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9.2E: Mazoezi

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    176461

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    Mazoezi hufanya kamili

    Mazoezi 1 - 22: Tatua Ulinganisho wa Quadratic wa Fomu\(ax^{2}=k\) Using the Square Root Property

    Katika mazoezi yafuatayo, tatua kila equation.

    1. \(a^{2}=49\)

    2. \(b^{2}=144\)

    3. \(r^{2}-24=0\)

    4. \(t^{2}-75=0\)

    5. \(u^{2}-300=0\)

    6. \(v^{2}-80=0\)

    7. \(4 m^{2}=36\)

    8. \(3 n^{2}=48\)

    9. \(\frac{4}{3} x^{2}=48\)

    10. \(\frac{5}{3} y^{2}=60\)

    11. \(x^{2}+25=0\)

    12. \(y^{2}+64=0\)

    13. \(x^{2}+63=0\)

    14. \(y^{2}+45=0\)

    15. \(\frac{4}{3} x^{2}+2=110\)

    16. \(\frac{2}{3} y^{2}-8=-2\)

    17. \(\frac{2}{5} a^{2}+3=11\)

    18. \(\frac{3}{2} b^{2}-7=41\)

    19. \(7 p^{2}+10=26\)

    20. \(2 q^{2}+5=30\)

    21. \(5 y^{2}-7=25\)

    22. \(3 x^{2}-8=46\)

    Jibu

    1. \(a=\pm 7\)

    3. \(r=\pm 2 \sqrt{6}\)

    5. \(u=\pm 10 \sqrt{3}\)

    7. \(m=\pm 3\)

    9. \(x=\pm 6\)

    11. \(x=\pm 5 i\)

    13. \(x=\pm 3 \sqrt{7} i\)

    15. \(x=\pm 9\)

    17. \(a=\pm 2 \sqrt{5}\)

    19. \(p=\pm \frac{4 \sqrt{7}}{7}\)

    21. \(y=\pm \frac{4 \sqrt{10}}{5}\)

    Mazoezi 23 - 46: Tatua Ulinganisho wa Quadratic wa Fomu\(a(x-h)^{2}=k\) Using the Square Root Property

    Katika mazoezi yafuatayo, tatua kila equation.

    23. \((u-6)^{2}=64\)

    24. \((v+10)^{2}=121\)

    25. \((m-6)^{2}=20\)

    26. \((n+5)^{2}=32\)

    27. \(\left(r-\frac{1}{2}\right)^{2}=\frac{3}{4}\)

    28. \(\left(x+\frac{1}{5}\right)^{2}=\frac{7}{25}\)

    29. \(\left(y+\frac{2}{3}\right)^{2}=\frac{8}{81}\)

    30. \(\left(t-\frac{5}{6}\right)^{2}=\frac{11}{25}\)

    31. \((a-7)^{2}+5=55\)

    32. \((b-1)^{2}-9=39\)

    33. \(4(x+3)^{2}-5=27\)

    34. \(5(x+3)^{2}-7=68\)

    35. \((5 c+1)^{2}=-27\)

    36. \((8 d-6)^{2}=-24\)

    37. \((4 x-3)^{2}+11=-17\)

    38. \((2 y+1)^{2}-5=-23\)

    39. \(m^{2}-4 m+4=8\)

    40. \(n^{2}+8 n+16=27\)

    41. \(x^{2}-6 x+9=12\)

    42. \(y^{2}+12 y+36=32\)

    43. \(25 x^{2}-30 x+9=36\)

    44. \(9 y^{2}+12 y+4=9\)

    45. \(36 x^{2}-24 x+4=81\)

    46. \(64 x^{2}+144 x+81=25\)

    Jibu

    23. \(u=14, u=-2\)

    25. \(m=6 \pm 2 \sqrt{5}\)

    27. \(r=\frac{1}{2} \pm \frac{\sqrt{3}}{2}\)

    29. \(y=-\frac{2}{3} \pm \frac{2 \sqrt{2}}{9}\)

    31. \(a=7 \pm 5 \sqrt{2}\)

    33. \(x=-3 \pm 2 \sqrt{2}\)

    35. \(c=-\frac{1}{5} \pm \frac{3 \sqrt{3}}{5} i\)

    37. \(x=\frac{3}{4} \pm \frac{\sqrt{7}}{2} i\)

    39. \(m=2 \pm 2 \sqrt{2}\)

    41. \(x=3+2 \sqrt{3}, x=3-2 \sqrt{3}\)

    43. \(x=-\frac{3}{5}, x=\frac{9}{5}\)

    45. \(x=-\frac{7}{6}, x=\frac{11}{6}\)

    Mazoezi 47 - 68: Mazoezi ya mchanganyiko

    Katika mazoezi yafuatayo, tatua kutumia Mizizi ya Mizizi ya Mraba.

    47. \(2 r^{2}=32\)

    48. \(4 t^{2}=16\)

    49. \((a-4)^{2}=28\)

    50. \((b+7)^{2}=8\)

    51. \(9 w^{2}-24 w+16=1\)

    52. \(4 z^{2}+4 z+1=49\)

    53. \(a^{2}-18=0\)

    54. \(b^{2}-108=0\)

    55. \(\left(p-\frac{1}{3}\right)^{2}=\frac{7}{9}\)

    56. \(\left(q-\frac{3}{5}\right)^{2}=\frac{3}{4}\)

    57. \(m^{2}+12=0\)

    58. \(n^{2}+48=0\)

    59. \(u^{2}-14 u+49=72\)

    60. \(v^{2}+18 v+81=50\)

    61. \((m-4)^{2}+3=15\)

    62. \((n-7)^{2}-8=64\)

    63. \((x+5)^{2}=4\)

    64. \((y-4)^{2}=64\)

    65. \(6 c^{2}+4=29\)

    66. \(2 d^{2}-4=77\)

    67. \((x-6)^{2}+7=3\)

    68. \((y-4)^{2}+10=9\)

    Jibu

    47. \(r=\pm 4\)

    49. \(a=4 \pm 2 \sqrt{7}\)

    51. \(w=1, w=\frac{5}{3}\)

    53. \(a=\pm 3 \sqrt{2}\)

    55. \(p=\frac{1}{3} \pm \frac{\sqrt{7}}{3}\)

    57. \(m=\pm 2 \sqrt{2 i}\)

    59. \(u=7 \pm 6 \sqrt{2}\)

    61. \(m=4 \pm 2 \sqrt{3}\)

    63. \(x=-3, x=-7\)

    65. \(c=\pm \frac{5 \sqrt{6}}{6}\)

    67. \(x=6 \pm 2 i\)

    Mazoezi 69 - 70: Mazoezi ya kuandika

    69. Kwa maneno yako mwenyewe, kuelezea Mizizi ya Mizizi ya Mraba.

    70. Kwa maneno yako mwenyewe, eleza jinsi ya kutumia Mizizi ya Mizizi ya Mraba ili kutatua equation ya quadratic\((x+2)^{2}=16\).

    Jibu

    69. Majibu yatatofautiana.

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili linatoa orodha ya kutathmini ustadi wa malengo ya sehemu hii. Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations quadratic ya fomu mara x squared sawa k kwa kutumia mali ya Mizizi ya Mraba. € € â € kwa ujasiri, â € â € € kwa msaada fulani, â € au †hakuna, mimi donâ €™ t kupata hivyo.â € Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations quadratic ya fomu mara mraba wa x minus h sawa k kwa kutumia Mizizi ya Mizizi ya Mizizi ya Mizizi. € € kwa ujasiri, â € â € â € kwa msaada fulani, â € au â€no, mimi donâ €™ t kupata hiyo.â €
    Kielelezo 9.1.23

    Chagua jinsi gani unaweza kujibu kauli “Naweza kutatua equations quadratic ya fomu mara mraba wa\(x\) minus\(h\) sawa\(k\) kutumia Mizizi ya Square Mali.” “Kwa ujasiri,” “kwa msaada fulani,” au “Hapana, siipati.”

    b Kama wengi wa hundi yako walikuwa:

    ... kwa ujasiri. Hongera! Umefanikiwa malengo katika sehemu hii. Fikiria ujuzi wa kujifunza uliyotumia ili uweze kuendelea kuitumia. Ulifanya nini ili uwe na ujasiri wa uwezo wako wa kufanya mambo haya? Kuwa maalum.

    ... kwa msaada fulani. Hii lazima kushughulikiwa haraka kwa sababu mada huna bwana kuwa mashimo katika barabara yako ya mafanikio. Katika hesabu kila mada hujenga juu ya kazi ya awali. Ni muhimu kuhakikisha kuwa na msingi imara kabla ya kuendelea. Nani unaweza kuomba msaada? Washiriki wenzako na mwalimu ni rasilimali nzuri. Je, kuna mahali kwenye chuo ambapo waalimu hisabati zinapatikana? Je, ujuzi wako wa kujifunza unaweza kuboreshwa?

    ... hapana - Siipati! Hii ni ishara ya onyo na haipaswi kupuuza. Unapaswa kupata msaada mara moja au utazidiwa haraka. Angalia mwalimu wako haraka iwezekanavyo kujadili hali yako. Pamoja unaweza kuja na mpango wa kupata msaada unayohitaji.