Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 7
In Exercises 1–8, add or subtract as indicated and write the result in standard form. 8i - (14 - 9i)
Verified step by step guidance1
Identify the expression to simplify: \(8i - (14 - 9i)\).
Distribute the negative sign across the terms inside the parentheses: \(8i - 14 + 9i\).
Group the real parts and the imaginary parts separately: \((-14) + (8i + 9i)\).
Combine like terms: the real part remains \(-14\), and the imaginary parts add up to \$17i$.
Write the final expression in standard form \(a + bi\): \(-14 + 17i\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Numbers and Standard Form
Complex numbers are expressed in the form a + bi, where a is the real part and b is the imaginary part. Writing the result in standard form means combining like terms so the expression is clearly separated into real and imaginary components.
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05:02
Multiplying Complex Numbers
Distributive Property
The distributive property allows you to remove parentheses by multiplying a term outside the parentheses by each term inside. For example, subtracting (14 - 9i) means distributing the negative sign to both 14 and -9i.
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Guided course
04:15Multiply Polynomials Using the Distributive Property
Combining Like Terms
After distributing, combine the real parts together and the imaginary parts together. This simplifies the expression into a single complex number in standard form, making it easier to interpret and use.
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5:22Combinations
Related Practice
Textbook Question
A new car worth \$36,000 is depreciating in value by \$4000 per year. a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be \$12,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.
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Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (2, ∞)
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Textbook Question
A new car worth \$45,000 is depreciating in value by \$5000 per year. a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be \$10,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
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Textbook Question
Solve and check each linear equation. 11x - (6x - 5) = 40
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