Question

question 10 (5 points)
listen
what is the value of x to the nearest tenth?
7
12
x

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = 7\), \(c=12\), and \(b=x\). So \(x^{2}+7^{2}=12^{2}\).

Step2: Solve for \(x^{2}\)

\(x^{2}=12^{2}-7^{2}\). Since \(12^{2}=144\) and \(7^{2} = 49\), then \(x^{2}=144 - 49=95\).

Step3: Find \(x\)

\(x=\sqrt{95}\approx9.7\) (using a calculator to find the square root of 95 and rounding to the nearest tenth).

Answer:

\(9.7\)