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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.
x2 + 4x = x2 + 3x + 2 Simplify.
4x = 3x + 2 Subtract x2 from each side.
x = 2 Solve for x.
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
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.
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
13 = x
ANSWER
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
x = 8 ANSWER
Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
3 = x ANSWER
Warm-Up Exercises EXAMPLE 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 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
Warm-Up Exercises GUIDED PRACTICE for Example 3
Find the value of x. 4.
x = 2 ANSWER
Warm-Up Exercises GUIDED PRACTICE for Example 3
Find the value of x. 5.
x = 24 5
ANSWER
Warm-Up Exercises GUIDED PRACTICE for Example 3
Find the value of x. 6.
x = 8 ANSWER
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
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
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
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
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.
Warm-Up Exercises EXAMPLE 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 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
Warm-Up Exercises Daily Homework Quiz
ANSWER 2
1.
Find the value of x. Round to the nearest tenth,if necessary.
Warm-Up Exercises Daily Homework Quiz
2.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 9
Warm-Up Exercises Daily Homework Quiz
3.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 15
Warm-Up Exercises Daily Homework Quiz
4.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 20.25
Warm-Up Exercises Daily Homework Quiz
5.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 11.3
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