A food scientist is developing a new recipe. He needs it to have between 3 and 5 teaspoons of sugar per serving and between 3 an
d 6 grams of fiber. Each teaspoon of sugar has 5 carbohydrates. Each gram of fiber counts as a carbohydrate when counting total carbohydrates. If the recipe already has 10 carbohydrates per serving from other sources, create a linear programming feasible region to minimize the total carbohydrates in the recipes nutrition profile.
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No, it's not possible for the sides of a triangle to have those lengths.
According to the triangle inequality theorem, the sum of any two sides of the triangle has to be bigger than the last side. Let's test this.
This inequality satisfies the triangle inequality theorem.
This also satisfies the theorem.
Uh oh. This does not satisfy the triangle inequality theorem. Thus, it is not possible for a triangle to have these side lengths.
According to the triangle inequality theorem, the sum of any two sides of the triangle has to be bigger than the last side. Let's test this.
This inequality satisfies the triangle inequality theorem.
This also satisfies the theorem.
Uh oh. This does not satisfy the triangle inequality theorem. Thus, it is not possible for a triangle to have these side lengths.