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Midterm 2: Version E Answer Key

  1. x−y=−3x−y=−3
    xx yy
    0 3
    −3 0
    x+2y=3x+2y=3
    xx yy
    3 0
    0 3232

    Graph with lines intersecting at (-1,2)

  2. aa
    (2x−5y=−2)(−3)(3x−4y=−4)(2)−6x+15y=6+6x−8y=87y=14y=22x−5(2)=−22x−10=−2+10+102x=8x=4(2x−5y=−2)(−3)(3x−4y=−4)(2)−6x+15y=6+6x−8y=87y=14y=22x−5(2)=−22x−10=−2+10+102x=8x=4
    (4,2)(4,2)
  3. aa
    (4x+3y=−29)(−2)(3x+2y=−21)(3)−8x−6y=−58+9x+6y=−63x=−53(−5)+2y=−21−15+2y=−21+15+152y=−6y=−3(4x+3y=−29)(−2)(3x+2y=−21)(3)−8x−6y=−58+9x+6y=−63x=−53(−5)+2y=−21−15+2y=−21+15+152y=−6y=−3
    (−5,−3)(−5,−3)
  4. aa
    (x+y−3z=0)(−2)−2x−2y+6z=0+2x−3y=16−5y+6z=16(2y−2z=−12)(3)6y−6z=−36+−5y+6z=−16y=−202x−3y=162x−3(−20)=162x+60=16−60−602x=−44x=−222y−2z=−122(−20)−2z=−12−40−2z=−12+40+40−2z=28z=−14(x+y−3z=0)(−2)−2x−2y+6z=0+2x−3y=16−5y+6z=16(2y−2z=−12)(3)6y−6z=−36+−5y+6z=−16y=−202x−3y=162x−3(−20)=162x+60=16−60−602x=−44x=−222y−2z=−122(−20)−2z=−12−40−2z=−12+40+40−2z=28z=−14
    (−22,−20,−14)(−22,−20,−14)
  5. 5−4[2x−2(6x−5)01−(7−2x)]5−4[2x−2(6x−5)01−(7−2x)]
    5−4[2x−2(1)−7+2x]5−4[2x−2(1)−7+2x]
    5−4[4x−9]5−4[4x−9]
    5−16x+365−16x+36
    −16x+41−16x+41
  6. 3ab4(a2−25)3ab4(a2−25)
    3a3b4−75ab43a3b4−75ab4
  7. x2+3x−6×x2+3x−6x4+3x3−6x23x3+9x2−18x+−6x2−18x+36x4+6x3−3x2−36x+36x2+3x−6×x2+3x−6x4+3x3−6x23x3+9x2−18x+−6x2−18x+36x4+6x3−3x2−36x+36
  8. aa
  9. x2−3z+7x−21x2−3z+7x−21
    x(x−3)+7(x−3)x(x−3)+7(x−3)
    (x−3)(x+7)(x−3)(x+7)
  10. 4x2(x+1)−9(x+1)4x2(x+1)−9(x+1)
    (x+1)(4x2−9)(x+1)(4x2−9)
    (x+1)(2x−3)(2x+3)(x+1)(2x−3)(2x+3)
  11. (2x)3−(3y)3(2x)3−(3y)3
    (2x−3y)(4x2+6xy+9y2)(2x−3y)(4x2+6xy+9y2)
  12. x4−625x2+x2−625x4−625x2+x2−625
    x2(x2−625)+1(x2−625)x2(x2−625)+1(x2−625)
    (x2+1)(x2−625)(x2+1)(x2−625)
    (x2+1)(x−25)(x+25)(x2+1)(x−25)(x+25)
  13. B+G=20⇒B=20−GB+G=20⇒B=20−G
    G−4=2(B−4)G−4=2B−8G−4=2(20−G)−8G−4=40−2G−8G−4=32−2G+2G+44+2G3G=36G=12B=20−GB=20−12=8G−4=2(B−4)G−4=2B−8G−4=2(20−G)−8G−4=40−2G−8G−4=32−2G+2G+44+2G3G=36G=12B=20−GB=20−12=8
  14. x=16% solution
    16x+6(20)=12(x+20)16x+120=12x+240−12x−120−12x−1204x=120x=1204=30 ml
  15. a
    (C+R=60)(−3.40)−3.40C−3.40R=−204+3.40C+3.90R=−2130.50R=−9R=90.50 or 18 kgC+R=−60C+18=−60−18−18C=−42 kg

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