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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