Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 101

Chapter 1, Problem 101

Evaluate each expression for p=-4, q=8, and r=-10. q+r / q+p

Verified step by step guidance

Identify the given values: $ p = -4 $, $ q = 8 $, and $ r = -10 $.

Write down the expression to evaluate: $ \frac{q + r}{q + p} $.

Substitute the given values into the expression: $ \frac{8 + (-10)}{8 + (-4)} $.

Simplify the numerator and denominator separately: numerator is $ 8 - 10 $, denominator is $ 8 - 4 $.

Write the simplified fraction $ \frac{8 - 10}{8 - 4} $ and prepare to simplify further.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This step is essential to evaluate the expression for specific values of p, q, and r, allowing you to simplify and calculate the result.

Order of Operations

The order of operations (PEMDAS) dictates the sequence in which parts of an expression are evaluated: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Correct application ensures accurate evaluation of expressions.

Simplifying Rational Expressions

A rational expression is a fraction where the numerator and denominator are expressions. Simplifying involves performing arithmetic operations on both parts and reducing the fraction if possible, which is necessary to find the final value of the given expression.

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Simplifying Algebraic Expressions

Related Practice

Textbook Question

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [2(2x-3)^1/3 - (x-1)(2x-3)^-2/3] / [(2x-2)^-2/3]

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Textbook Question

Perform each division. See Examples 9 and 10.

$\frac{(3 x^{3} - 2 x + 5)}{(x - 3)}$

Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (R ∪ N) ∩ M′

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Textbook Question

Add or subtract as indicated. 32.56 + 47.356 + 1.8

Textbook Question

Factor by any method. See Examples 1–7. 4z²+28z+49

Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2

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