Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.
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Transcript of Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.
![Page 1: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/1.jpg)
Warm-Up Exercises
ANSWER –1, –3
1. x2 + 4x + 3 = 0
ANSWER 3
2. 6x – 9 = x2
Solve the equation.
![Page 2: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/2.jpg)
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
![Page 3: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/3.jpg)
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.
![Page 4: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/4.jpg)
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.
![Page 5: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/5.jpg)
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
![Page 6: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/6.jpg)
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.
![Page 7: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/7.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
13 = x
ANSWER
![Page 8: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/8.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
x = 8
ANSWER
![Page 9: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/9.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
Find the value(s) of x.
3 = x
ANSWER
![Page 10: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/10.jpg)
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.
![Page 11: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/11.jpg)
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
![Page 12: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/12.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Find the value of x.4.
x = 2
ANSWER
![Page 13: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/13.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Find the value of x.5.
x = 245
ANSWER
![Page 14: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/14.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Find the value of x.6.
x = 8
ANSWER
![Page 15: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/15.jpg)
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
![Page 16: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/16.jpg)
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
![Page 17: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/17.jpg)
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
![Page 18: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/18.jpg)
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
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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.
![Page 20: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/20.jpg)
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.
![Page 21: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/21.jpg)
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
![Page 22: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/22.jpg)
Warm-Up ExercisesDaily Homework Quiz
ANSWER 2
1.
Find the value of x. Round to the nearest tenth,if necessary.
![Page 23: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/23.jpg)
Warm-Up ExercisesDaily Homework Quiz
2.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 9
![Page 24: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/24.jpg)
Warm-Up ExercisesDaily Homework Quiz
3.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 15
![Page 25: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/25.jpg)
Warm-Up ExercisesDaily Homework Quiz
4.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 20.25
![Page 26: Warm-Up Exercises ANSWER –1, –3 1.x 2 + 4x + 3 = 0 ANSWER 3 2.6x – 9 = x 2 Solve the equation.](https://reader035.fdocuments.in/reader035/viewer/2022062309/5697bf8c1a28abf838c8bcd8/html5/thumbnails/26.jpg)
Warm-Up ExercisesDaily Homework Quiz
5.
Find the value of x. Round to the nearest tenth,if necessary.
ANSWER 11.3