Warm-Up Exercises

ANSWER –1, –3

1. x2 + 4x + 3 = 0

ANSWER 3

2. 6x – 9 = x2

Solve the equation.

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

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.

Warm-Up ExercisesEXAMPLE 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.

x2 + 4x = x2 + 3x + 2 Simplify.

4x = 3x + 2 Subtract x2 from each side.

x = 2 Solve for x.

Warm-Up ExercisesEXAMPLE 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

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

13 = x

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

x = 8

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

3 = x

ANSWER

Warm-Up ExercisesEXAMPLE 3 Find lengths using Theorem 10.16

Use the figure at the right to find RS.

SOLUTION

256 = x2 + 8x

0 = x2 + 8x – 256

RQ2 = RS RT

162 = x (x + 8)

x –8 + 82 – 4(1) (– 256)

2(1)=

x = – 4 + 4 17

Use Theorem 10.16.

Substitute.

Simplify.

Write in standard form.

Use quadratic formula.

Simplify.

Warm-Up ExercisesEXAMPLE 3 Find lengths using Theorem 10.16

Use the positive solution, because lengths cannot be negative.

= – 4 + 4 17So, x 12.49, and RS 12.49

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Find the value of x.4.

x = 2

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Find the value of x.5.

x = 245

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Find the value of x.6.

x = 8

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

7.

x = – 7 + 274

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

8.

x = 8

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

8.

x = 16

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

9. In the diagram for Theorem 10.16, what must be true about EC compared to EA ?

EC < EA

ANSWER

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 4 Solve a real-world problem

SOLUTION

DC DB = AD2 Use Theorem 10.16.

83,000 DB 203,0002 Substitute.

DB 496,494 Solve for DB.

ANSWER

Cassini is about 500,000 kilometers from Tethys.

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesDaily Homework Quiz

ANSWER 2

1.

Find the value of x. Round to the nearest tenth,if necessary.

Warm-Up ExercisesDaily Homework Quiz

2.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 9

Warm-Up ExercisesDaily Homework Quiz

3.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 15

Warm-Up ExercisesDaily Homework Quiz

4.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 20.25

Warm-Up ExercisesDaily Homework Quiz

5.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 11.3