Question

1. the width of a rectangle is w, and the length of the rectangle is 5 more than the width. if the area of the rectangle is 36 feet, what is the value of the length? (1 pt) a. 4 ft b. -9 ft c. 9 ft d. 5 ft 9. jalen and jessie are both asked to solve ( x^{2}=81 ). jessie says the solution to the function is ( x = 9 ). jalen says the solution to ( x^{2}=81 ) is ( x = 9 & x = -9 ). who is correct and why? (3 pts) a. jessie because the square root of a number can only be positive. b. jalen because a quadratic always has two solutions c. jessie because ( 9 \times 9 ) is 81. d. jalen because ( -9 \times -9 ) and ( 9 \times 9 ) equals 81.

Explanation:

Step1: Solve the rectangle problem

Let the width of the rectangle be \(w\). Then the length \(l=w + 5\). The area of a rectangle \(A=l\times w\). Given \(A = 36\), so \((w + 5)\times w=36\), which simplifies to \(w^{2}+5w - 36=0\).
Factor the quadratic equation: \((w + 9)(w - 4)=0\). So \(w=-9\) or \(w = 4\). Since width cannot be negative, \(w = 4\). Then length \(l=w + 5=4+5 = 9\)

Step2: Solve the quadratic equation problem

For the equation \(x^{2}=81\), take the square root of both sides. By the property \(x^{2}=a\) (\(a\geq0\)), \(x=\pm\sqrt{a}\). So \(x=\pm9\) because \((-9)\times(-9)=81\) and \(9\times9 = 81\)

Answer:

1. B. \(9\) ft
2. D. Jalen because \(-9\times - 9\) AND \(9\times9\) equals \(81\)