The equation A(w)=w2+5w represents the relationship between the area in square units
and the width of a rectangle whose length is 5 units longer than its width.
Select the sentence that describes an accurate relationship between A
and w
.
(1 point)
Responses
A(w)
has a minimum value at w=5
.
cap A times w has a minimum value at w is equal to 5.
A(w)
increases as w
increases when w>0
.
cap A times w increases as w increases when w is greater than 0.
A(w)
has a maximum value at w=5
.
cap A times w has a maximum value at w is equal to 5.
A(w)
increases as w
increases for 0<w<5
.
cap A times w increases as w increases for 0<w<5.
The accurate relationship between A and w is: "A(w) increases as w increases when w > 0."
The correct sentence that accurately describes the relationship between A and w is:
A(w) increases as w increases when w > 0.
To understand this relationship, we can analyze the equation A(w) = w^2 + 5w. The area A of the rectangle is determined by the width w. As the width w increases (and is greater than 0), the term w^2 will increase, resulting in a larger area A. Hence, the area A(w) increases as the width w increases when w > 0.