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chapter9.1b
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à 9.1è Evaluating Variable Expressions
äïPlease evaluate the following Variable Expressions at the
given specified values of the variable.
#âèEvaluateï5∙(2x - yì)ïby replacing x with "2" and y with "3".
#ê 5∙(2x - yì)ï=ï5∙(2∙2 - 3ì)ï=ï5∙(2∙2 - 9)ï=ï5∙(4 - 9)
êêê5∙(4 + (-9))ï=ï5∙(-5)ï=ï-25
#Thus, the value of 5∙(2x - yì) when x is "2" and y is "3" is -25.
#éSèIn order to evaluate the Variable Expression, 5∙(2x - yì) ,
when x is "2" and y is "3", it is necessary to substitute "2" in place
of x and "3" in place of y.
#êêêêï5∙(2x - yì)
#êêêë =ï5∙(2∙2 - 3ì)
After the substitution, you should simplify using the correct order of
operations and the rules for operations on signed numbers that were
given in the last chapter.ïFirst, clear the exponent inside the paren-
çs.êêêï5∙(2∙2 - 9)
Then, perform the multiplication inside the parençs.
êêêêï5∙(4 - 9)
This is followed by the subtraction inside the parençs.
êêêêè5∙(4 + (-9)
êêêê=ï5∙(-5)
Finally, the last multiplication is performed.
êêêêè-25
#Thus, the value of the Variable Expression, 5∙(2x - yì), when x is "2"
and y is "3" is -25.
1
#êëEvaluateïxì + 5yìïif x is "-3" and y is "-4".
êïA)ï36ê B)ï54êïC)ï89êïD)ïå
ü
#êêêêë xì + 5yì
#êêêê=ï(-3)ì + 5(-4)ì
êêêê=ë9 + 5∙16
êêêê=ë9 + 80
êêêê=ë 89
ÇïC
2
êëEvaluateï3x - 5yïif x is "4" and y is "3".
êïA)ï-3ê B)ï5êèC)ï6êèD)ïå
ü
êêêêë3x - 5y
êêêê=è3(4) - 5(3)
êêêê=è 12 - 15
êêêê=è12 + (-15)
êêêê=ë -3
ÇïA
3
êèEvaluateïa∙(3b + c) if a is "5", b is "-4", and c is "-5".
êïA)ï-55êB)ï-85ê C)ï46êïD)ïå
ü
êêêêèa∙(3b + c)
êêêë =è5∙(3∙(-4) + (-5))
êêêë =è5∙((-12) +(-5))
êêêë =è5∙(-17)
êêêë =è-85
ÇïB
4
#êèEvaluateïa∙(bì - cì) if a is "2", b is "-4", and c is "5".
êïA)ï-6ê B)ï12êïC)ï-18êïD)ïå
ü
#êêêê a∙(bì - cì)
#êêêè =è2∙((-4)ì - 5ì)
êêêè =è2∙(16 - 25)
êêêè =è2∙(16 + (-25))
êêêè =è2∙(-9)
êêêè =è-18
ÇïC
5êê 3x - y
#êêEvaluateï───────èif x is "4"ïand y is "-6".
êêêè x + y
êïA)ï23ê B)ï-9êïC)ï46êèD)ïå
ü
è3x - yê 3(4) - (-6)ê12-(-6)ê12 + 6ê18
#è───────è=è───────────è=è───────è=è──────è=è──ï=ï-9
è x + yêï4 + (-6)êè -2êë-2êï-2
ÇïB
6
#êêèEvaluateï3xì - 5x + 15ïif x is "-3".
êïA)ï57ê B)ï-37ê C)ï42êèD)ïå
ü
#êêêê 3xì - 5x + 15
#êêêè =è3(-3)ì - 5(-3) + 15
êêêè =è3∙9 - 5(-3) + 15
êêêè =è27 - (-15) + 15
êêêè =è27 + 15 + 15
êêêè =è57
ÇïA
7
êê Find "d" if d = r∙t , r is 40, and t is 2.
êïA)ï60ê B)ï80êïC)ï50êèD)ïå
ü
êêêêèd = r∙t
êêêêèd = (40)(2)
êêêêèd = 80
ÇïB
8
êèFind "I" if I = P∙r∙t , P is $4,000, r is .06, and t is 10.
ê A)ï$2,400ë B)ï$24ê C)ï$240êïD)ïå
ü
êêêêïI = P∙r∙t
êêêêïI = (4,000)(.06)(10)
êêêêïI = $2,400
ÇïA
9êêë1
#êïFind "A" ifèA =ï─∙(B + b)∙h,ïB is 14, b is 12ïand h is 4.
êêêê2
êïA)ï46ê B)ï24êïC)ï52êèD)ïå
ü
êêêëA = 1/2∙(B + b)∙h
êêêëA = 1/2∙(14 + 12)∙4
êêêëA = 1/2∙(26)∙4
êêêëA = 13∙4
êêêëA = 52
ÇïC
# 10êêè 2xì - 3x - 5
#êêïEvaluateè ────────────èif x is "2".
#êêêê xì + 4x + 6
êïA)ï-1/6ë B)ï27êïC)ï33/12êD)ïå
#üêï2xì - 3x - 5ê2(2)ì - 3(2) - 5ê2∙4 - 3∙2 - 5
#êê ────────────è=è────────────────è=è─────────────
#êêïxì + 4x + 6êï2ì + 4∙2 + 6êè 4 + 8 + 6
êê 8 - 6 - 5ê2 - 5ê-3êè1
#êè =è─────────è=è─────è=è──è=è- ──
êêë18êë18ê 18êè6
ÇïA