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cupoosta [38]
3 years ago
8

Which of the following expressions is this one equivalent to?

Mathematics
2 answers:
Alborosie3 years ago
8 0
We know that 
the euclid's division A/B implies A= BQ + R
wher Q = the quotient, and R is the remainder
<span>after doing euclid's division, (3x^3+15x^2+17x+3)/x+5 = 3x²+17and R= - 82
so </span>(3x^3+15x^2+17x+3= (3x²+17) (x+5) -82

the answer is x^3+15x^2+17x+3= (3x²+17) (x+5) - 82
arsen [322]3 years ago
3 0

Answer:

option (c) is correct,

3x^2+17-\frac{82}{x+5} is the equivalent fraction to the given expression \frac{3x^3+15x^2+17x+3}{x+5}

Step-by-step explanation:

Given expression ,  \frac{3x^3+15x^2+17x+3}{x+5}

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

3x^2+17-\frac{82}{x+5}

Taking LCM , Multiply 3x^2+17 by (x+5) , we get,

\frac{3x^2(x+5)+17(x+5)-82}{x+5}

On solving , we get,

\frac{3x^3+15x^2+17x+85-82}{x+5}

On simplifying, we get,

\frac{3x^3+15x^2+17x+3}{x+5}

Which is equal to the given expression.

Thus, option (c) is correct,

3x^2+17-\frac{82}{x+5} is the equivalent fraction to the given expression \frac{3x^3+15x^2+17x+3}{x+5}

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Fill in the missing expression
padilas [110]

Answer:

The complete table is:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]          +     [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +    [ a + 1 ]       +   [  -3a  ]    =   [     1      ]

  =                      =                     =                     =

[ 7a + 2b ]  +   [ 3a + 8 ]    +     [   0   ]    =   [10a + 2b + 8 ]

Explanation:

You can determine the content of each box by subtraction, running the rows and the columns.

The expressions are:

[ 5a ]  +    [          ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[      ]   +   [         ]   +      [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u>1. First row:</u>

[ 5a ]  +    [          ]   +    [ 4a ]     =    [ 10a + 3 ]

[      ] = [10a+ 3]  - [ 4a ] - [ 5a ] = 10a - 4a - 5a + 3 = a + 3

<u>2. Second colum:</u>

[ a + 3 ] + [ 4 + a ] + [       ] =  [ 3a + 8 ]

[        ] = [ 3a + 8 ] - [ a + 3 ] - [ 4 + a ] = 3a - a  + a  + 8 - 4 - 3 = a + 1

So far, you have completed this:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[      ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u></u>

<u>3. Complete the row 3:</u>

<u></u>

     [      ]   +   [ a + 1 ]   +      [  -3a  ]  =   [     1      ]

    [      ]   =    [     1      ]   -   [ a + 1 ]   -    [  -3a  ]  = - a + 3a + 1 - 1 = 2a

So far, you have completed this:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [              ]

  +              +                   +                    +

[   2a   ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u></u>

<u>4. Complete the fourth column:</u>

[ 10a + 3 ] + [    ] + [   1   ] = [10a + 2b + 8 ]

[    ] = 10a + 2b + 8 - 10a - 3 - 1 = 2b + 4

So far, this is the results:

[ 5a ]  +    [ a + 3 ]   +    [ 4a ]     =    [ 10a + 3 ]

  +                +                +                    +

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [  2b + 4 ]

  +              +                   +                    +

[   2a   ]   +   [ a + 1 ]   +     [  -3a  ]  =   [     1      ]

  =               =                   =                   =

[      ]  +   [ 3a + 8 ]  +  [         ]    =   [10a + 2b + 8 ]

<u>5. Complete the second row:</u>

[ 2b ]  +   [ 4 + a ]   +     [      ]     =    [  2b + 4 ]

 [      ]   =   [  2b + 4 ] - [ 2b ]  -   [ 4 + a ]  = 2b - 2b + 4 - 4 - a = - a

So far:

[ 5a ]  +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                +                    +                    +

[ 2b ]  +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +               +                     +                    +

[   2a   ]   +   [ a + 1 ]   +   [  -3a  ]  =   [     1      ]

  =               =                    =                   =

[      ]  +   [ 3a + 8 ]  +     [         ]    =   [10a + 2b + 8 ]

<u>6. Complete the first colum:</u>

[ 5a ] + [ 2b ] + [2a ] = [   ]

[   ] = [ 7a + 2b ]

So far:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]           +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +   [ a + 1 ]       +   [  -3a  ]    =   [     1      ]

  =                      =                     =                    =

[ 7a + 2b ]  +   [ 3a + 8 ]   +     [         ]    =   [10a + 2b + 8 ]

<u>7. Complete the last row:</u>

[ 7a + 2b ]  +   [ 3a + 8 ]   +     [         ]    =   [10a + 2b + 8 ]

[         ]    =   [10a + 2b + 8 ] - [ 7a + 2b ] - [ 3a + 8 ] = 0

The complete table is:

[ 5a ]           +    [ a + 3 ]      +    [ 4a ]     =    [ 10a + 3 ]

  +                         +                    +                    +

[ 2b ]           +   [ 4 + a ]      +     [ -a  ]     =    [  2b + 4 ]

  +                       +                     +                    +

[ 2a ]          +   [ a + 1 ]       +     [ -3a  ]    =   [     1      ]

  =                      =                     =                     =

[ 7a + 2b ]  +   [ 3a + 8 ]    +     [   0  ]     =   [10a + 2b + 8 ]

5 0
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Brut [27]
61.67$ because you round the 7 up to the nearest hundredth
7 0
2 years ago
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