Respuesta :
Answer: " 1035 " .
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→ " F(10) = 1035 " .
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Step-by-step explanation:
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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:
Please Excuse My Dear Aunt Sally [or: Susan—either name is fine] :
or the variant:
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Be Excused, My Dear Aunt Sally/Susan .
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in which the letters of the first words of the sentence in this mnemonic device represent the order of operations performed, as follows:
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(Parentheses, followed by Exponents); if these occur; in that order;
or: using the variant:
{Brackets, followed by Exponents}; if these occur, in that order;
— in which "Parentheses" are considered a type of "Brackets" ;
— and in which if both : Brackets and Parentheses occur,
the "Brackets", take first in the order of operations
[if they occur]; followed by: "Parentheses" ;
and then followed by: "Exponents" (if they occur);
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then: Multiplication (if it occurs) and Division (if it occurs);
However, instead of "Multiplication followed by Division" ;
the difference is that these operations are performed from left to right— as they appear (if both Multiplication and Division occur) within the expression ;
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then: Addition (if it occurs) and Subtraction (if it occurs);
However, instead of "Addition followed by Subtraction" ;
the difference is that these operations are performed from left to right— as they appear (if both Addition and Subtraction occur) within the expression.
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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 .
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The answer is: 1035 .
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Hope this is helpful to you.
Best wishes!
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