Four doughnuts and 4 coffees cost $12. The cost of the 4 coffees is half the cost of the 4 doughnuts. What is the cost of each c
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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
B) A rectangle with a length of 15 cm and a width of 9 cm.
EXPLANATION
The given rectangle, A, has length, 10cm and its width is 6cm.
The rectangle that is similar to rectangle A, has the corresponding sides in the same proportion.
For option A, the triangle has length 9cm and width 6cm.
The ratio of the corresponding sides are:
Since the ratios are not equal, the two triangles are not similar.
For the triangle in option B, the length is 15cm and the width is 9cm.
The ratio of the corresponding sides are:
Since the sides of the triangle are in the same proportion, the two triangles are similar.
For option C, the proportions are not the same.
The proportions are not the same for the triangle in option D.
B) A rectangle with a length of 15 cm and a width of 9 cm.
EXPLANATION
The given rectangle, A, has length, 10cm and its width is 6cm.
The rectangle that is similar to rectangle A, has the corresponding sides in the same proportion.
For option A, the triangle has length 9cm and width 6cm.
The ratio of the corresponding sides are:
Since the ratios are not equal, the two triangles are not similar.
For the triangle in option B, the length is 15cm and the width is 9cm.
The ratio of the corresponding sides are:
Since the sides of the triangle are in the same proportion, the two triangles are similar.
For option C, the proportions are not the same.
The proportions are not the same for the triangle in option D.