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Find the sum of the next two numbers in the sequence 4, 5, 8, 14, 24, 40, 62. Solve the equality 4-2(r+4) >= 12

Mathematics

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Answer

214

r≤−8r \le -8

Step-by-step solution

9 steps

Haya Ocen, hapa kuna masuluhisho ya maswali yako:

1. Tafuta jumla ya namba mbili zinazofuata katika mfuatano:
Mfuatano uliotolewa ni: $4, 5, 8, 14, 24, 40, 62$.

  1. Tafuta tofauti kati ya namba zinazofuatana.

    Tofauti za kwanza:
    5−4=15 - 4 = 1
    8−5=38 - 5 = 3
    14−8=614 - 8 = 6
    24−14=1024 - 14 = 10
    40−24=1640 - 24 = 16
    62−40=2262 - 40 = 22
    Mfuatano wa tofauti za kwanza ni: 1,3,6,10,16,221, 3, 6, 10, 16, 22.

  2. Tafuta tofauti kati ya tofauti za kwanza (tofauti za pili).

    Tofauti za pili:
    3−1=23 - 1 = 2
    6−3=36 - 3 = 3
    10−6=410 - 6 = 4
    16−10=616 - 10 = 6
    22−16=622 - 16 = 6
    Mfuatano wa tofauti za pili ni: 2,3,4,6,62, 3, 4, 6, 6.

  3. Tambua muundo katika tofauti za pili na utabiri tofauti zinazofuata.

    Muundo wa tofauti za pili unaonekana kuwa 2,3,4,6,62, 3, 4, 6, 6. Inawezekana muundo unaendelea kwa kuongeza 6.
    Tofauti ya pili inayofuata itakuwa 6.
    Tofauti ya kwanza inayofuata (baada ya 22) itakuwa 22+6=2822 + 6 = 28.
    Namba inayofuata katika mfuatano (baada ya 62) itakuwa 62+28=9062 + 28 = 90.

  4. Tafuta namba ya pili inayofuata.

    Tofauti ya pili baada ya 6 itakuwa 6.
    Tofauti ya kwanza inayofuata (baada ya 28) itakuwa 28+6=3428 + 6 = 34.
    Namba ya pili inayofuata katika mfuatano (baada ya 90) itakuwa 90+34=12490 + 34 = 124.

  5. Tafuta jumla ya namba mbili zinazofuata.

    Namba mbili zinazofuata ni 90 na 124.
    Jumla yao ni 90+124=21490 + 124 = 214.
    Jumla ya namba mbili zinazofuata ni 214\boxed{214}.

    2. Tatua usawa:

    4−2(r+4)≥124 - 2(r + 4) \ge 12
  6. Panua usemi ndani ya mabano.

    4−2r−8≥124 - 2r - 8 \ge 12
  7. Unganisha namba zisizobadilika upande wa kushoto.

    −4−2r≥12-4 - 2r \ge 12
  8. Ongeza 4 pande zote mbili za usawa.

    −2r≥12+4-2r \ge 12 + 4 −2r≥16-2r \ge 16
  9. Gawanya pande zote mbili kwa −2-2.

    Kumbuka kugeuza alama ya usawa unapogawanya au kuzidisha kwa namba hasi.

    r≤16−2r \le \frac{16}{-2} r≤−8r \le -8

    Suluhisho la usawa ni r≤−8\boxed{r \le -8}.

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