Math Worksheet - Show Work ### Algebra and Functions - Problem Set#### 1. Simplification of Radicalsa. Simplify \(\sqrt{81x^{16}y^4}\).b. Simplify \(\sqrt[5]{a^{20}b^9c^3}\).#### 2. Factoring Polynomialsa. Factor \(x^2 - 13x + 40\).b. Factor \(x^2 - x - 42\).c. Factor \(50x^2 - 200\).d. Factor \(x^2 + 4\).#### 3. Complex Numbers*For #8, use \(i = \sqrt{-1}\) if necessary*.a. Multiply \(2i(6i-10)\).b. Simplify \(\frac{7}{i}\).c. Simplify \(\sqrt{-100}\).#### 4. Solving Quadraticsa. Solve \((x + 1)^2 = 7\).b. Solve \(x^2 - 6x = 2\).#### 5. Analysis of a Quadratic Function*Consider \(f(x) = (x + 4)^2 + 6\)*.a. Write the coordinates of the vertex.b. Find the y-intercept(s).c. Find the x-intercept(s).#### 6. Function Composition*If \(f(x) = 5x + 1\) and \(g(x) = 3x - 4\), find \((f \circ g)(x)\)*.#### 7. Logarithmsa. Simplify \(\log_4 64\).b. Simplify \(\log 10,000\).c. Simplify \(\log_3 3\).d. Simplify \(\log(8) + \log(25) - \log(2)\).#### 8. Solving Logarithmic and Exponential Equationsa. Solve \(\ln(x + 4) = \ln(3x - 2)\).b. Solve \(2^{x-4} = 8\).c. Solve \(\log_3(x - 1) = 2\).#### 9. Inverse Functions*Given \(f(x) = 3x + 1\), find \(f^{-1

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1. a. Simplify √√81x16y4 b. Simplify Va²0b⁹c3 2. Factor a. x² 13x + 40 b. x²-x-42 c. 50x² - 200 d. x² + 4 3. For #8, use i = √-1 if necessary a. Multiply 21 (61-10). b. Simplify 4. So 5. Cc a b. C

1. a. Simplify √√81x16y4 b. Simplify Va²0b⁹c3 2. Factor a. x² 13x + 40 b. x²-x-42 c. 50x² - 200 d. x² + 4 3. For #8, use i = √-1 if necessary a. Multiply 21 (61-10). b. Simplify 4. So 5. Cc a b. C

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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