Question

Mia has 50 feet of fencing to make a rectangular kennel for her dog. She decides to use part of her house as one side (width) of the kennel. She needs a minimum enclosed area of 300 square feet. Let l represent the length of the kennel. Which inequality represent this situation, and what is the solution set? Select all the correct answers.

Answer 1

Answer:

-2l^2+50l-300 ≥ 0

l(50 − 2l) ≥ 300

(l − 15)(l − 10) ≤ 0

Explanation:

Explanation:

Area of the kennel: l(50 − 2l)

Minimum enclosed area required: 300 square feet

The situation is represented by the non-strict inequality l(50 − 2l) ≥ 300.

Solving the inequality, gives several equivalent statements:

50l − 2l2 ≥ 300

-2l2 + 50l − 300 ≥ 0

-2(l2 − 25l + 150) ≥ 0

-2(l − 15)(l − 10) ≥ 0

(l − 15)(l − 10) ≤ 0

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Answer 2

I(50 - 2l) > 300

10 < I < 15

Explanation:

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