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Midterm 1: Version D Answer Key

  1. 3(4)−√42−4(4)(1)3(4)−√42−4(4)(1)
    12−√16−161212−√16−1612
  2. aa
    2x−8+8=−6+3x+92x=3x+3−3x−3x−x=3x=−32x−8+8=−6+3x+92x=3x+3−3x−3x−x=3x=−3
  3. (1R=1r1+1r2)(Rr1r2)(1R=1r1+1r2)(Rr1r2)
    r1r2=−Rr2+Rr1−Rr2−Rr2r1r2−Rr2=Rr1r2(r1−R)=Rr1r2=Rr1r1−Rr1r2=−Rr2+Rr1−Rr2−Rr2r1r2−Rr2=Rr1r2(r1−R)=Rr1r2=Rr1r1−R
  4. (x15−x−33=13)(15)(x15−x−33=13)(15)
    x−5(x−3)=5x−5x+15=5−15−15−4x−4=−10−4x=52x−5(x−3)=5x−5x+15=5−15−15−4x−4=−10−4x=52
  5. y=5y=5
    point at (-2,5) y=5
  6. aa
    m=ΔyΔx23=y−4x−−22(x+2)=−3(y−4)2x+4=−3y−12−3y+12−3y+122x−3y+16=0y=23x+163m=ΔyΔx23=y−4x−−22(x+2)=−3(y−4)2x+4=−3y−12−3y+12−3y+122x−3y+16=0y=23x+163
  7. aa
    1st slope:m=ΔyΔxm=−9−−78−12m=−2−4m=12Now:m=ΔyΔx12=y−−9x−8x−8=2(y+9)x−8=2y+18−2y−18−2y−18x−2y−26=01st slope:m=ΔyΔxm=−9−−78−12m=−2−4m=12Now:m=ΔyΔx12=y−−9x−8x−8=2(y+9)x−8=2y+18−2y−18−2y−18x−2y−26=0
  8. aa
    Line on graph passes through (0,-2) and (3,0)
  9. aa
    −27≤6x−9≤3+9+9+9−186≤6x6≤126−3≤x≤2−27≤6x−9≤3+9+9+9−186≤6x6≤126−3≤x≤2
    -3 , or equal to x < or equal to 2
  10. aa
    2x+26=22x+26=−22x+2=2⋅62x+2=12−2−22x2=102x=52x+2=−2⋅62x+2=−12−2−22x2=−142x=−72x+26=22x+26=−22x+2=2⋅62x+2=12−2−22x2=102x=52x+2=−2⋅62x+2=−12−2−22x2=−142x=−7
    x=5, x=-7
  11. aa
    2x−1<−66<2x−1+1+1+1+12x2<−5272<2x2x<−52x>722x−1<−66<2x−1+1+1+1+12x2<−5272<2x2x<−52x>72
  12. y=|2x|−1y=|2x|−1
    xx yy
    3 5
    2 3
    1 1
    0 −1
    −1 1
    −2 3
    −3 5

    V line with point at (0,-1)

  13. aa
    A1=A2A3=2A1−10∘A1+A2+A3=180∘A1+A1+2A1−10∘=180∘+10∘+10∘4A14=190∘4A1=47.5∘A2=47.5∘A3=2A1−10∘A3=2(47.5∘)−10∘A3=95∘−10∘A3=85∘A1=A2A3=2A1−10∘A1+A2+A3=180∘A1+A1+2A1−10∘=180∘+10∘+10∘4A14=190∘4A1=47.5∘A2=47.5∘A3=2A1−10∘A3=2(47.5∘)−10∘A3=95∘−10∘A3=85∘
  14. x,x+2
    x+x+2=x−202x+2=x−20−x−2−x−2x=−22
    numbers are −22, −20
  15. a
    y=kmn2d1st datay=16k=find 1stm=3n=4d=6y=kmn2d16=k(3)(4)26k=16⋅63⋅(4)2k=22nd datay=find 2ndk=2m=−2n=4d=8y=kmn2dy=(2)(−2)(4)28y=−8

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