-FTTPO1SBDUJDF-FWFM#
*À>VÌViÊ
,%33/.
&ORUSEWITHPAGESn
]
-ÛiÊÌ
iÊiµÕ>̰
x°Iq z
]
ΰ X Iq z
Ê £° X I
Ó° X I
Ê {° X X I
x° X zzX ]
]
Ȱ X zX z]
zzI
Ê Ç° X Iq z n° X Iq z ° X ]
Iqz
7ÀÌiÊÌ
iÊiÝ«ÀiÃÃÊ>ÃÊ>ÊV«iÝÊÕLiÀÊÊÃÌ>`>À`ÊvÀ°
Ê£ä° II I
££° II I
Ê£Ó° II I
£Î° II I
Ê£{° II I
£x° II I
ʣȰ II I
£Ç° II I
Ê£n° II I
£° III I
ÊÓä° I I
Ó£° II ÊÓÓ° ]z
]
zzz]
zzI
zzI zzI
Óΰ ]z
]
zz]
zI
zzI ]
]
Óx° ]z
I ]
zz]
zI
zzI
zzI
zzqz qzz
ÊÓ{° ]z
]
z
zz]
zI
]
qzzzI
`ÊÌ
iÊ>LÃÕÌiÊÛ>ÕiÊvÊÌ
iÊV«iÝÊÕLiÀ°
]
--" Ê{°È
]
]
]
Ón° q zIq z q z
Óǰ Iq z ÊÓȰ I *ÌÊÌ
iÊÕLiÀÃÊÊ>ÊV«iÝÊ«>i°
ÊÓ° I
Îä° I
룡 I
1Ã}ÊÌ
iÊ«À«iÀÌiÃÊvÊiÝ«iÌÃ]ÊÜÀÌiÊÌ
iÊV«iÝÊÕLiÀÊÊ
ÃÌ>`>À`ÊvÀ°
ÊÎÓ° I Îΰ I I
Î{° I Îx° I I
ÊÎȰ I Îǰ I În° I ΰ I Ê{ä° 0ATTERN2ECOGNITION 5SINGTHEINFORMATIONFROM%XERCISES nWRITEAGENERAL
STATEMENTABOUTTHEVALUEOFI NWHERENISAPOSITIVEFACTOROF5SETHISSTATEMENTTO
WRITEI
INSTANDARDFORM )FTHEEXPONENTOFIISAFACTOROFTHEEXPRESSIONCANBEREDUCED
Ê
TO4OSIMPLIFYIRAISEDTOANYNATURALNUMBERFACTOROUTTHEMULTIPLESOFINTHEEXPONENTAND
SIMPLIFYTHEREMAININGEXPRESSIONI
IIII
!LGEBRA
,%33/.
#HAPTER2ESOURCE"OOK
*À>VÌViÊ
,%33/.
&ORUSEWITHPAGESn
Ê £° X X Ó° X X ΰ X X ]
Ê {° X X x° X zX z]
zz]
z Ȱ X X qz
]
]
qz
Ê Ç° X ]z
Xz]
z z]
zz]
z
n° X ]z
X]z
z]
zzq z ° X X z]
zz]
z
££° X XC X
Ê£Ó° X XC X
£Î° X XC ]
z|X]
z Ê£{° X XC ]
z|X]
z £x° X XC X
Ê£n° X X q z
£° X X I
]
ÊÓä° X X q z
]
ÊÓÓ° X X q z
]
q z
ÊÓ{° X X ]
z]
zI
]
Ó£° X X q z
Óΰ X X z]
zz
Ê££° X X TWOIMAGINARY
£Ó° X XX TWOREAL
Óx° X X ʣǰ X XX ]
zÊ
£° X X Óä° X X ÊÓ£° X X zÊ
Óΰ X X ]
ÊÓȰ YX X 3EEBELOW
 YX X YX
ÊÓn° YX X 3EEBELOW
Ó° YX XY|X]
z ]
z|]
z]
z Óx° X X z]
zz]
z
ÓÓ° X X Ó{° X X z]
zzz]
zz
ÓȰ X X z]
zz]
z
ÊÓǰ .EW#ARPET 9OUHAVENEWCARPETINGINSTALLEDIN
ARECTANGULARROOM9OUARECHARGEDFORSQUARE
YARDSOFCARPETANDFEETYARDSOFTACKSTRIP
4ACKSTRIPISUSEDALONGTHEPERIMETERTOSECURETHE
CARPETINPLACE$OYOUTHINKTHESElGURESARE
CORRECT%XPLAINYOURANSWER
.O4HEAREAOFTHEROOMISXXANDCANBEEXPRESSED
ASXXWHICHHASNOREALSOLUTIONS
`ÊÌ
iÊÛ>ÕiÊvÊݰ
ÊÎä° !REAOFRECTANGLE ]
q z
£{° X X ]
z]
z
]
q z
£È° X X ]
z]
zI
]
qz
£n° X X ]
z]
z
-ÛiÊÌ
iÊiµÕ>ÌÊÕÃ}ÊÌ
iʵÕ>`À>ÌVÊvÀÕ>°Ê/
iÊÃÛiÊÌ
iÊiµÕ>ÌÊ
LÞÊv>VÌÀ}ÊÌÊV
iVÊÞÕÀÊÃÕÌî°
7ÀÌiÊÌ
iʵÕ>`À>ÌVÊvÕVÌÊÊÛiÀÌiÝÊvÀ°Ê/
iÊ`iÌvÞÊÌ
iÊÛiÀÌiݰ
Σ° !REAOFTRIANGLE ÊÝiÀVÃiÃÊÓn q Σ]ÊÕÃiÊÌ
iÊvÜ}ÊvÀ>̰
BEMODELEDBYYX XWHEREXISTHESHOTPUTSHORIZONTALDISTANCE
INFEETANDYISTHECORRESPONDINGHEIGHTINFEET(OWLONGWASTHETHROW
2OUNDTHEANSWERTOTHENEARESTTENTH --" Ê{°Ç
ÊÎÓ° 3HOT0UT )NATRACKANDlELDEVENTACONTESTANTHADATHROWINTHESHOTPUTTHATCAN
ÓȰYX
,AUNCHED/BJECT !NOBJECTISLAUNCHEDUPWARDWITHANINITIALVELOCITYOFFEETPER
SECONDFROMAPLATFORMFEETHIGH
ÊÓn° 7RITEAHEIGHTMODELFORTHEOBJECT HT T
ÊÓ° (OWMANYSECONDSUNTILTHEMAXIMUMHEIGHTISREACHED SEC
ÊÎä° 7HATWILLBETHEMAXIMUMHEIGHT FT
ÊΣ° (OWMANYSECONDSUNTILTHEOBJECTHITSTHEGROUND SEC
Ón°YX !LGEBRA
#HAPTER2ESOURCE"OOK
&
£ä° X X TWOREAL
Ê£x° X XX £Ç° X X q z
]
n° X X TWOIMAGINARY
Ê ° X X ONEREAL
]
]
]
Ȱ X X ʣΰ X X q z
ʣȰ X X q zÊ
ΰ X X x° X X 1ÃiÊÌ
iʵÕ>`À>ÌVÊvÀÕ>ÊÌÊÃÛiÊÌ
iÊiµÕ>̰
-ÛiÊÌ
iÊiµÕ>ÌÊLÞÊV«iÌ}ÊÌ
iÊõÕ>Ài°
Ó° X X Ê {° X X Ê Ç° X X TWOREAL
Ê£ä° X XC X Ê £° X X `ÊÌ
iÊ`ÃVÀ>ÌÊ>`ÊÕÃiÊÌÊÌÊ`iÌiÀiÊvÊÌ
iÊÃÕÌÊ
>ÃÊiÊÀi>]Ê
ÌÜÊÀi>]ÊÀÊÌÜÊ>}>ÀÞÊÕLiÀî°
`ÊÌ
iÊÛ>ÕiÊvÊVÊÌ
>ÌÊ>iÃÊÌ
iÊiÝ«ÀiÃÃÊ>Ê«iÀviVÌÊõÕ>ÀiÊÌÀ>°Ê
/
iÊÜÀÌiÊÌ
iÊiÝ«ÀiÃÃÊ>ÃÊ>ÊõÕ>ÀiÊvÊ>ÊL>°
&ORUSEWITHPAGESn
`ÊÌ
iÊ`ÃVÀ>ÌÊvÊÌ
iʵÕ>`À>ÌVÊiµÕ>̰
--" Ê{°n
-ÛiÊÌ
iÊiµÕ>ÌÊLÞÊwÊ`}ÊõÕ>ÀiÊÀÌð
*À>VÌViÊ
!LGEBRA
#HAPTER2ESOURCE"OOK
*À>VÌViÊ
,%33/.
&ORUSEWITHPAGESn
iÌiÀiÊÜ
iÌ
iÀÊÌ
iÊÀ`iÀi`Ê«>ÀÊÃÊ>ÊÃÕÌÊvÊÌ
iÊiµÕ>ÌÞ°
Ê £° YX X NOTASOLUTION
Ó° YX X SOLUTION
Ê Î° YaX X SOLUTION
{° YqX X NOTASOLUTION
>ÌV
ÊÌ
iÊiµÕ>ÌÞÊÜÌ
ÊÌÃÊ}À>«
°
Ê x° YqX X "
°
Ȱ YX X !
ǰ Ya]zX X #
°
°
--" Ê{°
À>«
ÊÌ
iÊiµÕ>ÌÞ°
Ê n° YqX ° YX X
£ä° YaX X
Ê££° YX X
£Ó° YX X
Ê£{° YqX X
£Î° YqX X
£x° YX X
£È° YaX X
!LGEBRA
#HAPTER2ESOURCE"OOK
,%33/.
*À>VÌViÊÊ CONTINUED
,%33/.
&ORUSEWITHPAGESn
>ÌV
ÊÌ
iÊÃÞÃÌiÊvÊiµÕ>ÌiÃÊÜÌ
ÊÌÃÊ}À>«
°
ʣǰ YX X !
£n° YaX X #
°
Y]z
X °
YqX X
°
{°YXx°Y]
zXȰYX
ǰYXXn°YXX°YXX
&ORUSEWITHPAGESn
7ÀÌiÊ>ʵÕ>`À>ÌVÊvÕVÌÊÊÛiÀÌiÝÊvÀÊÜ
ÃiÊ}À>«
Ê
>ÃÊÌ
iÊ}ÛiÊ
ÛiÀÌiÝÊ>`Ê«>ÃÃiÃÊÌ
ÀÕ}
ÊÌ
iÊ}Ûiʫ̰
£° YaX X "
Ó° VERTEX
ΰ VERTEX
POINT YX POINT YX
POINT
{° VERTEX 3EEABOVE x° VERTEX 3EEABOVE
*À>VÌViÊ
£° VERTEX YX YX X
POINT
POINT
POINT
7ÀÌiÊ>ʵÕ>`À>ÌVÊvÕVÌÊÊÌiÀVi«ÌÊvÀÊÜ
ÃiÊ}À>«
Ê
>ÃÊÌ
iÊ}ÛiÊ
ÝÌiÀVi«ÌÃÊ>`Ê«>ÃÃiÃÊÌ
ÀÕ}
ÊÌ
iÊ}Ûiʫ̰
--" Ê{°
ǰ XINTERCEPTS 3EEABOVE n° XINTERCEPTS
YX X
Ó£° Yaz]z
zX X
XORX
--" Ê{°£ä
-ÛiÊÌ
iÊiµÕ>ÌÞÊ>}iLÀ>V>Þ°
Ó{° X Xa
aXa
ÊÝiÀVÃiÃÊÓÈqÓn]ÊÕÃiÊÌ
iÊvÜ}ÊvÀ>̰
££° XINTERCEPTS
POINT
YXX
POINT
£Ó° XINTERCEPTS
POINT
YXX
POINT
YXX
£Î° YX £{° YX X
£x° YX X
£È° YX X
£Ç° YX X £n° YX X
° XINTERCEPTS 3EEABOVE
POINT3EEABOVE
7ÀÌiÊ>ʵÕ>`À>ÌVÊvÕVÌÊÊÃÌ>`>À`ÊvÀÊÜ
ÃiÊ}À>«
Ê«>ÃÃiÃÊÌ
ÀÕ}
Ê
Ì
iÊ}ÛiÊ«Ìð
YX X
ÊÓΰ X X
ÓÓ° YX X
Yaz]z
zX X
POINT
£ä° XINTERCEPTS
À>«
ÊÌ
iÊÃÞÃÌiÊvÊiµÕ>Ìið
ÊÓä° YqX X
Ȱ VERTEX 3EEABOVE
Óx° X X
X]
z
ÊÝiÀVÃiÃÊ£Ê>`ÊÓä]ÊÕÃiÊÌ
iÊvÜ}ÊvÀ>̰
0OPULATION-ODEL 4HEFOLLOWINGTABLESHOWSTHEPOPULATIONOFATOWNFROMTO
!SSUMETHATTISTHENUMBEROFYEARSSINCEAND0ISMEASUREDINTHOUSANDSOFPEOPLE
9i>À]ÊÌ
*«Õ>Ì]Ê*
Ê£° 5SEAGRAPHINGCALCULATORTOlNDTHEBESTlTTINGQUADRATICMODELFORTHEDATA
0T T
ÊÓä° 5SINGTHEMODELWHATISTHEPOPULATIONIN &OOTBALL 4HEPATHOFAFOOTBALLKICKEDFROMTHEGROUNDCANBEMODELEDBY
HX XWHEREHISTHEHEIGHTINYARDSANDXISTHEHORIZONTAL
DISTANCEINYARDSFROMWHERETHEBALLISKICKED4HECROSSBARONAlELDGOAL
POSTISFEETABOVETHEGROUND
ÊÝiÀVÃiÃÊÓ£Ê>`ÊÓÓ]ÊÕÃiÊÌ
iÊvÜ}ÊvÀ>̰
/PERATING#OSTS 4HEFOLLOWINGTABLESHOWSTHEOPERATINGCOSTSOFASMALLBUSINESSFROM
TO!SSUMETHATTISTHENUMBEROFYEARSSINCEAND#ISTHECOSTIN
THOUSANDSOFDOLLARS
ÊÓȰ 7RITEANINEQUALITYTOlNDTHEVALUESOFXWHERETHEBALLISHIGHENOUGHTOGOOVER
THECROSSBAR X X]
z
ÊÓǰ 3OLVETHEINEQUALITY X
9i>À]ÊÌ
ÊÓn° !PLAYERATTEMPTSTOKICKAlELDGOALFROMYARDSAWAY7ILLTHEBALLHAVEENOUGH
"«iÀ>Ì}ÊVÃÌÃ]Ê
HEIGHTTOGOOVERTHECROSSBARFROMTHISDISTANCE YES
#T T
ÊÓ£° 5SEAGRAPHINGCALCULATORTOlNDTHEBESTlTTINGQUADRATICMODELFORTHEDATA
ÊÓÓ° 5SINGTHEMODELHOWMUCHARETHEOPERATINGCOSTSIN !LGEBRA
#HAPTER2ESOURCE"OOK
!LGEBRA
#HAPTER2ESOURCE"OOK
'
© Copyright 2026 Paperzz