Question

Question 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) increases as w increases for 0<w<5 . cap A times w increases as w increases for 0<w<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) has a minimum value at w=5 .

Answer 1

The correct response is: **A(w) increases as w increases when w>0.**

This is accurate because, for the quadratic function \(A(w) = w^2 + 5w\), as the width \(w\) increases, the area \(A(w)\) also increases for \(w > 0\). The equation is a parabola that opens upwards, meaning it does not have a maximum and continues to increase as \(w\) increases beyond zero.