levels A, B, and C
311
NAME
CLASS
DATE
Practice Masters Level A
3.6
Parametric Equations
Graph each pair of parametric equations for the interval ⴚ3 ⱕ t ⱕ 3.
1.
x(t) ⴝ t ⴙ 3
冦 y(t) ⴝ 2t
2.
x(t) ⴝ ⴚt ⴙ 2
冦 y(t) ⴝ ⴚ3t ⴙ 1
y
3.
冦
1 x(t) ⴝ t ⴙ 2 2 ⴚ1 y(t) ⴝ tⴚ1 2
y
y
4
8
4
2
4
2
⫺4 ⫺2
2
4
x
⫺8 ⫺4
4
8
x
⫺4 ⫺2
2
⫺2
⫺4
⫺2
⫺4
⫺8
⫺4
4
x
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Write each pair of parametric equations as a single equation in x and y.
x(t) ⴝ t ⴙ 3
4.
冦 y(t) ⴝ 2t
7.
冦 y(t) ⴝ ⴚt
10.
13.
x(t) ⴝ 2t ⴚ 2
冦
2 x(t) ⴝ t ⴙ 2 3 ⴚ3 y(t) ⴝ tⴚ1 4
x(t) ⴝ ⴚt ⴙ 2
5.
冦 y(t) ⴝ ⴚ3t ⴙ 1
8.
冦 y(t) ⴝ t
11.
x(t) ⴝ t ⴚ 1 2
冦
1 x(t) ⴝ t ⴙ 2 2 ⴚ1 y(t) ⴝ tⴚ1 2
x(t) ⴝ t
6.
冦 y(t) ⴝ 4 ⴚ t
9.
冦 y(t) ⴝ ⴚ3(t ⴙ 1)
12.
2
x(t) ⴝ 2(t ⴚ 3)
冦
1 x(t) ⴝ t 2 1 y(t) ⴝ t2 ⴚ 4t ⴙ 1 2
A catcher throws the baseball from home plate to second base. The following parametric equations describe the ball’s path: x(t) ⴝ 80t and y(t) ⴝ 15t ⴚ 16t2 The variables x and y are measured in feet per second, and t is measured in seconds. What horizontal distance will the baseball travel before it hits the ground?
Algebra 2
Practice Masters Levels A, B, and C
61
Answers 2.
Min: ⴚ14
Max: 11
100
ⴚ2 3. Max: 3 4. a.
冦
y
b.
Min: ⴚ4
80
(30, 74)
60
x ⴙ y ⱕ 400 50 ⱕ y ⱕ 250 x ⱖ 100
(90, 37)
40 (80, 30)
20
x
y
b.
20
400 350 300 250 200 150 100 50 ⫺100⫺50 ⫺100
x 100
200
300
40
60
80
c.
P ⴝ 2.25x ⴙ 4.5y
d.
P ⴝ $400.50
100
Lesson 3.6 Level A
400
y
1. 5 4 3 2 1
R ⴝ 540(0.759)x ⴙ 34.9(6.8)y R ⴝ 409.86x ⴙ 237.32y d. $126,197 c.
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1
1 2 3 4 5
⫺2 ⫺3 ⫺4 ⫺5
Lesson 3.5 Level C Copyright © by Holt, Rinehart and Winston. All rights reserved.
(90, 30)
y
1. 8 7 6 5 4
y
2. 8 4
2 1 ⫺2 ⫺1 ⫺1
x 1 2 3 4 5 6 7 8
⫺8
x
⫺4
4
8
⫺4
⫺2
2.
Max: 3
Min: ⴚ7
3.
Max: 6
Min: ⴚ8.5
4. a.
1.75x ⴙ 2y ⱕ 200 4x ⴙ 6.5y ⱖ 600 x ⱕ 90 y ⱖ 30
Algebra 2
Practice Masters Levels A, B, and C
313
Answers y
3.
y
2.
5 4 3 2 1
8 4
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1 ⫺2 ⫺3 ⫺4 ⫺5
4.
x
⫺4
3 4 5
1
4
8
16
1
3 4 5
⫺4 ⫺8
y ⴝ 2x ⴚ 6
y
3. 5 4 3 2 1
5.
y ⴝ 3x ⴚ 5
6.
y ⴝ 4 ⴚ x2
7.
yⴝ
8.
y ⴝ x 2 ⴙ 2x ⴙ 1
9.
yⴝ
ⴚ1 xⴚ1 2
x
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1 ⫺2 ⫺3 ⫺4
ⴚ3 x ⴚ 12 2
5 ⴚ9 xⴙ 10. y ⴝ 8 4
4.
y ⴝ 兹x ⴚ 2
5.
yⴝ
2 8 xⴚ 3 3
y ⴝ ⴚx ⴙ 1
6.
y ⴝ 2x 2 ⴙ 8x ⴙ 1
12.
y ⴝ 2x2ⴚ8x ⴙ 1
7.
y ⴝ 兹1 ⴚ x ⴚ 3
13.
about 99 feet
8.
y 5 4 3 2 1
Lesson 3.6 Level B y
1.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11.
⫺4 ⫺3 ⫺2 ⫺1 ⫺1
x 1 2 3 4 5
⫺2 ⫺3 ⫺4
8 4
⫺8
x
⫺4
4
8
⫺4
9.
about 225 feet
⫺8
314
Practice Masters Levels A, B, and C
Algebra 2
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