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spayn [35]
3 years ago
6

4.8/1 7/9 =(1.2b):6 2/3

Mathematics
1 answer:
Hunter-Best [27]3 years ago
8 0

Answer:

b = 15

Step-by-step explanation:

Solve for b:

\dfrac{4.8}{1\frac{7}{9}}=\dfrac{1.2b}{6\frac{2}{3}}

Cross multiply:

6\dfrac{2}{3}\cdot 4.8=1.2b\cdot 1\dfrac{7}{9}\\ \\\dfrac{6\cdot 3+2}{3}\cdot 4.8=1.2b\cdot \dfrac{9+7}{9}\\ \\\dfrac{20}{3}\cdot \dfrac{48}{10}=\dfrac{12b}{10}\cdot \dfrac{16}{9}\\ \\20\cdot 4=b\cdot \dfrac{16}{3}\\ \\5=b\cdot \dfrac{1}{3}\\ \\b=5\cdot 3\\ \\b=15

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HELP ME PLEASEE
Nina [5.8K]

Answers:

x = -8/5 or x = 8/5

Sum of the first ten terms where all terms are positive = 4092

========================================================

Explanation:

r = common ratio

  • first term = 4
  • second term = (first term)*(common ratio) = 4r
  • third term = (second term)*(common ratio) = (4r)*r = 4r^2

The first three terms are: 4, 4r, 4r^2

We're given that the sequence is: 4, 5x, 16

Therefore, we have these two equations

  • 5x = 4r
  • 4r^2 = 16

Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.

-----------------

To find the sum of the first n terms, we use this geometric series formula

Sn = a*(1 - r^n)/(1 - r)

We have

  • a = 4 = first term
  • r = 2, since we want all the terms to be positive
  • n = 10 = number of terms to sum up

So,

Sn = a*(1 - r^n)/(1 - r)

S10 = 4*(1 - 2^10)/(1 - 2)

S10 = 4*(1 - 1024)/(-1)

S10 = 4*(-1023)/(-1)

S10 = 4092

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Answer:

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