Expressions, Equations, Functions, & Relations

A variable is a letter that represents a number (of something). In programming and mathematics, variables are used to store and manipulate data. They can hold different values at different times, allowing for flexibility and dynamic calculations. The hint provided indicates that the answer has 8 letters, which matches with the word "variable".

The coefficient of a variable is the number in front of the variable. In algebraic expressions, variables are often multiplied by numbers, and the coefficient represents that number. It helps determine the scale or magnitude of the variable's impact on the expression. In this case, "coefficient" is the correct answer, and it has 11 letters.

The given expression translates from an English expression into an Algebraic expression as (a+b)-8 or (A+B)-8. This means that you take the sum of a and b (or A and B) and then subtract 8 from it.

The variable that should be put in the blank is "s" or "S". The function "Juggling (S) = 3 balls X _____" suggests that the number of seconds, represented by "s" or "S", is the variable that determines the number of balls being juggled.

Since Sara has 9 pencils and Sara and Kim together have 15 pencils, it means Kim has 15 - 9 = 6 pencils.
Also, Mark and Kim together have 10 pencils, so if Kim has 6 pencils, Mark must have 10 - 6 = 4 pencils.

Steve deposited $10 each week for 3 weeks, which means he added a total of $30 to his account. His total amount of money in the bank is now $70. To find out how much money he had to start with (x), we need to subtract the amount he deposited ($30) from the total amount in the bank ($70). Therefore, x = $70 - $30 = $40.

The coefficient of x is the number multiplied by x. In this case, the coefficient of x is 1.55 because 1.55x means that x is being multiplied by 1.55.

The correct answer is a-17 or A-17. This represents the English expression "a decreased by 17" translated into an algebraic expression. The variable "a" is being subtracted by 17.

The given question asks for the translation of the English expression "the ratio of m and n" into an algebraic expression. The correct answer is "m/n" or "M/N" as both expressions represent the ratio of m to n, where m is the numerator and n is the denominator.

A function is a "special" type of relationship. In mathematics, a function relates each input value to exactly one output value, which differentiates it from other types of relationships where one input can have multiple outputs.

The purpose of a function and relation is indeed to explain how something works and what is happening. Functions and relations use numbers and variables to describe what is happening, with numbers representing fixed values and variables representing values that can change. This statement accurately describes the purpose of functions and relations, making the answer true.

Math books often use the variable "y" instead of "f(x)". In this case, "y" and "f(x)" are used interchangeably to represent the same thing. For example, the equation "f(x) = x + 6" can also be written as "y = x + 6".

A function is a special type of relation because it assigns exactly one output value to each input value. In other words, for every input, there is only one corresponding output. However, a relation is not always a function because it can have multiple output values for a single input value. Therefore, the statement that a function is a special type of relation and a relation is not always a function is true.

If Brett started on the 10th floor and went up 10 floors, he would be on the 20th floor. Then, if he went down 7 floors, he would be on the 13th floor. Going up 4 floors would bring him to the 17th floor, and going down 6 floors would bring him to the 11th floor. Therefore, he must have started on the 10th floor.

The given expression is 22y/9. In this expression, the coefficient of y is 22/9. This is because the coefficient of a variable is the number that multiplies the variable. In this case, the variable y is being multiplied by 22/9. Therefore, the coefficient of y is 22/9.

The correct answers are all related to the purpose and benefits of weight lifting and juggling balls in class. By doing weight lifting and juggling, students can learn how to "describe a situation" using numbers and variables, understand the purpose of a function in explaining how something works, and decide what input, output, and variables to use in order to make their function easy to understand. These activities provide practical examples and applications of mathematical concepts, helping students develop problem-solving skills and apply mathematical principles in real-life situations.

A function is useful when trying to understand a situation because it provides an exact answer for every input and describes what is happening using numbers that don't change and variables for the things that can change. This allows for a comprehensive understanding of the situation and the ability to analyze different scenarios and variables.

The given equation is trying to express a relationship between Cassie's age and a certain value. The equation states that three times Cassie's age increased by nine is equal to twelve. By solving the equation, we find that the expression 3x + 9, where x represents Cassie's age, is equal to 12.

The algebraic expression for "a number f decreased by 18" is f - 18. This is because the phrase "decreased by" indicates subtraction, and the number being decreased is represented by the variable f. Therefore, f - 18 represents the value of f with 18 subtracted from it.

The correct answer is (3 + 22) / a. This is because the given expression states that the sum of three and twenty-two is divided by the number a. Therefore, we need to add three and twenty-two first, and then divide the sum by a.

The sum means to add. You want to add the two numbers AND then multiply it by four.

An equation and an expression are different in that an equation always contains an equal sign, while an expression does not. An equation represents a mathematical relationship between two or more quantities, indicating that they are equal. On the other hand, an expression is a combination of numbers, variables, and mathematical operations, but it does not show equality. Therefore, the correct answer is that an equation has an equal sign, but an expression does not.

The correct answer is "the product of 25 and k". In mathematical terms, "the product" refers to the result of multiplying two numbers together. Therefore, when we say "the product of 25 and k", it means that we are multiplying the value of 25 with the value of k.

The expression "four less than a number" implies that we are subtracting 4 from the number. In the expression x-4, we are subtracting 4 from x, which aligns with the given expression. Therefore, x-4 is the correct answer.