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Problem 1

 It is possible to draw a triangle

Explanation:

We use the triangle inequality theorem. Consider a triangle with sides a,b,c

A triangle is only possible if and only if the following three inequalities are all true

Basically, if we can add any two sides to get a sum larger than the third side, then we can form a triangle.

If a = 3, b = 4, and c = 5, then

All three conditions are met, therefore we have a triangle possible.

Problem 2

 No, a triangle is not possible

Explanation:

For this problem, and the next two problems, we'll use the triangle inequality theorem also.

Notice that a+b = 4+5 = 9 but this is not larger than c = 9

So the condition a+b > c is not true, and therefore we do not have a triangle possible.

Problem 3

 No, a triangle is not possible

Explanation:

Similar to problem 2. A triangle isn't possible because a+b = 5+6 = 11 which is not larger than c = 12.

Problem 4

 It is possible to draw a triangle

Explanation:

A triangle is possible here because

Problem 5

  a, c, b

Explanation:

Here are two rules we'll use here

This applies to triangles only.

From the diagram, we can see that the 28 inch side is the longest. Angle 'a' is opposite this, making angle 'a' to be the largest angle.

Then we see that angle b is opposite the smallest side, so angle b is the smallest angle. Angle c is somewhere in between angles 'a' and b. So that's why we get the order a, c, b when sorting the angles from largest to smallest.

answer: there are 453.592 grams in a pound.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225