SOLUTION: the sum of the length and the width of a rectangle is 14. Find the values of the width for which the area is AT LEAST 45. clearly write algebraic expressions, this is not guess-and

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Question 1049776: the sum of the length and the width of a rectangle is 14. Find the values of the width for which the area is AT LEAST 45. clearly write algebraic expressions, this is not guess-and-check.
Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
l+w=14
area=lw
area=(14-w)*w

(14-w)*w>=45
14w-w^2>=45
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5, 9. Here's your graph:
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