so, you're correct, it is the Food industry, and it went down from 2.7 to 2.5, well, so it really went down 2.7 - 2.5 or 0.2.
well, if we take 2.7 to be the 100% from that row, what is 0.2 off of it in percentage format?
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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The answer is 1 computer/8 students
We have that
x²<span> - y = -2
4y - 8 = x
using a graph tool
see the attached figure
the answer in the attached figure</span>
See, in these type of questions always first assume your original price to be x. And now try to write whatever information is given to you.
Now, you have that it has been sold for 12% profit, so basically it is sold at. (1 + (12/100))x = 1.12x
Now it is given that if it had been sold for 33₹ more. I.e. if it had been sold at. 1.12x + 33
Net gain would have been 14%.
So gain of 14%, means the cost to be (1+(14/100))x = 1.14x
And basically both 1.12x +33 and 1.14x are final costs, so
1.14x = 1.12x + 3
=> 1.14x - 1.12x = 3
=> 0.02x = 3
=> x = 3÷0.02
=> x= 1650₹
So original cost is 1650₹.
Hope you understand the solution and the way to tackle these type of problems if not then let me know.
hope it helps
pls mark my anwers as brainiest
