Answer:
B 10x+5
Step-by-step explanation:
:)
Answer: n minus c would equal c c minus b would equal z
Step-by-step explanation:
Answers:
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Part A) " (3x + 4) " units .
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Part B) "The dimensions of the rectangle are:
" (4x + 5y) " units ; <u>AND</u>: " (4x − 5y)" units."
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Explanation for Part A):
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Since each side length of a square is the same;
Area = Length * width = L * w ; L = w = s = s ;
in which: " s = side length" ;
So, the Area of a square, "A" = L * w = s * s = s² ;
{<u>Note</u>: A "square" is a rectangle with 4 (four) equal sides.}.
→ Each side length, "s", of a square is equal.
Given: s² = "(9x² + 24x + 16)" square units ;
Find "s" by factoring: "(9x² + 24x + 16)" completely:
→ " 9x² + 24x + 16 ";
Factor by "breaking into groups" :
"(9x² + 24x + 16)" =
→ "(9x² + 12x) (12x + 16)" ;
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Given: " (9x² + 24x + 16) " ;
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Let us start with the term:
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" (9x² + 12x) " ;
→ Factor out a "3x" ; → as follows:
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→ " 3x (3x + 4) " ;
Then, take the term:
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→ " (12x + 16) " ;
And factor out a "4" ; → as follows:
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→ " 4 (3x + 4) "
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We have:
" 9x² + 24x + 16 " ;
= " 3x (3x + 4) + 4(3x + 4) " ;
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Now, notice the term: "(3x + 4)" ;
We can "factor out" this term:
3x (3x + 4) + 4(3x + 4) =
→ " (3x + 4) (3x + 4) " . → which is the fully factored form of:
" 9x² + 24x + 16 " ;
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→ Or; write: " (3x + 4) (3x + 4)" ; as: " (3x + 4)² " .
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→ So, "s² = 9x² + 24x + 16 " ;
Rewrite as: " s² = (3x + 4)² " .
→ Solve for the "positive value of "s" ;
→ {since the "side length of a square" cannot be a "negative" value.}.
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→ Take the "positive square root of EACH SIDE of the equation;
to isolate "s" on one side of the equation; & to solve for "s" ;
→ ⁺√(s²) = ⁺√[(3x + 4)²] '
To get:
→ s = " (3x + 4)" units .
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Part A): The answer is: "(3x + 4)" units.
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Explanation for Part B):
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The area, "A" of a rectangle is:
A = L * w ;
in which "A" is the "area" of the rectangle;
"L" is the "length" of the rectangle;
"w" is the "width" of the rectangle;
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Given: " A = </span>(16x² − 25y²) square units" ;
→ We are asked to find the dimensions, "L" & "w" ;
→ by factoring the given "area" expression completely:
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→ Factor: " (16x² − 25y²) square units " completely '
Note that: "16" and: "25" are both "perfect squares" ;
We can rewrite: " (16x² − 25y²) " ; as:
= " (4²x²) − (5²y²) " ; and further rewrite the expression:
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Note:
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" (16x²) " ; can be written as: "(4x)² " ;
↔ " (4x)² = "(4²)(x²)" = 16x² "
Note: The following property of exponents:
→ (xy)ⁿ = xⁿ yⁿ ; → As such: " 16x² = (4²x²) = (4x)² " .
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Note:
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→ " (25x²) " ; can be written as: " (5x)² " ;
↔ "( 5x)² = "(5²)(x²)" = 25x² " ;
Note: The following property of exponents:
→ (xy)ⁿ = xⁿ yⁿ ; → As such: " 25x² = (5²x²) = (5x)² " .
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→ So, we can rewrite: " (16x² − 25y²) " ;
as: " (4x)² − (5y)² " ;
→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ;
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→ We have: " (4x)² − (5y)² " ;
→ Note that we are asked to "factor completely" ;
→ Note that: " x² − y² = (x + y) (x − y) " ;
→ {This property is known as the "<u>difference of squares</u>".}.
→ As such: " (4x)² − (5y)² " = " (4x + 5y) (4x − 5y) " .
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Part B): The answer is: "The dimensions of the rectangle are:
" (4x + 5y) " units ; AND: " (4x − 5y)" units."
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There is only one solution
When you graph both equations, they intersect therefore the intersection point tells you there is one solution. If it was infinitely many solutions then it would be the same line. If it was no solution then the graph would show to parallel lines.
