1.
A number's distance from zero on a number line is called the _____________ ______________.
Explanation
The distance from zero on a number line is referred to as the absolute value. It represents the magnitude or size of a number without considering its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
2.
The opposite of a number is called the ________________ ________________.
Explanation
The opposite of a number is called the additive inverse. This means that when you add a number to its additive inverse, the result is always zero. For example, the additive inverse of 5 is -5, because 5 + (-5) = 0. Similarly, the additive inverse of -3 is 3, because -3 + 3 = 0. The concept of additive inverse is important in mathematics and helps in solving equations and understanding number properties.
3.
An expression that contains a variable is called a _______________ ____________.
Explanation
An expression that contains a variable is called an algebraic expression. This is because algebraic expressions involve variables and can include operations such as addition, subtraction, multiplication, and division. These expressions are commonly used in algebra to represent mathematical relationships and equations.
4.
If three or more numbers are added or multiplied, the numbers can be regrouped without changing the result by using the ______________ property.
Explanation
The associative property states that when adding or multiplying three or more numbers, the numbers can be regrouped in any way without changing the result. This means that the order in which the numbers are grouped does not affect the final sum or product.
5.
Either of two number lines used to form a coordinate grid is called a ________________.
Explanation
An axis refers to either of the two number lines used to form a coordinate grid. It is a reference line that helps determine the position of points on the grid. The x-axis represents the horizontal line, while the y-axis represents the vertical line. These axes intersect at the origin, which is the point (0,0) on the grid.
6.
An expression consisting of two terms connected by a plus or minus sign is called a __________________.
Explanation
An expression consisting of two terms connected by a plus or minus sign is called a binomial. This term is used in algebra to describe a mathematical expression that contains two unlike terms connected by addition or subtraction. It is important to note that a binomial can also be a polynomial, but not all polynomials are binomials.
7.
The numerical factor when a term has a variable is called the _____________________.
Explanation
The numerical factor when a term has a variable is called the coefficient. The coefficient represents the value by which the variable is multiplied in the term. It helps determine the scale or magnitude of the variable in the equation or expression.
8.
If two numbers are added or multiplied, the operations can be done in any order. This is called the __________________ property
Explanation
The given answer is "commutative". This property states that for addition or multiplication, the order in which the numbers are arranged does not affect the result. In other words, if you add or multiply two numbers, you will get the same result regardless of the order in which you perform the operation. For example, 2 + 3 is equal to 3 + 2, and 4 x 5 is equal to 5 x 4.
9.
Any integer that is not a prime number is called a ______________ number.
Explanation
A composite number is any integer that is not a prime number. Prime numbers are only divisible by 1 and themselves, while composite numbers have additional factors. Therefore, the correct answer is "composite".
10.
In an algebraic expression, the number without the variable is called a _______________.
Explanation
In an algebraic expression, the number without the variable is called a constant. A constant is a fixed value that does not change. It is a term in the expression that does not contain any variables and represents a specific value. In algebraic equations, constants are used to represent known quantities or fixed values that are used in calculations.
11.
A method of locating points in the plane or in space by means of numbers is called _________________ plane.
Explanation
The method described in the question is known as the Cartesian plane. This method involves assigning numerical coordinates to points in order to locate them in the plane or in space. The term "Cartesian" refers to the mathematician RenÃ© Descartes, who developed this coordinate system.
12.
A variable that provides the output values of a function is called the ________________.
Explanation
The correct answer is the dependent variable. In a function, the dependent variable is the variable that is affected by the independent variable(s) and provides the output values. The range is the set of all possible output values of a function. "Y values" is a general term used to refer to the values of the dependent variable in a function.
13.
The answer to a subtraction problem is called the ____________________.
Explanation
The answer to a subtraction problem is called the "difference" because it represents the numerical result obtained when one quantity is subtracted from another.
14.
A property that relates two operations on numbers, usually multiplication and division, or multiplication and subtraction is called the ______________ property.
Explanation
The property that relates two operations on numbers, usually multiplication and division, or multiplication and subtraction, is called the distributive property. This property states that when multiplying a number by a sum or difference, you can distribute the multiplication to each term within the parentheses. This allows you to simplify expressions and perform calculations more efficiently.
15.
The set of all first coordinates from the ordered pairs of a relation is called the ___________________.
Explanation
The set of all first coordinates from the ordered pairs of a relation is referred to as the domain, x values, or independent variables. These terms are used interchangeably to describe the input values of a relation or function. The domain represents all the possible values that can be inputted into the relation or function to obtain corresponding output values.
16.
A mathematical sentence containing an equal sign is called an ____________________.
Explanation
An equation is a mathematical sentence that contains an equal sign. It represents the equality between two expressions or quantities. In an equation, both sides of the equal sign must be balanced or equivalent. This allows for solving the equation and finding the value of the unknown variable.
17.
A function in the form of f(x) = a^x, wher "x" is a real number, and "a" is positive and not 1 is called a _______________ function.
Explanation
A function in the form of f(x) = a^x, where "x" is a real number and "a" is a positive number (not equal to 1), is called an exponential function. Exponential functions involve a base "a" raised to the power of "x", resulting in a rapid increase or decrease in values as "x" changes. These functions are commonly used in various fields such as finance, population growth, and radioactive decay.
18.
A mathematical statement that does not contain an equal sign is called an _____________________.
Explanation
An expression is a mathematical statement that does not contain an equal sign. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Unlike an equation, which shows the equality between two expressions, an expression is simply a representation of a mathematical relationship or calculation.
19.
Any numbers multiplied by another number to produce a product is called a ______________________.
Explanation
A factor is a number that divides evenly into another number, resulting in a whole number quotient. It is one of the numbers that, when multiplied together, gives the product. A multiple, on the other hand, is a number that is obtained by multiplying a given number by any integer. In this context, both factors and multiples can be used to describe numbers that are multiplied together to produce a product.
20.
A method used to solve a quadratic equation that requires using the zero product property is called __________.
Explanation
Factoring is a method used to solve a quadratic equation that requires using the zero product property. The zero product property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. In the case of a quadratic equation, factoring involves finding two binomial factors that multiply to give the quadratic equation, and then setting each factor equal to zero to find the solutions.
21.
To write a rule in fuctions notation, you use the symbol f(x) in place of y is called ____________ notation.
Explanation
In functions notation, the symbol f(x) is used in place of y. This notation is called "function" notation. It is a way to represent a mathematical relationship between an input value (x) and its corresponding output value (f(x)). By using function notation, we can easily express and manipulate mathematical functions.
22.
A variable that provides the input values of a function is called a ________________ _____________.
Explanation
The correct answer is independent variable or x values. In mathematics and statistics, the independent variable is the variable that is manipulated or controlled in order to observe its effect on the dependent variable. It is also commonly referred to as the x variable or x values in the context of a function. The independent variable is crucial in determining the output or outcome of the function.
23.
A mathematical statement that one quantity is less that or greater than another is a________________.
Explanation
A mathematical statement that one quantity is less than or greater than another is called an inequality. Inequalities are used to compare two quantities and express the relationship between them. They are represented by symbols such as < (less than), > (greater than), â‰¤ (less than or equal to), and â‰¥ (greater than or equal to). Inequalities are an important concept in mathematics and are used in various fields such as algebra, calculus, and statistics.
24.
The set of whole numbers and their opposites is the _______________.
Explanation
The set of whole numbers includes all positive numbers and zero. However, the set of integers includes both positive and negative numbers, as well as zero. Therefore, the set of whole numbers and their opposites is the set of integers.
25.
Real numbers that cannot be expressed as a fraction are called ______________ numbers.
Explanation
Real numbers that cannot be expressed as a fraction are called irrational numbers. These numbers cannot be written as a ratio of two integers and their decimal representation goes on indefinitely without repeating. Examples of irrational numbers include âˆš2, Ï€, and e.
26.
A function that has a constant rate of change and can be modeled by a straight line is called a ______________ __________.
Explanation
A linear function is a function that has a constant rate of change and can be modeled by a straight line. This means that for every unit increase in the independent variable, the dependent variable also increases by a constant amount. The graph of a linear function is a straight line, and the equation of a linear function can be written in the form y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
27.
The sum of a set of numbers divided by the number of numbers in that set is called the ____________.
Explanation
The sum of a set of numbers divided by the number of numbers in that set is called the mean.
28.
In a list of data ordered from least to greatest or greatest to least, the middle number or the average of the middle two number is called the _____________.
Explanation
The middle number or the average of the middle two numbers in a list of data ordered from least to greatest or greatest to least is called the median.
29.
The smallest number in a set is called the ___________________.
Explanation
The smallest number in a set is called the minimum. This term is used to describe the value that is the lowest or smallest among all the numbers in a given set. It is often used in mathematical and statistical contexts to identify the smallest element or value in a data set or sequence. The minimum is an important concept in analyzing data and making comparisons between different values.
30.
In a list of data, the number or item occurring the most is called the _______________.
Explanation
The mode is the number or item that occurs the most frequently in a list of data. It represents the value that appears with the highest frequency, making it the most common or popular element in the dataset.
31.
One fo the numbers 1, 2, 3, 4, ... also called counting number are called the ___________ numbers.
Explanation
The numbers 1, 2, 3, 4, ... are known as natural numbers.
32.
The graph of a quadratic funciton is called a ________________.
Explanation
A parabola is the graph of a quadratic function. It is a U-shaped curve that opens either upwards or downwards, depending on the coefficient of the quadratic term. The term "parabola" comes from the Greek word meaning "to throw alongside" because a parabola is the shape formed when an object is thrown and follows a curved path. In mathematics, a parabola is a fundamental concept in algebra and is used to model various real-world phenomena, such as the trajectory of a projectile or the shape of a satellite dish.
33.
In algebra, an expresion consisting of two or more terms is called a _____________________.
Explanation
An expression consisting of two or more terms is called a polynomial. A polynomial is a mathematical expression that contains variables, coefficients, and exponents. It can have addition, subtraction, and multiplication operations between the terms. The terms in a polynomial are combined using these operations, and the resulting expression is considered a polynomial.
34.
A whole number greater than one having exactly two distinct factors, one and itself, is called a _____________ ___________.
Explanation
A prime number is a whole number greater than one that only has two distinct factors, which are one and itself. It cannot be divided evenly by any other number.
35.
How likely it is that an event will occur is called ______________.
Explanation
Probability refers to the likelihood or chance of an event occurring. It is a measure of the likelihood that a particular event will happen, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty. In other words, probability is a way to quantify how likely it is that a specific outcome will happen. It is a fundamental concept in statistics and is used in various fields such as mathematics, science, and finance to analyze and predict the likelihood of different events occurring.
36.
An equation that states that two reatios are equal is called a _____________________.
Explanation
An equation that states that two ratios are equal is called a proportion. In a proportion, the four quantities involved are in a specific relationship, where the product of the means is equal to the product of the extremes. This concept is used in various mathematical problems, such as solving for unknown values or comparing quantities.
37.
In a right triangle, the sum of the squares of the length of the legs is equal to the square of the length of the hypotenuse. This is called the ______________ ________________. (a^2 + b^2 = c^2)
Explanation
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This theorem is a fundamental concept in geometry and is used to calculate the length of one side of a right triangle when the lengths of the other two sides are known.
38.
A function that has an equation of the form y = ax^2 + bx + c, where "a" does not equal 0 is called a _____________ function.
Explanation
A function that has an equation of the form y = ax^2 + bx + c, where "a" does not equal 0 is called a quadratic function. In this type of function, the variable x is raised to the power of 2, making it a second degree polynomial. The coefficients a, b, and c determine the shape and position of the parabola that represents the function. Quadratic functions are commonly used to model various real-life situations, such as projectile motion or the shape of a satellite dish.
39.
The set of all the second coordinates from the set of ordered pairs of a relation is called the _________________.
Explanation
The set of all the second coordinates from the set of ordered pairs of a relation is called the range. It can also be referred to as outputs, y values, y-values, or the dependent variable.
40.
A number in the form of a fraction is called a _______________ number.
Explanation
A number in the form of a fraction is called a rational number. This is because a rational number can be expressed as the quotient or division of two integers, where the denominator is not zero. Rational numbers include both positive and negative fractions, as well as whole numbers and integers, making them a broad category of numbers.
41.
The zeros of an equation that occur at x-intercepts of the graph of a related function are called _______________.
Explanation
The zeros of an equation that occur at x-intercepts of the graph of a related function are referred to as roots or solutions. These terms are used interchangeably to describe the values of x for which the function equals zero.
42.
A set of ordered pairs of data is called a ______________.
Explanation
A set of ordered pairs of data is called a relation. In mathematics, a relation is a set of pairs that relate elements from one set to elements of another set. Each pair consists of an input value (x) and an output value (y), which are connected by a rule or condition. Relations can be represented as tables, graphs, or equations, and they are used to analyze and describe the relationship between different variables or quantities.
43.
The ratio of the vertical change to the horizontal change is called the _______________.
Explanation
The ratio of the vertical change to the horizontal change is called the slope. Slope represents the steepness or incline of a line and is calculated by dividing the change in y-coordinates by the change in x-coordinates. It is a fundamental concept in mathematics and is used to analyze the relationship between variables in various fields such as physics, engineering, and economics.
44.
A linear equation in the form y = mx + b, where m is the slope and b is the y-intercept is called ______ ________ _______.
Explanation
The given equation y = mx + b is in the form of a linear equation known as the slope-intercept form. In this form, m represents the slope of the line, which determines the steepness or direction of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis. Therefore, the correct answer is slope intercept form.
45.
An expression containing three terms connected by a plus or minus sign is called a __________________.
Explanation
An expression containing three terms connected by a plus or minus sign is called a trinomial.
46.
A letter that can assume different values is called a _____________.
Explanation
A letter that can assume different values is called a variable. This term is commonly used in programming and mathematics to refer to a symbol or name that represents a value that can change. Variables are used to store and manipulate data in order to perform calculations or execute instructions in a program. By assigning different values to a variable, its value can be altered and used in various computations or operations.
47.
The set of datural numbers and zero is called the ________________ numbers.
Explanation
The set of natural numbers includes all positive integers starting from 1. However, when we include zero in the set, it becomes the set of whole numbers. Therefore, the given set of natural numbers and zero is called the whole numbers.
48.
The x-intercepts of a quadratic equation that crosses the x-axis are called the ___________.
Explanation
The x-intercepts of a quadratic equation that crosses the x-axis are called zeros or solutions. Zeros refer to the values of x where the equation equals zero, while solutions refer to the values of x that satisfy the equation. These terms are used interchangeably to describe the points where the quadratic equation intersects the x-axis.