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Chapter 4: Problem 23

List four numbers that are greater than \(-2\) and less than 1

Short Answer

Expert verified
Four numbers could be (-1.5), (-0.5), 0, and 0.5.

Step by step solution

01

Understand the Range

First, identify the range of numbers we are dealing with. The numbers must be greater than (-2) and less than 1.
02

Identify Possible Integers

Look for integers within the range. Start from the smallest integer greater than (-2) which is (-1), and go up to the largest integer less than 1 which is 0.
03

Consider Possible Non-Integers

Between (-2) and 1, there are also non-integer numbers. Any real number like decimals can be included.
04

Select Four Numbers

Choose four numbers within the range (-2) to (1). For example, (-1.5), (-0.5), 0, and 0.5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integers
Integers are whole numbers and their opposites. These include positive numbers, negative numbers, and zero. Common examples are -3, -2, -1, 0, 1, 2, and 3. Integers do not have any fractional or decimal parts. They are often used in counting and basic arithmetic operations. In the given range of numbers that are greater than -2 and less than 1, the integers are -1 and 0.
Integers are important in everyday calculations, such as when you count objects or measure quantities, where fractions are not necessary.
Non-Integers
Non-integers are numbers that do not belong to the set of integers. They can be fractions, decimals, or irrational numbers. For example, 0.5, -1.5, or even \(\frac{1}{3}\). In the context of the range of numbers greater than -2 and less than 1, non-integers help fill in the gaps between whole numbers.
Non-integers allow for more precise measurements and calculations. When you measure something to a fraction of a unit or need a more exact value than a whole number, you are dealing with non-integers.
Real Numbers
Real numbers include all the numbers on the number line. They encompass both integers and non-integers. This set includes rational numbers (like 0.5, -1, and 2) and irrational numbers (like \(\frac{\text{pi}}{},\) which cannot be expressed as a simple fraction).
Real numbers are used in virtually all mathematical calculations in everyday life and science. They represent values that have magnitude and can be used to measure continuous quantities such as length, temperature, and time. Within the range greater than -2 and less than 1, all valid points on that segment of the number line are real numbers.
Decimal Numbers
Decimal numbers are a subset of real numbers that include numbers with a decimal point. For instance, -1.5, 0.75, and 0.333 are all decimal numbers. They can be either finite or infinite but non-repeating. In the given range, examples of decimal numbers include -1.9, -0.5, 0, and 0.5.
Decimal numbers are especially useful in measurements and calculations requiring precision. They help in expressing numbers that fall between integers. Understanding decimal places and how to manipulate these numbers is crucial for accuracy in various fields like science, finance, and engineering.

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Most popular questions from this chapter

Solve the systems of equations in Exercises \(12-15\) by elimination, and check your solutions. Give the following information: \(\cdot\) which equation or equations you rewrote \(\cdot\) how you rewrote each equation \(\cdot\) whether you added or subtracted equations \(\cdot\) the solution $$ \begin{array}{ll}{y=\frac{3}{4} x-4} & {[\mathrm{G}]} \\ {4 y=2 x+3} & {[\mathrm{H}]}\end{array} $$

Wednesday nights are special at the video arcade: customers pay \(\$ 3.50\) to enter the arcade and then only \(\$ 0.25\) to play each game. Roberto brought \(\$ 7.50\) to the arcade and still had some money when he left. Write an inequality for this situation, using \(n\) to represent the number of games Roberto played.

Solve the systems of equations in Exercises \(12-15\) by elimination, and check your solutions. Give the following information: \(\cdot\) which equation or equations you rewrote \(\cdot\) how you rewrote each equation \(\cdot\) whether you added or subtracted equations \(\cdot\) the solution $$ \begin{array}{ll}{2 a+5 b=12} & {[\mathrm{E}]} \\ {3 a+2 b=7} & {[\mathrm{F}]}\end{array} $$

There are six ways to pair these four equations. i. \(y=2 x+4\) ii. \(y+2 x=-4\) iii. \(x=4-\frac{y}{2}\) iv. \(2 y-4 x=10\) a. Predict which pairs of equations do not have a common solution. b. Verify your results for Part a by carefully graphing both equations in each pair you selected. Explain how the graphs do or do not verify your prediction. c. Predict which pairs, if any, have a common solution. d. Verify your results for Part c by graphing both equations in each pair you selected. Explain how the graphs do or do not verify your prediction. e. Use your graphs to find a common solution of each pair of equations you listed in Part c.

Solve this system of quadratic equations by drawing a graph. $$ y=x^{2} \quad y=4-3 x^{2} $$
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