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Nutka1998 [239]
3 years ago
12

What is the answer to F(10)= 5(x-1)(2x+3)

Mathematics
1 answer:
bekas [8.4K]3 years ago
5 0

Answer:  " 1035 " .

______________________________________________

       →    "  F(10) = 1035 " .

______________________________________________

Step-by-step explanation:

______________________________________________

To solve:

For the "right-hand side" of the equation;  substitute "10" for all "x" values:

Given:  

       F(10) = 5(x - 1)(2x + 3) ;

  →   F(10) = 5(10-1)(2*10 + 3) ;

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How, to simplify the right-hand side of the equation;

 Solve using PE MD AS ; the mnemonic device for the order of operations to use for simplifying an expression:

  <u>P</u>lease <u>E</u>xcuse <u>M</u>y <u>D</u>ear <u>A</u>unt <u>S</u>ally [or: <u>S</u>usan—either name is fine] :

or the variant:

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  <u>B</u>e <u>E</u>xcused,  <u>M</u>y <u>D</u>ear <u>A</u>unt <u>S</u>ally/<u>S</u>usan .

______________________________________________

in which the letters of the first words of the sentence in this mnemonic device represent the order of operations performed, as follows:

______________________________________________

 (<u>P</u>arentheses, followed by <u>E</u>xponents);  if these occur; in that order;

   or:  using the variant:

  {<u>B</u>rackets, followed by <u>E</u>xponents};  if these occur, in that order;

     — in which "<u>P</u>arentheses" are considered a type of "<u>B</u>rackets" ;

         — and in which if <u><em>both</em></u><em> </em>:  <u>B</u>rackets  <u><em>and</em></u><em>  </em><u>P</u>arentheses occur,

                 the "<u>B</u>rackets", take first in the order of operations

                 [if they occur];   followed by:  "<u>P</u>arentheses" ;

                  and then followed by:  "<u>E</u>xponents" (if they occur);

_________________________________________

then:  <u>M</u>ultiplication (if it occurs) <em><u>and</u></em> <u>D</u>ivision (if it occurs);

<em><u>However,  instead of </u></em>"<u>M</u>ultiplication followed by <u>D</u>ivision" ;

  the difference is that these operations are performed <u>from left to right</u>— <u>as they appear</u> (if <em>both</em> <u>M</u>ultiplication <em>and</em> <u>D</u>ivision occur) within the expression ;

______________________________________________

then:  <u>A</u>ddition (if it occurs) <em><u>and</u></em> Subtraction (if it occurs);

<em><u>However,  instead of </u></em><em> </em>"<u>A</u>ddition followed by <u>S</u>ubtraction" ;

  the difference is that these operations are performed <u>from left to right</u>— <u>as they appear</u> (if <em>both</em> <u>A</u>ddition <em>and</em> <u>S</u>ubtraction occur) within the expression.

______________________________________________

So:

  Given:  

       F(10) = 5(x - 1)(2x + 3) ;

  →   F(10) = 5(10-1)(2*10 + 3) ;

We can calculate—and simplify—the "right-hand side" of the equation; as follows:

We have:  

  →   " 5(10-1)(2*10 + 3) " ;

 

  →   that is;  " 5 * (10 - 1) * (2*10 + 3) ;

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We do have "parentheses" in this expression:

We shall begin by simplifying the values within the two (2) terms that are enclosed within parentheses:

 

Start with:  

" (10 - 1) " ;  

  10 - 1 = 9 .  

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Now, let us continue with the second term that is in parentheses:

   " (2*10 +3 ) " ;

    →   2*10 + 3 = ?? ;

    →  Note the order of operations rules—{as stated above]; state that "multiplication/division" come before "addition/subtraction" ;

    → So:  " 2*10 + 3 =  (2*10) + 3 = 20 + 3 = 23 .

On "the right-hand side" of the given equation; we have:

        →  " 5 * (10 - 1) * (2*10 + 3) ;        

Replace the terms:  "(10 - 1)" with:  "9" ;

                                  "(2*10 + 3)" with:  "23" ;

And rewrite:

        →  F(10) = 5 * 9 * 23 ;

                     =  45 * 23 ;

                     =  1035 .

______________________________________________

The answer is:  1035 .

______________________________________________

Hope this is helpful to you.

        Best wishes!

______________________________________________

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