Domanda del libro di testo
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 15
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). (2x+3y)/(x+1), for x=-2 and y=4
Guida verificata passo dopo passo1
Step 1: Begin by substituting the given values of the variables into the algebraic expression. Replace x with -2 and y with 4 in the expression \((2x + 3y) / (x + 1)\).
Step 2: Substitute the values into the numerator \(2x + 3y\). This becomes \(2(-2) + 3(4)\).
Step 3: Substitute the value of x into the denominator \(x + 1\). This becomes \((-2) + 1\).
Step 4: Simplify the numerator \(2(-2) + 3(4)\) by performing the multiplication and addition operations.
Step 5: Simplify the denominator \((-2) + 1\) by performing the addition operation. Combine the simplified numerator and denominator to form the final fraction.
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Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression (2x + 3y) / (x + 1) combines both variables and constants, and understanding how to manipulate these expressions is crucial for evaluation.
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Introduction to Algebraic Expressions
Substitution
Substitution is the process of replacing variables in an expression with their corresponding numerical values. For the given expression, substituting x = -2 and y = 4 allows us to simplify the expression into a numerical form, which is essential for evaluating the expression correctly.
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5:48Solving Systems of Equations - Substitution
Order of Operations
The order of operations is a set of rules that dictates the sequence in which calculations are performed in an expression. It is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Following this order ensures that the evaluation of the expression yields the correct result.
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Pratica correlata
Domanda del libro di testo
Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers.
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Domanda del libro di testo
In Exercises 15–58, find each product. (x+1)(x2−x+1)
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Domanda del libro di testo
In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (x2−14x+49)/(x2−49)
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Multiply or divide as indicated.
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Domanda del libro di testo
Evaluate each exponential expression in Exercises 1–22.
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