Do the side lengths 28 ft, 45 ft, and 53 ft create a right, acute, or obtuse triangle?

They create an Acute triangle.
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Explanation: Use the Triangle Inequality Theorem to see if your lengths even make a triangle.

Our sides are 28, 45 and 53.

28 + 45 = 73

73 > 53 Because 73 is greater, we have an actual triangle and can use the Pythagorean Theorem to classify your triangle.

Now we use the Pythagorean Theorem.

a^2 + b^2 = c^2

53 + 28 = 45

53 squared is 7.28. 28 squared is 5.29. 45 squared is 6.7.

Add 5.29 to 6.7 you get 11.99.

11.99 is a greater number than 7.28 so therefore the triangle is acute.

Hope this helped. :)

I'll do number 11 for you so that you can understand, and do the rest on your own.

Step-by-step explanation:

Number 11 asks to factor x^2+3x+2.

So you have to find a number that multiples to equal 2, but adds to equal 3.

You know that when you multiply 2 and 1 you get 2, and when you add 2 and 1, you get 3.

So, it would be factored into (x+2)(x+1)