Answer:
The farmer should plant 14 additional trees, for maximum yield.
Step-by-step explanation:
Given



So, we have:


Required
The additional trees to be planted for maximum yield
The function is:


Open bracket



Rewrite as:

Differentiate

Equate
to 0 and solve for x to get the maximum of x


Divide by -4

The farmer should plant 14 additional trees, for maximum yield.
The answer to this question is 600-28w > 300. This inequality can be described as $600 (money in the savings account) subtracted by $28w (withdrawal of $28 a week for food) should be greater than $300. It proves that the money will not drop below $300.
Answer:
m = 12h
Step-by-step explanation:
Since Bill charges $12 per hour, it implies for every hour he charges $12. Therefore, the amount of money he makes, m, is dependent on the number of hours he works, h. The higher the number of hours, the more his money. And vice versa.
So that;
m = 12h
Thus if Bill works for 6 hours, his amount of money would be;
m = 12 (6)
= 72
m = $72
Bill would make $72 after working for 6 hours.
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."
_______________________________________________________
Ok so Ethel starts off with 11% of $5,000 that is $550 of commission
and 14% on sales above 5,000 for 14,000 all of her commission would be 14% that means she would get $1,000 because 14% of 14,000 is 1,000
hope this helped.