Question

Can someone help me solve by showing me how to..

Answer 1

#15) B. 41

#16. A. 6

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.

Answer 2

`15. \: x = \sqrt{ {9}^(2) + {40}^(2) } = √(81 + 1600) = √(1681) = 41 \\ 16. \: x = \sqrt{ {10}^(2) - {8}^(2) } = √(100 - 64) = √(36) = 6`