Question

13 multiple choice 2 points the lengths of three sides of a triangle are 5, 9, and x, all measured in centimeters. what are all possible values of x? ( 0 < x < 14 ) ( 5 < x < 15 ) ( 4 < x < 14 ) ( 3 < x < 9 ) 14 multiple choice 2 points what is 47,000,000 in scientific notation? ( 4.7 \times 10^{7} ) ( 0.47 \times 10^{8} ) ( 4.7 \times 10^{6} ) ( 0.47 \times 10^{7} ) 15 multiple choice 2 points what is x? 63 inches 45 inches 9 inches 24 inches

Explanation:

13. Triangle Side - Length Relationship

Step1: Apply the triangle - inequality theorem

The triangle - inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|First, find \(b - a\): \(9-5=4\).
Second, find \(a + b\): \(5 + 9=14\).
So, \(4

14. Scientific Notation

Step1: Recall the formula for scientific notation

Scientific notation is of the form \(a\times10^{n}\), where \(1\leqslant|a|<10\) and \(n\) is an integer.
For \(47000000\), move the decimal point 7 places to the left to get \(a = 4.7\). Since we moved the decimal point 7 places to the left, \(n = 7\). So, \(47000000=4.7\times10^{7}\).

15. Pythagorean Theorem

Step1: Use the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = 27\) and \(b = 36\), and \(x\) is the hypotenuse.
\(x=\sqrt{27^{2}+36^{2}}=\sqrt{729 + 1296}=\sqrt{2025}\).
Since \(\sqrt{2025}=45\), \(x = 45\) inches.

Answer:

1. C. \(4 < x < 14\)
2. A. \(4.7\times10^{7}\)
3. B. 45 inches