Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
1 answer:
The systems of linear equations have been matched with their respective solutions as shown in the image attached below.
<h3>What is a system of linear equations?</h3>A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.
Read more on linear equations here: brainly.com/question/2030026
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Answer: " 2x (2x - 1) (x + 1) " .
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Step-by-step explanation:
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Given:
f(x) = 9x³ + 2x² − 5x + 4 ;
g(x) = 5x³ − 7x + 4 ;
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What is: f(x) − g(x) ?
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Plug in: " 9x³ + 2x² − 5x + 4 " for: " f(x) " ;
and: " (5x³ − 7x + 4) " ; for: "g(x)" ;
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→ " f(x) − g(x) =
" 9x³ + 2x² − 5x + 4 − (5x³ − 7x + 4) " .
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Rewrite this expression as:
→ " 9x³ + 2x² − 5x + 4 − 1(5x³ − 7x + 4) " .
→ {since: " 1 " ; multiplied by "any value" ; is equal to that same value.}.
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Now, let us example the following portion of the expression:
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" − 1(5x³ − 7x + 4) "
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Note the "distributive property" of multiplication:
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→ a(b + c) = ab + ac ;
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Likewise:
→ a(b + c + d) = ab + ac + ad .
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As such:
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→ " − 1(5x³ − 7x + 4) " ;
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= (-1 * 5x³) + (-1 * 7x) + (-1 * 4) ;
= - 5x³ + (-7x) + (-4) ;
= - 5x³ − 7x − 4 ;
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Now, add the "beginning portion of the expression" ; that is:
" f(x) " ; to the expression ; which is:
→ 9x³ + 2x² − 5x + 4 ;
→ as follows:
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→ 9x³ + 2x² − 5x + 4 − 5x³ − 7x − 4 ;
→ {Note that the: " - " sign; that is;
the "negative sign", in the term: " -5x³ " ;
becomes a: " − " sign; that is; a "minus sign" .}.
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Now, combine the "like terms" of this expression; as follows:
+ 9x³ − 5x³ = + 4x³ ;
− 5x − 7x = − 2x ;
+ 4 − 4 = 0 ;
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and we have:
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→ " 4x³ + 2x² − 2x ".
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Now, to write this answer in "factored form" :
Note that among all 3 (three) terms in this expression, each term has a factor of "2" . The lowest coefficient among these 3 (three) terms is "2" ; so we can "factor out" a "2".
Also, each of the 3 (three) terms in this fraction is a coefficient to a variable. That variable takes the form of "x". The term in this expression with the variable, "x"; with the lowest degree has the variable: "x" (i.e. "x¹ = x" ) ; so we can "factor out a "2x" (rather than just the number, "2".).
So, by factoring out a "2x" ; take the first term [among the 3 (three) terms in the expression] —which is: "4x³ " .
2x * (?) = 4x³ ? ;'
↔ ? ;
→ 4/2 = 2 ;
;
As such: 2x * (2x²) = 4x³ ;
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Now, by factoring out a "2x" ; take the second term [among the 3 (three) terms in the expression] — which is: "2x² " .
2x * (?) = 2x² ? ;
↔ ?
→ 2/2 = 1 ;
→ ;
As such: 2x * (x) = 2x²
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Now, by factoring out a "2x" ; take the third term [among the 3 (three) terms in the expression] — which is: " − 2x " .
2x * (?) = - 2x ;
↔ -1 ;
As such: 2x * (-1) = − 2x .
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So:
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Given the simplified expression:
→ " 4x³ + 2x² − 2x " ;
We can "factor out' a: " 2x " ; and write the this answer is: "factored form" ; as:
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"2x (2x² + x − 1 ) . "
Now, we can further factor the:
" (2x² + x − 1) " ; portion;
Note: "(2x² + x - 1)" =
2x² + 2x - 1x -1 = (2x -1) + x (2x - 1 ) =
(2x - 1) ( x + 1)
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Now, bring down the "2x" ; and write the Full "factored form" ; as follows:
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→ " 2x (2x - 1) (x + 1) " .
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Hope this helps!
Wishing you the best!
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