Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

What is the value of x?

What Is The Value Of X class=

Sagot :

Answer:

B

Step-by-step explanation:

Since UV is a tangent then ∠ WUV = 90°

WZ = WU = x - 1 ( both radii of the circle ) , then

WV = x - 1 + 2 = x + 1

Using Pythagoras' identity in the right triangle

WU² + UV² = WV² , that is

(x - 1)² + (2x - 4)² = (x + 1)² ← expand factors using FOIL

x² - 2x + 1 + 4x² - 16x + 16 = x² + 2x + 1

5x² - 18x + 17 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides

4x² - 20x + 16 = 0 ← divide through by 4

x² - 5x + 4 = 0

(x - 1)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

But x ≠ 1 as radius x - 1 = 0

Thus x = 4 → B

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.