1. Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.

2. Warm-Up Exercises ANSWER 4 3. 3(x + 4) = (2 + 4)(4) 4.21(x – 4) = (2x – 7)(x + 2) Solve the equation. ANSWER 5, 7

3. Warm-Up Exercises ANSWER 47.6 5. If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number. Solve the equation.

4. Warm-Up Exercises EXAMPLE 1 Find lengths using Theorem 10.14 Find ML and JK. SOLUTION NK NJ = NL NM Use Theorem 10.14. x (x + 4)= (x + 1) (x + 2) Substitute. x 2 + 4x = x 2 + 3x + 2 Simplify. 4x4x = 3x + 2 Subtract x 2 from each side. x = 2 Solve for x.

5. Warm-Up Exercises EXAMPLE 1 Find lengths using Theorem 10.14 Find ML and JK by substitution. ML= ( x + 2 ) + ( x + 1) = 2 + 2 + 2 + 1 = 7 JK= x + ( x + 4) = 2 + 2 + 4 = 8 SOLUTION

6. Warm-Up Exercises EXAMPLE 2 Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)= 3 (x + 3) Substitute. 36 = 3x + 9 Simplify. 9 = x Solve for x ANSWER The correct answer is D.

7. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. 13 = x ANSWER

8. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. x = 8 ANSWER

9. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. 3 = x ANSWER

10. Warm-Up Exercises EXAMPLE 3 Find lengths using Theorem 10.16 Use the figure at the right to find RS. SOLUTION 256= x 2 + 8x 0= x 2 + 8x – 256 RQ 2 = RS RT 16 2 = x (x + 8) x –8 + 8 2 – 4(1) (– 256) 2(1) = x = – 4 + 4 17 Use Theorem 10.16. Substitute. Simplify. Write in standard form. Use quadratic formula. Simplify.

11. Warm-Up Exercises EXAMPLE 3 Find lengths using Theorem 10.16 Use the positive solution, because lengths cannot be negative. = – 4 + 4 17 So, x 12.49, and RS 12.49

12. Warm-Up Exercises GUIDED PRACTICE for Example 3 Find the value of x.4. x = 2 ANSWER

13. Warm-Up Exercises GUIDED PRACTICE for Example 3 Find the value of x.5. x = 24 5 ANSWER

14. Warm-Up Exercises GUIDED PRACTICE for Example 3 Find the value of x.6. x = 8 ANSWER

15. Warm-Up Exercises GUIDED PRACTICE for Example 3 Determine which theorem you would use to find x. Then find the value of x. 7. x = – 7 + 274 ANSWER

16. Warm-Up Exercises GUIDED PRACTICE for Example 3 Determine which theorem you would use to find x. Then find the value of x. 8. x = 8 ANSWER

17. Warm-Up Exercises GUIDED PRACTICE for Example 3 Determine which theorem you would use to find x. Then find the value of x. 8. x = 16 ANSWER

18. Warm-Up Exercises GUIDED PRACTICE for Example 3 9. In the diagram for Theorem 10.16, what must be true about EC compared to EA ? EC < EA ANSWER

19. Warm-Up Exercises EXAMPLE 4 Solve a real-world problem SCIENCE Tethys, Calypso, and Telesto are three of Saturn’s moons. Each has a nearly circular orbit 295,000 kilometers in radius. The Cassini-Huygens spacecraft entered Saturn’s orbit in July 2004. Telesto is on a point of tangency. Find the distance DB from Cassini to Tethys.

20. Warm-Up Exercises EXAMPLE 4 Solve a real-world problem SOLUTION DC DB = AD 2 Use Theorem 10.16. 83,000 DB 203,000 2 Substitute. DB 496,494 Solve for DB. ANSWER Cassini is about 500,000 kilometers from Tethys.

21. Warm-Up Exercises GUIDED PRACTICE for Examples 4 11. Why is it appropriate to use the approximation symbol in the last two steps of the solution to Example 4 ? Since the distances given are not exact, it is appropriate to use the approximation symbol in the solution. ANSWER

22. Warm-Up Exercises Daily Homework Quiz ANSWER 2 1. Find the value of x. Round to the nearest tenth,if necessary.

23. Warm-Up Exercises Daily Homework Quiz 2. Find the value of x. Round to the nearest tenth,if necessary. ANSWER 9

24. Warm-Up Exercises Daily Homework Quiz 3. Find the value of x. Round to the nearest tenth,if necessary. ANSWER 15

25. Warm-Up Exercises Daily Homework Quiz 4. Find the value of x. Round to the nearest tenth,if necessary. ANSWER 20.25

26. Warm-Up Exercises Daily Homework Quiz 5. Find the value of x. Round to the nearest tenth,if necessary. ANSWER 11.3