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Diano4ka-milaya [45]
3 years ago
10

Ellen is playing a video game in which she captures butterflies. There are 5 butterflies onscreen, but the number of butterflies

doubles every minute. After 4 minutes, she was able to capture 7 of the butterflies.
Part 1 out of 2
Enter an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer.
Mathematics
1 answer:
vovikov84 [41]3 years ago
5 0
(Each minute+1)((Number of butterflies)^2)
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When the reciprocal of the larger of two consecutive even integers is subtracted from 4 times the reciprocal of the smaller, the
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<u>Step-by-step explanation:</u>

1st number: x

2nd number: x + 2

  • reciprocal of the larger is \frac{1}{x+2}
  • 4 times the reciprocal of the smaller is 4(\frac{1}{x})
  • reciprocal of the larger of two consecutive even integers is subtracted from 4 times the reciprocal of the smaller is 4(\frac{1}{x}) - \frac{1}{x+2}
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Solve the equation:

4(\frac{1}{x}) - \frac{1}{x+2} = 56

\frac{4(x(x + 2))}{x} - \frac{1(x(x + 2))}{x+2} = 56(x(x + 2))

4x + 8 - x = 56x² + 112x

     3x + 8 = 56x² + 112x

             0 = 56x² + 109x - 8

Use the quadratic formula to solve:

x = \frac{-109+/-11\sqrt{113}}{112}

The result is NOT AN INTEGER so there is NO SOLUTION

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