Answer:
Average weight of the bags of potatoes is 3.8 pounds.
Step-by-step explanation:
Given:
Weight of the first bag, 
pounds.
Weight of the second bag is 0.4 pounds less than twice the weight of first bag. This means,
Weight of the third bag is 0.6 pounds more than that of the first bag. This means,
Weight of the fourth bag is 0.3 pounds less than that of the second bag. This means,
Therefore, the average weight of the bags of potatoes is given as the sum of all the weights and then divide the sum by 4. Therefore,
Therefore, average weight of the bags of potatoes is 3.8 pounds.
I think it's 21/100 because I found the common denominator by multiplying by ten so I multiplied 1 times ten to get 10. Does that help?
Answer:
11cm^2
Step-by-step explanation:
The area of a rhombus is the diagonals multiplied divided by two. 5.5*4/2. 22/2 =11. A=11cm^2
Answer:
<em>The answer is a = 6.</em>
Answers:
_____________________________________________________
Part A) " (3x + 4) " units .
_____________________________________________________
Part B) "The dimensions of the rectangle are:
" (4x + 5y) " units ; <u>AND</u>: " (4x − 5y)" units."
_____________________________________________________
Explanation for Part A):
_____________________________________________________
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)" ;
_______________________________________________________
Given: " (9x² + 24x + 16) " ;
_______________________________________________________
Let us start with the term:
_______________________________________________________
" (9x² + 12x) " ;
→ Factor out a "3x" ; → as follows:
_______________________________________
→ " 3x (3x + 4) " ;
Then, take the term:
_______________________________________
→ " (12x + 16) " ;
And factor out a "4" ; → as follows:
_______________________________________
→ " 4 (3x + 4) "
_______________________________________
We have:
" 9x² + 24x + 16 " ;
= " 3x (3x + 4) + 4(3x + 4) " ;
_______________________________________
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 " ;
____________________________________________________
→ Or; write: " (3x + 4) (3x + 4)" ; as: " (3x + 4)² " .
____________________________________________________
→ 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.}.
____________________________________________________
→ 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 .
_______________________________________________________
Part A): The answer is: "(3x + 4)" units.
____________________________________________________
Explanation for Part B):
_________________________________________________________<span>
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;
_______________________________________________________
Given: " A = </span>(16x² − 25y²) square units" ;
→ We are asked to find the dimensions, "L" & "w" ;
→ by factoring the given "area" expression completely:
____________________________________________________
→ 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:
________________________________________________________
Note:
________________________________________________________
" (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 " .
_______________________________________________________
Note:
_______________________________________________________
→ " (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 " .
______________________________________________________
→ So, we can rewrite: " (16x² − 25y²) " ;
as: " (4x)² − (5y)² " ;
→ {Note: We substitute: "(4x)² " for "(16x²)" ; & "(5y)² " for "(25y²)" .} . ;
_______________________________________________________
→ 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) " .
_______________________________________________________
Part B): The answer is: "The dimensions of the rectangle are:
" (4x + 5y) " units ; AND: " (4x − 5y)" units."
_______________________________________________________
