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Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A93
100. ( )5, 6− − and ( )1, 0
101. ( )3, 0− and ( )6, 9
102. ( )7, 5− − and ( )2, 0−
103. ( )2, 12− − 104. ( )12, 7−
105. 7
, 23 −
106. ( )8, 5
107. 17
, 12
− −
108. 11
6,4
109. 1 17
, 21 172
+ − +
and
1 17
, 21 172
− − −
110. 47 13 11
1 11,2
−− +
and
47 13 11
1 11,2
+− −
111. 16 11 6
3 6,3
−− +
and
16 11 6
3 6,3
+− −
112. 3 417 108 417
,6 6
− + −
and
3 417 108 417
,6 6
− − +
113. 32448 ft
114. a. 254 in. b. 327 in.
115. a. 2196 cmπ b. 31372cm
3π
116. 158 117. 4021
118. 2034− 119. 66−
120. 393− 121. 237
8−
122. 1777
32 123. 3 22 8 2x x+ −
124. 4 210 12 2 1x x x− − −
125. 5 4 26 4 10 2 7x x x x− − − − +
126. 4 3 29 2 5 4x x x x− − − +
127. 4 3 24 3 9 9 1x x x x− − + +
128. 5 4 3 28 4 5 13 8 10x x x x x− + − − +
129. 5 4 3 23 12 5 3 5 2x x x x x+ + − + −
130. 36 18 10x x− + −
131. 219 10 10x x− −
132. 4 324 4 16 11x x x− + + −
133. 4 3 23 2 12 2 13x x x x+ + − −
134. 5 4 317 2 7 10 5x x x x− + − − +
135. 5 3 26 8 13 6 10x x x x− − + + +
Chapter 8 8.1 Start Thinking
1. Start with 5, then add 2 to the prior term to find each consecutive term.
2. Start with 23, then take the prior term and multiply
the numerator by 2 and add 4 to the denominator to find each consecutive term.
3. Start with 8, then subtract 32
from the prior term to
find each consecutive term.
4. Start with 3, then multiply the prior term by 2− to
find each consecutive term.
8.1 Warm Up
1. ( ) ( ) ( ) ( )( )1 0, 2 2, 3 4, 4 6,
5 8
f f f f
f
= = = =
=
2. ( ) ( ) ( ) ( )( )1 2, 2 4, 3 8, 4 16,
5 32
f f f f
f
= = = =
=
3. ( ) ( ) ( ) ( )( )1 1, 2 3, 3 5, 4 7,
5 9
f f f f
f
= = = =
=
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A94
4. ( ) ( ) ( ) ( )( )1 5, 2 5, 3 5, 4 5,
5 5
f f f f
f
= − = = − =
= −
5. ( ) ( ) ( ) ( )
( )
1 2 4 81 , 2 , 3 , 4 ,
3 3 3 316
53
f f f f
f
= = = =
=
6. ( ) ( ) ( ) ( )( )1 1, 2 4, 3 9, 4 16,
5 25
f f f f
f
= = − = = −
=
8.1 Cumulative Review Warm Up
1. 4x = 2. 4x =
3. 1
ln 4 ln 22
x = = 4. 1x =
5. 2
12 1.865x
e= − ≈ 6. 3x =
8.1 Practice A
1. 2, 1, 0, 1, 2, 3− − 2. 3, 2, 1, 0, 1, 2− −
3. 1, 8, 27, 64, 125, 216 4. 4, 1, 4, 11, 20, 31− −
5. 4, 16, 64, 256, 1024, 4096
6. 0, 3, 8, 15, 24, 35− − − − −
7. Start with 1, then each consecutive term is 3 more than the previous term: 13, 3 2.na n= −
8. Start with 1, then each consecutive term is 3 raised to a power 1 more than the power 3 is raised to in the previous term: 81, 13 .n
na −=
9. Start with 1.5, then each consecutive term is 1.5 more than the previous term: 7.5, 1.5 .na n=
10. Start with 4.2, then each consecutive term is 1.6 more than the previous term: 10.6, 2.6 1.6 .na n= +
11. Start with 4.7, then each consecutive term is 1.3 less than the previous term: 0.5, 6 1.3 .na n− = −
12. Start with 5,− then the absolute value of each
consecutive term is 5 more than the absolute value of the previous term, and the signs alternate:
( )25, 1 5 .n
na n− = −
13. Start with 1
,6
then the numerator of each consecutive
term is 1 more than the numerator of the previous
term: 5
, .6 6
nn
a =
14. Start with 3
,2
then the denominator of each
consecutive term is 2 more than the denominator
of the previous term: 3 3
, .10 2
nan
=
15. ( )110 2nna −=
16. 5
1
4n
n= 17. ( )
5
1
6 3n
n=
− 18. ( )1
6 5n
n∞
=−
19. ( )1
2 3n
n∞
=− 20.
1
1
5nn
∞
= 21.
1 6n
n
n
∞
= +
22. 30 23. 90 24. 55
25. 93 26. 73 27. 153
28
28. ( )6
1
105; 28 3n
n=
−
8.1 Practice B
1. 5, 8, 13, 20, 29, 40 2. 1, 1, 3, 9, 27, 81
3
3. 1, 0, 1, 4, 9, 16
4. 2, 1, 6, 13, 22, 33− − − − −
5. 1 2 3 4 1 6, , , , ,
6 7 8 9 2 11− − − − − −
6. 1 2 3 4 5 6, , , , ,
2 5 8 11 14 17
7. Start with 2, then each consecutive term is 5 more than the previous term: 22, 5 3.na n= −
00
200
600
400
2 4 6 n
an
Answers
Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A95
8. Start with 2.7, then each consecutive term is 3.5 more than the previous term: 16.7, 3.5 0.8.na n= −
9. Start with 6.4, then each consecutive term is 2.9 less than the previous term: 5.2, 9.3 2.9 .na n− = −
10. Start with 1
,7
− then each consecutive term is 1
7
less than the previous term: 5
, .7 7
nn
a− = −
11. Start with 5
,2
then the denominator of each
consecutive term is twice the denominator of the
previous term: 5 5
, .32 2
n na =
12. Start with 3
,1
then the numerator of each consecutive
term is 3 times the numerator of the previous term, and the denominator of each term is 1 more than the
denominator of the previous term: 243 3
, .5
n
nan
=
13. Start with 2
,3
then each consecutive term is 2
3times
the previous term: 32 2
, .243 3
n
na =
14. Start with 2, then each consecutive term is 10 times
the previous term: ( )120,000, 2 10 .nna −=
15. 100 7na n= +
16. ( )5
1
7 1n
n=
− 17. ( )1
3 7n
n∞
=+
18. ( )2
1
4n
n∞
=− 19.
1 4nn
n∞
=
20. 1
2
4n n
∞
= + 21. ( ) ( )5
1
1 2 1n
n
n=
− −
22. 189 23. 450 24. 103
25. 107
210 26. 45 27. 300
28. ( )7
1
294; 34 2i
i=
+
8.1 Enrichment and Extension
1. a. 2 b. 2 1n − c. 2n
2. a. 3 b. 3n c. ( )31
2n n +
3. a. k b. nk c. ( )12
kn n +
4. The series is equivalent to 2 3log 10 log 10 log 10 log 10n+ + + which by
the Power Property of Logarithms, is equivalent to log 10 2 log 10 3 log 10 log 10.n+ + + +
By Exercise 3, the sum is ( )log 101 .
2n n + Because
log 10 1,= this reduces to ( )1 .2
nn +
5. ( ) ( )ln 1 or 1
2 2
e nn n n+ +
6. ( )log1
2b a
n n +
8.1 Puzzle Time
RASH DECISIONS
8.2 Start Thinking
1. 2, 4, 6, 8, 10; 2na n=
2. 9.5, 9, 8.5, 8, 7.5; 1
102
na n= −
3. 2.5, 4, 5.5, 7, 8.5; 3
12
na n= +
Sample answer: All the graphs appear to be linear and the rules are linear equations.
8.2 Warm Up
1. ( )2, 5− − 2. ( )3, 2 3. ( )4, 8−
4. ( )2, 2− 5. 3 5
,2 2 −
6. 1
0,6
00
100
140
120
2 4 6 n
an
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A96
8.2 Cumulative Review Warm Up
1. ( ) 3 23 2 6f x x x x= + − −
2. ( ) 3 23 3 1f x x x x= + − −
3. ( ) 4 3 22 12 6f x x x x x= − − +
4. ( ) 4 3 22 3 32 48f x x x x x= + − −
5. ( ) 4 3 24 6 20 7f x x x x x= + − − −
6. ( ) 4 3 210 69 80 75f x x x x x= − + +
8.2 Practice A
1. yes; 3d = −
2. no; no common difference
3. yes; 1
3d =
4. no; no common difference
5. a. 4 9na n= − b. 12 3na n= −
6. 207 8; 148na n a= + =
7. 2071 9 ; 109na n a= − = −
8. 2015 40; 260na n a= − =
9. 203 9 51
;2 2 2
na n a= − =
10. The number 27 was used as the first term in the formula instead of 27.−
Use 1 27a = − and 15.d =
( )27 1 15na n= − + −
42 15na n= − +
11. 4 1na n= −
12. 28 4na n= −
13. 4 13na n= + 14. 6 18na n= +
15. 72 10na n= − 16. 15 7na n= −
17. 124
1241
15,500; 2 ; 248; 2 15,500nn
a n a n=
= = =
8.2 Practice B
1. no; no common difference
2. yes; 4d = − 3. yes; 1
6d = 4. yes;
3
10d =
5. a. 19 7na n= − b. 10 18na n= −
6. 2045 8 ; 115na n a= − = −
7. 204 16 64
;3 3 3
na n a= − =
8. 202.1 1.9; 40.1na n a= − =
9. 202.9 0.7 ; 11.1na n a= − = −
10. The formula ( )1 1na n n d= − − was used instead
of the formula ( )1 1 .na n n d= + −
Use 1 27a = − and 15.d =
( )27 1 15na n= − + −
42 15na n= − +
11. 4 15na n= +
00
10
30
20
2 4 6 n
an
00
10
30
20
2 4 6 n
an
00
12
36
24
2 4 6 n
an
Answers
Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A97
12. 1 11
2 2na n= +
13. 5 24na n= + 14. 80 17na n= −
15. 6 27na n= − 16. 218
3na n= +
17. 25062,500; 2 1; 499;na n a= − =
( )250
1
2 1 62,500n
n=
− =
8.2 Enrichment and Extension
1. 54 2. 23 3. 85
4. 38 5. 42 6. 91
7. 75 8. 8181 9. 7876
10. ( ) ( )3nt a b n a b= − + +
11. 3, 2x y= =
8.2 Puzzle Time
POULTRYGEIST
8.3 Start Thinking
1. 2, 4, 8, 16; 2nna =
2. 1 1 1 1 1
, , , ;2 4 8 16 2
n
na =
3. ( ) ( ) ( )2, 4, 8, 16; 1 2 2n n n
na− − = − = −
Sample answer: The first two graphs appear to be exponential growth and decay. The third graph oscillates between negative and positive values. All the equations involve exponential expressions.
8.3 Warm Up
1. 30 2. 27− 3. 1270
4. 6− 5. 15 6. 11
16−
8.3 Cumulative Review Warm Up
1.
2.
3.
4.
5.
6.
00
4
12
8
2 4 6 n
an
x
y
2
4
6
−2 2
x
y
2
4
6
−2 2
−2
2
2 4 6 x
y
4
2
2 4 6 x
y
2
2 4 x
y
x
y
2
6
−2 2
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A98
8.3 Practice A
1. yes; 1
2r = 2. no; no common ratio
3. no; no common ratio 4. yes; 6r =
5. a. ( ) 15 3
nna
−= − b. 1
154
6
n
na−
=
6. ( ) 173 2 ; 192
nna a
−= =
7. ( ) 177 3 ; 5103
nna a
−= =
8. 1
71
192 ; 32
n
na a−
= =
9. 1
72 256
36 ;3 81
n
na a−
= =
10. 13nna −=
11. ( ) 13 4
nna
−=
12. 1
140
2
n
na−
=
13. ( ) 113 2
nna
−= −
14. r, not 1,a should be raised to the ( )1n − power.
11
nna a r −=
21147 7a=
13 a=
( ) 13 7
nna
−=
15. $304.22
8.3 Practice B
1. no; no common ratio
2. yes; 1
3r = 3. yes; 5r = 4. yes; 2r =
5. a. ( ) 112 7
nna
−= − b. 1
162
2
n
na−
=
6. ( ) 179 2 ; 576
nna a
−= =
7. 1
71 5
80 ;4 256
n
na a−
= =
8. 1
72 192
3 ;5 15,625
n
na a−
= =
9. ( ) 171.2 2 ; 76.8
nna a
−= − =
10. ( ) 12 5
nna
−=
00
100
300
200
2 4 6 n
an
00
1000
3000
2000
2 4 6 n
an
00
12
36
24
2 4 6 n
an
00
2000
6000
4000
2 4 6 n
an
00
−600
−200
−400
2 4 6 n
an
Answers
Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A99
11. 1
154
3
n
na−
=
12. ( ) 114 3
nna
−= −
13. 1
1256
4
n
na−
= −
14. The number 147 is the third term of the sequence, not the first term.
11
nna a r −=
21147 7a=
13 a=
( ) 13 7
nna
−=
15. $368.33
8.3 Enrichment and Extension
1. 160, 80, 40 2. 7, 10, 13
3. 2, 4, 6, 9 or 1 3
2, , , 94 2
−
4. When 20, 2;d a= = When 21, 3.d a= =
5. 2
2
ac bx
b c a
−=− −
6. Sample answer: Arithmetic mean is 2 2
.2
a b+
Geometric mean is ab or .ab−
Show: 2 2
2
a bab
+ ≥ and 2 2
2
a bab
+ ≥ −
Because all squares are nonnegative,
( )20;a b− ≥ So 2 22a ab b− + ≥ 0 and
2 2
.2
a bab
+ ≥ − Because all squares are
nonnegative, ( )20;a b+ ≥ So
2 22 0a ab b+ + ≥ and 2 2
.2
a bab
+ ≥ −
8.3 Puzzle Time
SEE A MOOOVIE
8.4 Start Thinking
0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001, 0.0000001, 0.00000001, 0.000000001, 0.0000000001;
0.1111111111; 1
0.19
=
8.4 Warm Up
1. 31 2. 25
3. 25,22011.53
2187≈ 4. 531,440−
5. 9050− 6. 3,587,226.5
8.4 Cumulative Review Warm Up
1.
domain: all real numbers except 1, range: all real numbers except 3
0
20
60
40
20 4 6 n
an
020 4 6 n
an−3000
−2000
−1000
120
240
02 6 n
an
x
y
4
−2 2
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A100
2.
domain: all real numbers except 3,− range: all real
numbers except 0
3.
domain: all real numbers except 2, range: all real numbers except 4
4.
domain: all real numbers except 5,− range: all real
numbers except 1
5.
domain: all real numbers except 1
,2
range: all real
numbers except 3
2
6.
domain: all real numbers except 3, range: all real numbers except 2−
8.4 Practice A
1. 1 2 3 4 51 1 7 5 31
, , , ,3 2 12 8 48
S S S S S= = = = =
As n increases, 2
.3
S ≈
2. 1 2 3 425 95 325
5, , , ,3 9 27
S S S S= = = =
51055
81S =
As n increases, 15.S ≈
3. 28
3S = 4. does not exist
5. 15
2S = 6. 18S = −
7. a can be any value, but the absolute value of r must be less than 1.
For this series, 15
2a = and
1.
3r =
1
5 55 3 152 2
1 21 2 2 413 3
aS
r= = = = • =
− −
8. 40 ft 9. 2
11 10. 5
9 11. 5
3
12. about $8,333,333
8.4 Practice B
1. 1 2 3 4 53 13 10 121
, 1, , ,4 12 9 108
S S S S S= = = = =
As n increases, 9
.8
S ≈
x
y
2
4
6
−2 2 4
2
−2
x
y
−2 2
x
y
−4
4
−12 −8 −4
x
y
2
−2
−2−4
2
−3
x
y
1−1 4
Answers
Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A101
2. 1 2 3 4 538 130 422
6, 10, , ,3 9 27
S S S S S= = = = =
As n increases, 18.S ≈
3. 20
3S = 4. does not exist
5. does not exist 6. 3
5S =
7. 1 r− is equal to 2
,3
not 1
.3
For this series, 15
2a = and
1.
3r =
1
5 55 3 152 2
1 21 2 2 413 3
aS
r= = = = • =
− −
8. yes; 11 2
2, , 4122
a r S= = = =
9. 5
11 10. 5
99 11. 13
9 12. $6000
8.4 Enrichment and Extension
1. 2
11 1;
1x
x− < <
− 2. 1 1 1
;3 3 1 3
xx
− < <−
3. 12 4;
4x
x< <
− 4. 1
0 2;xx
< <
5. 2x < − or 2;2
xx
x>
+
6. 2
2
22 2;
6 3
xx
x− < <
+
7. 2sin 1x < is true when , so2
x nπ π≠ +
2 22
2 2
sin sintan .
1 sin cos
x xS x
x x= = =
−
8. 2tan 1x− < simplifies to 2tan 1,x < which
is true when . So4 4
xπ π− < <
( )2 2 2 2
2 22
2
tan tan sin cos
sec cos1 tan
sin .
x x x xS
x xx
x
= = =− −
=
This is also true when 3 5
.4 4
xπ π< <
9. When the values are substituted into the sum formula, r will be greater than 1.
8.4 Puzzle Time
BLOODHOUND
8.5 Start Thinking
1. To determine each term in the sequence, you add the two terms that come before it. For example,
3a = 1 2 ,a a+ or 3 1 2.= + Then to find 7 ,a
you find the sum of 5a and 6 ,a or 8 13 21.+ =
2. To determine each term in the sequence, you multiply the two terms that come before it. For example, 3 1 2 ,a a a= ⋅ or 2 1 2.= ⋅ Then to
find 7 ,a you find the product of 5a and 6 ,a or
8 32 256.• =
3. To determine each term in the sequence, you find the difference of the two terms that come before it. For example, 3 1 2 ,a a a= − or 5 10 5.= − Then
to find 7 ,a you find the difference 5a and 6 ,a or
( )5 5 10.− − =
4. To determine each term in the sequence, you multiply the two terms that come before it. For example, 3 1 2a a a= • or ( )( )2 2 1 .= − − Then
to find 7 ,a you find the product of 5a and 6 ,a or
( )( )4 8 32.− = −
8.5 Warm Up
1. 7 5 3
, 3, , 2, , 12 2 2
2. 7 10 13 16 194, , , , ,
2 3 4 5 6
3. 2, 6, 12, 20, 30, 42 4. 9 27 81 2432, 3, , , ,
2 4 8 16
5. 9, 2, 17, 54, 115, 206− −
6. 1, 4, 7, 10, 13, 16
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A102
8.5 Cumulative Review Warm Up
1. 1 7
3x
±= 2. 4 14x = ±
3. 2, 1x = 4. 2x = ±
5. 5 19x = ± 6. 8, 2
3x = −
8.5 Practice A
1. 1, 6, 11, 16, 21, 26
2. 1, 3, 7, 11, 15, 19− − − − −
3. 3, 12, 48, 192, 768, 3072
4. 4 4 4 412, 4, , , ,
3 9 27 81
5. 1; 3; 11; 123; 15,131; 228,947,163
6. 2, 2, 2, 2, 2, 2
7. 1 132, 8n na a a −= = −
8. 1 147, 12n na a a −= − = +
9. 1 12, 3n na a a −= =
10. 1 15, 2n na a a −= = −
11. 1 11
21,3
n na a a −= =
12. 1 11, 6n na a a −= = +
13. 1 2 2 12, 3, n n na a a a a− −= = = +
14. ( )( )1 2 2 12, 3, n n na a a a a− −= = =
15. 1 17, 2n na a a −= = +
16. 1 17, 3n na a a −= − = −
17. 1 12, 13n na a a −= = −
18. 1 18, 10n na a a −= =
19. 1 12, 7n na a a −= − =
20. 1 11, 0.8n na a a −= = −
21. 1 195, 20n na a a −= = +
22. 8 3na n= − 23. 9 5na n= +
24. ( ) 13 2
nna
−= − 25. 1
120
2
n
na−
=
8.5 Practice B
1. 1, 10, 19, 28, 37, 46 2. ,1 1 1
32, 8, 2, ,2 8 32
3. 24, 36, 54, 81, 121.5, 182.25
4. 1, 0, 1, 0, 1, 0− − 5. 1, 4, 3, 7, 10, 17− −
6. 1 1
256, 2,128, , 8192,64 524,288
7. 1 130, 9n na a a −= = −
8. 1 13, 5n na a a −= = − 9. 1 11
28,7
n na a a −= =
10. 1 11, 11n na a a −= = +
11. ( )( )1 2 2 12, 6, n n na a a a a− −= = =
12. 1 2 2 11, 7, n n na a a a a− −= = = +
13. 1 2 2 161, 39, n n na a a a a− −= = = −
14. 1 15, n na a a n−= − = +
15. 1 14, 3n na a a −= − = +
16. 1 16, 15n na a a −= =
17. 1 116, 9n na a a −= − =
18. 1 12.1, 0.3n na a a −= − = +
19. 1 11 1
,3 5
n na a a −= − =
20. 1 11
, 72
n na a a −= =
21. 1 126, 1.002n na a a −= =
22. 26.2 7.2na n= − + 23. ( ) 17 0.45
nna
−= −
24. 23 1
6 6na n= + 25.
11
93
n
na−
= −
8.5 Enrichment and Extension
1. a. 3, 5, 2, 3, 5, 2, 3, 5, − − − b. 3−
2. a. 1 1 14, 8, 2, , , , 4, 8,
4 8 2 b.
1
4
Answers
Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers
A103
3. a. 5
b. 2n − additional diagonals; 4 2,d =
1 2n nd d n−= + −
4. 1 2 1;n nS S n+ = + +
8.5 Puzzle Time
KING CONGA
Cumulative Review
1. 2.
3. 4.
5. 6.
7. 8.
9.
10. 7x = 11. 3x = 12. 11x = −
13. 60x = 14. 48x = 15. 39x =
16. 9x = − 17. 4x = − 18. 2x =
19. 6x = 20. 4x = 21. 3x =
22. 51 3T h= + 23. 44 2T h= −
24. 22,302 25. 4091− 26. 46,348
27. 29,222− 28. 62,598− 29. 706−
30. 22 4 24x x− + + 31. 3 23 7 3 5x x x+ + +
32. 5 4 3 211 10 4 6 4x x x x x− + + + + −
33. 5 4 3 27 7 2 7 14 6x x x x x+ + + − −
34. 3 22 5 15 9x x x− + −
35. 4 3 26 15 8 11 10x x x x+ − + −
36. 4 3 26 13 6 3 8x x x x− − + + −
37. 5 4 3 25 22 20 3 27 9x x x x x− + − − + +
38. 4 3 221 35 21x x x− +
39. 6 5 4 3 256 120 88 24 56 72x x x x x x− + + − −
40. 3 230 31 51 14x x x− + + +
41. 4 3 244 147 64 7x x x x+ − −
42. 4 3 256 22 93 34 3x x x x− + − +
43. 4 3 22 6 31 97 12x x x x− − + −
44. 3 23 18 40x x x+ − −
45. 3 22 13 10x x x+ − +
46. 3 24 16 64x x x+ − −
47. 3 211 38 40x x x− + −
x y
2 −8
3 −23
4 −44
5 −71
x y
4 −18
8 −62
12 −106
16 −150
x y
2 2
4 38
6 74
8 110
x y
2 12
3 37
4 72
5 117
x y
6 49
12 85
18 121
24 157
x y
2 −3
3 17
4 45
5 81
x y
0 −2
1 −1
2 1
3 5
x y
0 4
1 3
2 1
3 −3
x y
0 −11
1 −9
2 −3
3 15
...
...
...
...
... ...
n
n +n
+n+1
Answers
Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A104
48. 3 220 27 6x x x+ + −
49. 3 224 58 7 5x x x+ − −
50. 2 12 36x x+ + 51. 2 49x −
52. 2 16 64x x− + 53. 24 44 121x x+ +
54. 236 132 121x x− + 55. 281 180 100x x+ +
56. 512 11
4x
x− +
+ 57. 196
5 297
xx
− ++
58. 329 17
2x
x+ +
−
59. 2 15814 33 225
7x x
x+ + +
−
60. 3 2 13765 23 87 346
4x x x
x− + − +
+
61. 3 2 24753 20 100 496
5x x x
x− + − +
+
62. a. ( )2 4 ftx + b. 240 ft
63. a. ( )4 5 ftx + b. 2153 ft c. 9 ft d. 17 ft
64. ( )( )8 3x x x+ − 65. ( )( )9 1c c c+ −
66. ( )( )5 8m m m− − 67. ( )( )1 3a a a− +
68. ( )( )28 8 64d d d+ − +
69. ( )( )23 3 9g g g− + +
70. ( )( )25 5 25y y y− + +
71. ( )( )27 7 49n n n+ − +
72. ( )( )22 5 4 10 25b b b+ − +
73. ( )( )23 7 9 21 49w w w− + +
74. ( )( )2 3 7f f+ − 75. ( )( )2 2 3 5r r− +
76. ( )( )( )1 1 5 8h h h+ − −
77. ( )( )2 4 3 7s s+ − 78. ( )( )3 7 4 1v v+ −
79. ( )( )3 9 7 2p p− +
80. 6, 0,z z= − = and 2z =
81. 3, 0,x x= − = and 11x =
82. 4, 0,m m= − = and 11m =
83. 10, 3,h h= − = − and 0h =
84. 9, 5,v v= − = − and 0v =
85. 0, 4,f f= = and 8f =
86. 4, 0,x x= − = and 7x =
87. 8, 0,x x= − = and 3x =
88. 0, 10,x x= = and 12x =
89. 0, 2,x x= = and 5x =
90. 0, 2,x x= = and 10x =
91. 3, 0,x x= − = and 11x =
92. a. ( )3 5 in.x + b. 264 in.
93. a. ( )6 11x + in. b. 2400 in. c. 20 in.
Chapter 9 9.1 Start Thinking
Sample answer:
1 1 2 25 1 7
2 in., 1 in., 3 in., 2 in.8 2 16
x y x y≈ ≈ ≈ ≈
1. 1 10.5
3 2
y = = 2. 1 70.88
3 8
x = ≈
3. 1
1
40.57
7
y
x= ≈ 4. 2 1
0.54 2
y = =
5. 2 550.86
4 64
x = ≈ 6. 2
2
320.58
55
y
x= ≈
It appears that regardless of the size of the 30°-60°-90° triangle, the ratios of corresponding sides are equal or approximately equal.
9.1 Warm Up
1. 3 5 2. 39 3. 4 6
