Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 4+5(x-7)3, for x =9
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Ch. P - Fundamental Concepts of Algebra
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 1, Problem 8
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25
Verified step by step guidance1
Step 1: Begin by identifying the components of the expression. The given expression is √144 + 25, which involves a square root and an addition operation.
Step 2: Evaluate the square root of 144. Recall that the square root of a number is a value that, when multiplied by itself, equals the original number. For example, √144 means finding a number x such that x² = 144.
Step 3: Once the square root of 144 is determined, substitute its value back into the expression. The expression will now be in the form of a simple addition problem.
Step 4: Add the result of the square root to 25. Perform the addition operation to simplify the expression further.
Step 5: Verify that the result is a real number. Since the square root of 144 is a real number and addition does not introduce any imaginary components, the final result will also be a real number.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 144 is 12, since 12 × 12 = 144. Understanding how to calculate square roots is essential for evaluating expressions that involve them.
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Imaginary Roots with the Square Root Property
Real Numbers
Real numbers include all the rational and irrational numbers that can be found on the number line. This concept is crucial when determining whether the result of an expression, such as a square root, is a real number or not. For instance, the square root of a negative number is not a real number.
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03:31Introduction to Complex Numbers
Order of Operations
The order of operations is a set of rules that dictates the sequence in which different mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is vital when evaluating complex expressions.
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8:38Performing Row Operations on Matrices
Related Practice
Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x3+5x2−8x+9)+(17x3+2x2−4x−13)
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Textbook Question
In Exercises 1–10, factor out the greatest common factor. x(2x+1)+4(2x+1)
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16
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Textbook Question
Evaluate each exponential expression in Exercises 1–22. (−3)0
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Textbook Question
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x2−6x+9)
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