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3 years ago

6

1. If the same number is added to the numerator and subtracted from the denominator of 23/12, the resulting fraction is equivale

nt to the reciprocal of 2/3. What is the number?

1 answer:

ICE Princess25 [194]3 years ago

8 0

Answer:

The number is -2

Step-by-step explanation:

step 1

Find the reciprocal of 2/3

Remember that when multiply a number by its reciprocal, the result is 1

so

The reciprocal of 2/3 is 3/2

step 2

Let

x-----> the number added to the numerator and denominator

$\frac{23+x}{12-x}=\frac{3}{2}$

Solve for x

$2(23+x)=3(12-x)\\46+2x=36-3x\\2x+3x=36-46\\5x=-10\\x=-2$

step 3

verify

$\frac{23+x}{12-x}$

substitute x=-2

$\frac{23-2}{12+2}$

$\frac{21}{14}$

Simplify

$\frac{3}{2}$ ----> is ok

therefore

The number is -2

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Step-by-step explanation:

<u>A)a1=-2 and d=4</u>

We know that the arithmetic sequence formula is

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

Similarly

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Substituting the given value we get

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

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Substituting the given value we get

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

<u>B</u><u> $a_n=a_{(n-1)}-8$ with $a_1=10$ </u>

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Substituting the given value

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

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Substituting the value

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

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Substituting the value

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

<u>C) $a_1=3, a_2=1$ </u>

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

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

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

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$a_{4}= -3$

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

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$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

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