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USPshnik [31]
3 years ago
7

How do I solve equations with fractions?

Mathematics
1 answer:
ratelena [41]3 years ago
4 0

2y - 3/5 = 1/2

  • Add 3/5 to both sides.

2y = 1/2 + 3/5

  • Let's make the two fractions have common denominators.
  • Multiply 1/2 by 5/5 and 3/5 by 2/2.
  • 1/2 * 5/5 = 5/10
  • 3/5 * 2/2 = 6/10

2y = 5/10 + 6/10

Add the two fractions.

2y = 11/10

Divide both sides by 2.

  • 11/10 ÷ 2
  • Use the Keep, Change, Flip method.
  • Keep 11/10, change ÷ to ×, and flip the 2 (reciprocal).
  • 11/10 × 1/2 = 11/20

y = 11/20

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What is the sum of the first 70 consecutive odd numbers? Explain.
expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N

So, the final result is

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

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the wheel of a unicycle has a radius of 14 inches. About how many rotations will it take for the unicyle to tavel 440 inches
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Answer:

z = 110

Step-by-step explanation:

z + 35 + 35 = 180

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z = 110

8 0
3 years ago
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ladessa [460]

Answer:

True

Step-by-step explanation:

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3 0
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spayn [35]

Answer:

yes if u use Pemdas and both sides of the equation have the same answer, they both are equivalent.

Good job!

7 0
3 years ago
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