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labwork [276]
3 years ago
5

An investment is currently worth 1.2×107 dollars . Twenty years ago, the investment was worth ​ 9.6×105 ​ dollars. How many time

s greater is the value of the investment today than the value of the investment twenty years ago? 0.125 12.5 125 12,500
Mathematics
1 answer:
Pepsi [2]3 years ago
7 0

Answer:

12.5

Step-by-step explanation:

Let an old value be A

and a new value be B

Also, let B is greater than A

The number of times B is greater than A is found by dividing B by A

Now, in terms of scientific notation, how would we do the division? It is shown below:

\frac{a*10^b}{z*10^y}=(\frac{a}{z})*10^{b-y}

Now, coming to our question, let's do the math using the statements and formulas we have seen above:

\frac{1.2*10^7}{9.6*10^5}\\=(\frac{1.2}{9.6})*10^{7-5}\\=0.125*10^2

10^2 means 100, so we do the multiplication:

0.125*10^2\\0.125*100\\12.5

So, it is 12.5 times greater

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Step-by-step explanation:

Rewrite

100

x

2

100

x

2

as

(

10

x

)

2

(

10

x

)

2

.

(

10

x

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2

+

60

x

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9

(

10

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2

+

60

x

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9

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9

9

as

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2

3

2

.

(

10

x

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2

+

60

x

+

3

2

(

10

x

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2

+

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x

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3

2

Check the middle term by multiplying

2

a

b

2

a

b

and compare this result with the middle term in the original expression.

2

a

b

=

2

⋅

(

10

x

)

⋅

3

2

a

b

=

2

⋅

(

10

x

)

⋅

3

Simplify.

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a

b

=

60

x

2

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b

=

60

x

Factor using the perfect square trinomial rule

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2

+

2

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b

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=

(

a

+

b

)

2

a

2

+

2

a

b

+

b

2

=

(

a

+

b

)

2

, where

a

=

10

x

a

=

10

x

and

b

=

3

b

=

3

.

(

10

x

+

3

)

2

3 0
3 years ago
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