The sum of the measure of the interior angles of a polygon is 2160°. What polygon is it? 14-gon 12-gon 13-gon 15-gon

Part A

4 < 5 < 9 is given to us. Apply the square root to each term to end up with this inequality: sqrt(4) < sqrt(5) < sqrt(9)

So sqrt(5) is between sqrt(4) and sqrt(9)

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Part B

Simplify those two mentioned square roots

sqrt(4) = sqrt(2^2) = 2

sqrt(9) = sqrt(3^2) = 3

Therefore, sqrt(5) is also between 2 and 3

We can see this through using a calculator: sqrt(5) = 2.23607 approximately

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Part C

We can now say:

2 < sqrt(5) < 3

Multiply all three sides by 6

6*2 < 6*sqrt(5) < 6*3

So the expression 6*sqrt(5) is between 6 x 2 and 6 x 3

Sure enough, a calculator confirms this

6*sqrt(5) = 13.416408

since 6*2 = 12 and 6*3 = 18. We see that 13.416 is between 12 and 18.

Integers are numbers like ...-3, -2, -1, 0, 1, 2, 3... and so on. So, according to this definition, let's solve this problem:

28. We know that the product of three integers is -3. So, the statement states that we have three factor, so:

a.b.c = -3

The possible values of the factors are:

• Factors are: 3, 1 and -1 in which case:

(3)(1)(-1) = -3

• Factors are: -3, 1 and 1 in which case:

(-3)(1)(1) = -3

29. In this problem we know two nonzero integers, that is, they cannot be equal to zero. Thus, they must have different sign, that is, one of them must be positive and the other negative.For instance:

• -9 and 2

(-9)(2) = -18, So -18 is less than -9 and 2

Another example:

• 1 and -8

(1)(-8) = -8, So -8 is equal to -8 and -8 is less than 1.

30. The sign of the product of two integers with the same sign is positive, that is:

(+)(+) = (+) and

(-)(-) = (+)

So, the sign of the product of three integers with the same sign are two options:

• Option 1. The three integers are positive in which case:

(+)(+)(+) = (+), So the sign of the product is positive

• Option 2. The three integers are negative in which case:

(-)(-)(-) = (-), So the sign of the product is negative.

This option two gives us that result because:

(-)(-) = (+) and (+)(-) = (-)