Answer:
Step-by-step explanation:
Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)
Given P = 30ft, on substituting P = 30 into the expression;
30 = 2(x+y)
x+y = 15
y = 15-x
Also since the area of the rectangle is xy;
A = xy
Substitute y = 15-x into the area;
A = x(15-x)
A = 15x-x²
The function that models its area A in terms of the length x of one of its sides is A = 15x-x²
The side of length x yields the greatest area when dA/dx = 0
dA/dx = 15-2x
15-2x = 0
-2x = -15
x = -15/-2
x = 7.5 ft
Hence the side length, x that yields the greatest area is 7.5ft.
Since y = 15-x
y = 15-7.5
y = 7.5
Area of the rectangle = 7.5*7.5
Area of the rectangle = 56.25ft²
Answer:
The youngest child will receive $2000
Step-by-step explanation:
A father decided to give 25% of his monthly income to his three children as their monthly allowance.
The eldest child got 45% of the allowance and the youngest got 20%. This means that the second child got:
100 - (45 + 20) = 100 - 65 = 35%
The second child received $3500.
Let the 25% of his monthly income be x.
Hence:
35% of x = 3500
=> 

x = $10000
The amount the man shared among his children is $10000.
Hence, the youngest child (20%) will receive:
20% of $10000

= $2000
The youngest child will receive $2000.
Answer:
Therefore the results from adding the equation in this system is

Step-by-step explanation:
Given:
Equations as
.......................1
.......................2
To Find :
Result when adding equation 1 and 2 = ?
Solution
On adding equation 1 and 2 the "3y" term will get cancel and the like terms will combine that is add (11x and -4x ) and ( -17 and - 18) as shown below
11x - 3y = -17
-4x + 3y = - 18
-------------------------------------------
7x + 0 = - 35
---------------------------------------------
Therefore the results from adding the equation in this system is

Answer:
y≤
Step-by-step explanation:
Since the graph is facing down, We know the equation is y<mx+b
Since slope is rise/run the slope is 1/3.
Since the y intercept (The point where the line hits y) is 1, the equation is
y<1/3x+1
BUT WAIT!
The line is solid meaning that we have to include the line as part of the values. This will make the new equation
y≤