Julie Miller, Molly O'Neill, Nancy Hyde
ISBN #9781259610233
5th Edition
5,614 Questions
Homework Questions
Intermediate Algebra is a comprehensive guide that reinforces essential algebraic concepts while steadily progressing to more advanced topics. The book starts by solidifying foundational skills such as combining like terms and solving linear equations, and then expands into areas including systems of equations, polynomial operations, and rational expressions. It methodically introduces complex topics like quadratic equations, exponential and logarithmic functions, and conic sections, emphasizing both theoretical understanding and practical applications. By integrating clear explanations with real-world problem-solving strategies, the text equips students with a robust mathematical toolkit for tackling diverse challenges in later studies and various applied fields.
Chapter 0
Review of Basic Algebraic Concepts
Chapter 1
Linear Equations and Inequalities in One Variable
Chapter 2
Linear Equations in Two Variables and Functions
Chapter 3
Systems of Linear Equations and Inequalities
Chapter 4
Polynomials
Chapter 5
Rational Expressions and Rational Equations
Chapter 6
Radicals and Complex Numbers
Chapter 7
Quadratic Equations, Functions, and Inequalities
Chapter 8
Exponential and Logarithmic Functions and Applications
Chapter 9
Conic Sections
Chapter 10
Binomial Expansions, Sequences, and Series
Chapter 11
Transformations, Piecewise-Defined Functions, and Probability
Problem 1
a. Consider a line with slope $m$ and $y$ -intercept (0, $b$ ). The slope-intercept form of an equation of the line is _____. b. An equation of a line written in the form $A x+B y=C$, where $A$ and $B$ are not both zero, is said to be in _____ form. c. A line defined by an equation $y=k$, where $k$ is a constant is a (horizontal/vertical) line. d. A line defined by an equation $x=k$, where $k$ is a constant is a (horizontal/vertical) line. e. Given the slope-intercept form of an equation of a line, $y=m x+b,$ the value of $m$ is ______ the and $b$ is the _____. f. Given a point $\left(x_{1}, y_{1}\right)$ on a line with slope $m,$ the point-slope formula is given by _____.
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Problem 2
a. A ______ in the variable, $x$, is a single term or a sum of terms of the form $a x^{n}$, where $a$ is a real number and $n$ is a nonnegative integer. b. Given the term $a x^{n}, a$ is called the ______ and _______ is called the degree of the term. c. Given the term $x,$ the coefficient of the term is _______ and the degree is _____. d. A monomial is a polynomial with exactly ______ term(s). e. A_______ is a polynomial with exactly two terms. f. A ______ is a polynomial with exactly three terms. g. The term in a polynomial with the highest degree is called the _____ term and its coefficient is called the _______ ______. h. The degree of a polynomial is the _____ degree of all of its terms. i. The degree of a nonzero constant such as 7 is ______ j. If a term of a polynomial has more than yariable, then the degree of the term is the sum of the _____ of the variables contained in the term. k. A ______ function is a function defined by a finite sum of terms of the form $a x^{n},$ where $a$ is a real number and $n$ is a whole number.
Problem 3
a. A set of ordered pairs $(x, y)$ is called a __________ in $x$ and $y$ . b. The _____________ of a relation is the set of first components in the ordered pairs. c. The ______________of a relation is the set of second components in the ordered pairs.
Problem 4
a. If $n$ is an integer greater than $1,$ then radical notation for $a^{1 / n}$ is ______. b. Assume that $m$ and $n$ are positive integers that share no common factors and $n>1 .$ If $\sqrt[n]{a}$ exists, then in radical notation a^{m / n}= ______. c. The radical notation for $x^{-1 / 2}$ is _______. d. $8^{1 / 3}=$ _______ and $8^{-1 / 3}=$ _______..
Problem 5
a. Factoring a polynomial means to write it as a ______ of two or more polynomials. b. The ______ ______ ______ (GCF) of a polynomial is the greatest factor that divides each term of the polynomial evenly. c. The first step toward factoring a polynomial is to factor out the ______ ______ ______. d. To factor a four-term polynomial, we try the process of factoring by ______.
Problem 6
a. Integers that follow one after the other without “gaps” are called ________ integers. b. The integers $-2,0,2,$ and 4 are examples of consecutive ________ integers, and the integers $-3,-1,1,$ and 3 are examples of consecutive ________ integers. c. Two consecutive integers differ by ________, two consecutive odd integers differ by ________, and two consecutive even integers differ by ________. d. If $x$ represents the smaller of two consecutive integers, then the expression ________ represents the next greater consecutive integer. e. If $x$ represents the smaller of two consecutive odd integers, then the expression ________ represents the next greater consecutive odd integer. f. If $x$ represents the smallest of three consecutive even integers, then the expressions ________ and ________ represent the next two greater consecutive even integers. g. Simple interest is interest computed on the principal invested or borrowed. Simple interest is computed as $I=$ ________ where $P$ is the principal, $r$ is the annual ________ rate, and $t$ is the time in years. h. If $\$ 5000$ is borrowed at $6.5 \%$ simple interest for 4 yr, then the amount of simple interest is ________. i. Suppose that $12 \%$ of a solution is acid by volume and the remaining $88 \%$ is water. Then the amount of acid in a 4-L container of solution is ________. The amount of acid in a container containing $x+8$ liters of solution is represented by the expression _______. j. If $d=r t,$ then $r=\frac{\square}{\square}$ and $t=\frac{\square}{\square}$.
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