Simplyfying Radical Equation and Rational Exponent
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100
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32
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5
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100
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1000
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81
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216 2
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1296 3
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48
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192
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486
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Simplifying Radical Equations and Rational Exponents, Study notes of Materials Physics
Various topics related to simplifying radical equations and working with rational exponents. It includes examples and step-by-step solutions for simplifying expressions with square roots, cube roots, and other rational exponents. Additionally, the document explores solving quadratic equations using the square root property, completing the square, and factoring or using the quadratic formula. It also covers solving radical equations and absolute value equations. A comprehensive overview of these fundamental algebraic concepts, which are essential for students in high school and college-level mathematics courses. By studying this document, students can develop a deeper understanding of these topics, improve their problem-solving skills, and be better prepared for exams and assignments in their mathematics studies.
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2022/2023
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Simplyfying Radical Equation and Rational Exponent
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Solving quadratic eqaution using the square root property and completing the square
- r = 78
2
- b = 4
2
n
2
- 4 x - 6 = 74
2
- 3 m + 7 = 301
2
- (p - 5 ) = 9
2
3 x
2
- t + 8 t + 15 = 0
2
- 9 n - 6 n = 1
2
- m (m + 10 )= 2
Solving Radical Equations
- 9 x - 5 - 2 = 9
- 6 = 6 x - 3 - 3
x
x 2
2
- x - 3 x - 5 = 5
- m + 18 + 2 = m
- x + 2 = 2 x + 5
- x + 18 = x - 2
- 10 x - 10 = - 60
- n + 6 n + 19 = 2
- x - 5 = x + 1
Solving absolute value equation
| 7 x + 4 |
- |n + 8 | =
- | - 4 + 5 x| =
- 7 | 3 - 3 x| = -
- 8 |x + 7 | - 3 =
- 3 - | 8 x - 6 | =
- 3 - | 8 x - 6 | =
- =
- 2 - 5 | 5 m - 5 | =
- 8 |x + 4 | + 5 =
- 5 + 8 | - 10 x - 2 | =
Circles
Write the equation of the circle and graph
- Center (- 2 , 5 ); radius = 1
- Endpoint of the diameter are (- 2 , 4 ) and ( 6 , - 2 )
- Endpoint of the diameter are (- 3 , 11 ) and ( 3 , - 13 )
- Center (- 11 , - 8 ); radius = 4
- Center ( 14 , 17 ); and a point ( 15 , 17 )
- Center ( 2 , - 5 ) and point (- 7 , - 1 )
- x + y + 14 x - 12 y + 4 = 0
2 2
x
y
22 x
6 y
2 2
- 2 x + 2 y - 32 x + 12 y + 90 = 0
2 2
- 8 x + 32 y + y = - 263 - x
2 2