Select the correct answer.
Which expression is equivalent to the given expression?
[tex]$(3 y-4)(2 y+7)+11 y-9$[/tex]
A. [tex]$6 y^2+11 y+19$[/tex]
B. [tex]$16 y-6$[/tex]
C. [tex]$9 y-37$[/tex]
D. [tex]$6 y^2+24 y-37$[/tex]
Answer (3)
The algebraic expression for the length of the kennel L in terms of the width W is: L = 2 120 − W
Let's denote the length of the rectangular kennel as L. Since Steve is using his house as one side, the other side (opposite the house) will also be
The perimeter P of a rectangle is given by the formula:
P=2L+2W
In this case, the total length of the fence is given as 120 feet. Since one side is the house and the other side is the kennel, we can set up the equation:
120=L+L+W
Simplify the equation:
120=2L+W
Now, solve for L, the length of the kennel:
2L=120−W
L = 2 120 − W
So, the algebraic expression for the length of the kennel L in terms of the width W is:
L = 2 120 − W
To determine the length of Steve's rectangular kennel, where 120 feet of fencing is used and one side is formed by the house, you can use the equation L = 120 - 2W, where L is the length and W is the width.
Rectangular Kennel Problem
Steve has 120 feet of fence to create a rectangular kennel for his dogs, using his house as one side. To find an algebraic expression for the kennel's length, let’s denote the length of the kennel parallel to the house as L and the width as W.
Since the house forms one side, we only need to fence the other three sides:
The two widths (W) opposite to each other.
The length (L) perpendicular to the house.
The total fencing used is: 2W + L = 120
From this equation, we can express the length in terms of width:
L = 120 - 2W
This equation represents the length of the kennel in terms of its width and ensures that the total fencing used is 120 feet.
The algebraic expression for the length of the kennel is L = 120 − 2 W , where W is the width of the kennel. This relationship reflects how the total fencing of 120 feet is allocated for the three sides of the kennel. By substituting different values for W , you can find the corresponding L .
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