Chapter 2

Fill in the blank. Consider a collection of ordered pairs of the form \((x, y) .\) If \(y\) tends to increase as \(x\) increases, then the collection is said to have a __________ correlation.

Fill in the blank(s). It is sometimes possible to write two inequalities as one inequality, called a _____ inequality.

Fill in the blank. An equation of the form \(a x^{2}+b x+c=0,\) where \(a, b,\) and \(c\) are real numbers and \(a \neq 0,\) is a _______ , or a second-degree polynomial equation in \(x .\)

Fill in the blank. The general form of a ____ equation is $$a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}=0$$

Match the type of complex number with its definition. (a) real number (b) imaginary number (c) pure imaginary number (i) \(a+b i, a=0, b \neq 0\) (ii) \(a+b i, b=0\) (iii) \(a+b i, a \neq 0, b \neq 0\)

Fill in the blank(s). The points \((a, 0)\) and \((0, b)\) are called the______ and _______ respectively, of the graph of an equation.

Fill in the blank. A (n) ________ is a statement that two algebraic expressions are equal.

To find the least squares regression line for data, you can use the ___________ feature of a graphing utility.

Fill in the blank. The part of the Quadratic Formula \(b^{2}-4 a c,\) known as the __________ , determines the type of solutions of a quadratic equation.

Fill in the blank. To clear the equation \(\frac{4}{x}+5=\frac{6}{x-3}\) of fractions, multiply each side of the equation by the least common denominator _____ .

The imaginary unit \(i\) is defined as \(i=\)_________ . where \(i^{2}=\) __________.

Fill in the blank(s). A ______ of a function is a number \(a\) such that \(f(a)=0\)

In a collection of ordered pairs \((x, y), y\) tends to decrease as \(x\) increases. Does the collection have a positive correlation or a negative correlation?

Fill in the blank(s). The solutions of \(|x| \geq a\) are those values of \(x\) such that _____ or _____.

List four methods that can be used to solve a quadratic equation.

Fill in the blank. Describe the step needed to remove the radical from the equation \(\sqrt{x+2}=x.\)

The set of real multiples of the imaginary unit \(i\) combined with the set of real numbers is called the set of ____________ numbers, which are written in the standard form _________.

Fill in the blank. When solving an equation, it is possible to introduce a(n) ______ solution, which is a value that does not satisfy the original equation.

You find the least squares regression line for a set of data. The correlation coefficient is 0.1 14. Is the model a good fit?

What does the equation \(s=-16 t^{2}+v_{0} t+s_{0}\) represent? What do \(v_{0}\) and \(s_{0}\) represent?

Fill in the blank. Is the equation \(x^{4}-2 x+4=0\) of quadratic type?

What method for multiplying two polynomials can you use when multiplying two complex numbers?

Fill in the blank. Many real-life problems can be solved using ready-made equations called _______.

Constructing a Scatter Plot The following ordered pairs give the years of experience \(x\) for 15 sales representatives and the monthly sales \(y\) (in thousands of dollars). $$\begin{aligned} &(1.5,41.7),(1.0,32.4),(0.3,19.2),(3.0,48.4)\\\ &(4.0,51.2),(0.5,28.5),(2.5,50.4),(1.8,35.5)\\\ &(2.0,36.0),(1.5,40.0),(3.5,50.3),(4.0,55.2)\\\ &(0.5,29.1),(2.2,43.2),(2.0,41.6) \end{aligned}$$ (a) Create a scatter plot of the data. (b) Does the relationship between \(x\) and \(y\) appear to be approximately linear? Explain.

Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. $$4 x^{4}-16 x^{2}=0$$

Are the inequalities \(x-4<5\) and \(x>9\) equivalent?

Write the quadratic equation in general form. Do not solve the equation. $$2 x^{2}=3-5 x$$

What is the additive inverse of the complex number \(2-4 i ?\)

Fill in the blank. Is the equation \(x+1=3\) an identity, a conditional equation, or a contradiction?

Constructing a Scatter Plot The following ordered pairs give the scores on two consecutive 15 -point quizzes for a class of 18 students. $$\begin{aligned} &(7,13),(9,7),(14,14),(15,15),(10,15),(9,7)\\\ &(14,11),(14,15),(8,10),(9,10),(15,9),(10,11)\\\ &(11,14),(7,14),(11,10),(14,11),(10,15),(9,6) \end{aligned}$$ (a) Create a scatter plot of the data. (b) Does the relationship between consecutive quiz scores appear to be approximately linear? If not, give some possible explanations.

Which property of inequalities is shown below? $$a