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[tex]15. \: x = \sqrt{ {9}^{2} + {40}^{2} } = \sqrt{81 + 1600} = \sqrt{1681} = 41 \\ 16. \: x = \sqrt{ {10}^{2} - {8}^{2} } = \sqrt{100 - 64} = \sqrt{36} = 6[/tex]

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Answer:

#15) B. 41

#16. A. 6

Step-by-step explanation:

#15:

You are given the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse of the right triangle.

In problem 15, x is the hypotenuse and 9 and 40 are the legs, so you can substitute these values into the formula and solve for c (x).

  • (9)^2 + (40)^2 = c^2

Evaluate the exponents.

  • 81 + 1600 = c^2

Add the like terms together.

  • 1681 = c^2

Square root both sides of the equation.

  • c = 41

Since c = x, the answer for #15 is b. 41.

#16:

x and 8 are the legs and 10 is the hypotenuse, so substitute these values into the formula. Make x = a.

  • a^2 + (8)^2 = (10)^2

Evaluate the exponents.

  • a^2 + 64 = 100

Subtract 64 from both sides of the equation.

  • a^2 = 36

Square root both sides of the equation.

  • a = 6

The answer is A. 6.

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