A cheque recevied from ram 3400 in full settlement of 3500 journal entry
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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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Answer:
Range is always greater than zero.
Step-by-step explanation:
An exponential growth means that the growth rate of a given quantity increases exponentially.
The graph of an exponential function is shown below.
From the above graph, it's quite clear that the range of the function is never negative.
Hence, one characteristic of exponential growth is that the range(y values on the graph) is always greater than zero.
