S_Alg 2 Team Sol
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Capital City Regional 3/8/2008 Algebra 2 Bowl Solutions 1 Algebra Two Team Question # 1 Infinite geometric series: Bounces Down 3 2 1 9 - = ∞ a + Bounces Up 3 2 1 6 - = ∞ a Ball traveled 27 + 18 = ;45 feet . Algebra Two Team Question # 2 x- coordinate of Vertex: 2 7 3 + = 5. Points: (3,0)-> c b a + + = ) 3 ( ) 3 ( 0 2 (7,0)-> c b a + + = ) 7 ( ) 7 ( 0 2 (5,8)-> c b a + + = ) 5 ( ) 5 ( 8 2 Solve the system: 8 5 25 0 7 49 0 3 9 = + + = + + = + + c b a c b a c b a 42 20 2 ) ( 2 - + - = x x x f -2 + 20 + -42 = -24 Algebra Two Team Question # 3 5 2 5 3 3 ≤ - ≤ - x or 5 2 5 3 3 ≤ + - ≤ - x 10 5 3 6 ≤ - ≤ - x or 10 5 3 6 ≤ + - ≤ - x 15 3 1 ≤ ≤ - x or 5 3 11 ≤ - ≤ - x 5 3 1 ≤ ≤ - x or 3 5 3 11 - ≥ ≥ x interval notation: - 5 , 3 5 Algebra Two Team Question # 4 Rate * time = distance Cousin 1 r 2 2r Cousin 2 r + 8 2 2r + 16 2r + (2r + 16) = 224; 4r + 16 = 224; 4r = 208; r=52, r+8=60 A= 52mph B= 60mph C= 3(52)+3(60) = 336 miles apart. 336-2(52+60) = 112
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S_Alg 2 Team Sol
Transcript of S_Alg 2 Team Sol
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Capital City Regional 3/8/2008 Algebra 2 Bowl Solutions
1
Algebra Two Team Question # 1 Infinite geometric series:
Bounces Down
321
9
=
a + Bounces Up
321
6
=
a
Ball traveled 27 + 18 = ;45 feet.
Algebra Two Team Question # 2 x- coordinate of Vertex:
273 +
= 5.
Points: (3,0)-> cba ++= )3()3(0 2 (7,0)-> cba ++= )7()7(0 2 (5,8)-> cba ++= )5()5(8 2
Solve the system:
85250749
039
=++
=++
=++
cbacba
cba
42202)( 2 += xxxf
-2 + 20 + -42 = -24
Algebra Two Team Question # 3 5
2533 x or 5
2533 + x
10536 x or 10536 + x 1531 x or 5311 x
531 x or
35
311
x interval notation:
5,
35
Algebra Two Team Question # 4 Rate * time = distance Cousin 1 r 2 2r Cousin 2 r + 8 2 2r + 16
2r + (2r + 16) = 224; 4r + 16 = 224; 4r = 208; r=52, r+8=60 A= 52mph B= 60mph C= 3(52)+3(60) = 336 miles apart.
336-2(52+60) = 112
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Capital City Regional 3/8/2008 Algebra 2 Bowl Solutions
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Algebra Two Team Question # 5 )6,3,2,1(=
qp
use synthetic division to try possible roots:
-1 | 1 -2 -5 4 6 -1 3 2 -6 1 -3 -2 6 | 0 623 23 + xxx , factor )3)(2()3(2)3( 22 = xxxxx So, ).3)(2)(2)(1( ++ xxxx
Algebra Two Team Question # 6
=
=
5332
5332
9101B
=
=
13212134
2335
2335
C
B X C =
=
=
2335
13212134
5332
BXC ( hint: AIA
andIAA
=
=1
)
Answer:
2335
Algebra Two Team Question # 7 Let iiiiiA 52513)512(13)2( 619 === iiiiB 512)2())1(()1( 99218 ==+=+= iiiC =+= 8)21)(32(
-525i + 512i - (8 - i) = i128
Algebra Two Team Question # 8
algebraically: )37135(4
)4894(5
=+
=
yx
yx +
1485220
2404520
=
=
yx
yx 38897 =
y;
41
;38897
== yy
)37135(9
)4894(13
=+
=
yx
yx +
33311745
62411752
=+
=
yx
yx 29197 =
x;
31
;29197
== xx
41
,
31
Algebra Two Team Question # 9
23
=A , 21
=B , 35
=C ; .217
21551
23)
35(3)
21(2
23
or=++=+
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Capital City Regional 3/8/2008 Algebra 2 Bowl Solutions
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Algebra Two Team Question # 10 123 22 = xy 1
412
22
=
xy
A 1212)0(3 22 =+=y B ;3xy = 32 =m C center (0,0).x-coordinate for foci will be 0. D 1512)1(3 22 =+=y (12)(3)-(0)(15) = 36
Algebra Two Team Question # 11 Geometric progression: 133 )05.1(44000 =a ; 23 )100
105(44000=a
00.48510$)11025(4.43 ==a Algebra Two Team Question # 12
System of equations: 4510.005.0
4=+
=
dndn
multiply the bottom by 100 to simplify and use substitution. 450010)4(5 =+ dd 450030 =d 150 dimes, so 150 X 4 = 600 nickels
(600,150)
Algebra Two Team Question # 13 by elimination, +
725
22
22
=
=+
yx
yx 322 2 =x 162 =x ; 4=x
By substitution: 25)4( 22 =+ y 92 =y ; 3=y (4,3),(-4,3),(4,-3),(-4,-3). A = 4 + 4 = 8 B = -3 + -3 = -6 A-B = 8 - -6 = 14
Algebra Two Team Question # 14
188
1021
12
=++
+=
+=
cba
ba
bac
by substitution you get: 188)12)1021(()10
21( =+++++ bbbb
b = 60; so a = 40 and c = 88
40, 60, 88
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Capital City Regional 3/8/2008 Algebra 2 Bowl Solutions
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Algebra Two Team Question # 15
=
=
===
17140
1714
51350
51560
:
516
851
515
518
653
58
)348(1
70)16(5)10(1)2712(5)26112(1det
1
answer
B
A
