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Chapter 4: Problem 71

Identify the coefficient in the expression \(5 x+9\).

Short Answer

Expert verified
The coefficient is 5.

Step by step solution

01

Understand the Expression

Look at the given expression, which is: \(5x + 9\)
02

Identify the Variable Term

In the expression \(5x + 9\), the term that includes the variable is \(5x\).
03

Find the Coefficient

In the term \(5x\), the number that is multiplying the variable \(x\) is 5. This number is called the coefficient.

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Key Concepts

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

Variable Term
In algebra, expressions often include variable terms. A variable term is any part of the expression that contains a variable, which is typically represented by letters like \(x\), \(y\), or \(z\).

The variable term can stand alone or be attached to a number, known as the coefficient. For example, in the expression \(5x + 9\), the variable term is \(5x\). This means that \(x\) is the variable, and it is being multiplied by the coefficient 5. Recognizing the variable term is essential because it helps you understand how changes to the variable will affect the entire expression.
Algebraic Expression
An algebraic expression is a combination of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. It can be as simple as a single number or variable, or more complex like \(5x + 9\).

Algebraic expressions do not have an equal sign, so they differ from equations. They are used to represent mathematical relationships and can be simplified, evaluated, or transformed in various ways to find an answer or prove a point. Learning to identify parts of an algebraic expression, like coefficients and variable terms, is a crucial skill in algebra.
Multiplication of Variables
When working with algebraic expressions, you will often come across terms where variables are multiplied by numbers. This process is called the multiplication of variables.

For instance, in the term \(5x\), the variable \(x\) is being multiplied by 5. The number 5 is called the coefficient. Understanding this multiplication helps simplify expressions and solve algebraic problems.

To multiply variables, you just place the coefficient next to the variable. For example, if you have 7 multiplied by \(y\), you write it as \(7y\). If you are multiplying two variables together, like \(x\) and \(y\), you write it as \(xy\). This notation keeps expressions neat and clear.

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Most popular questions from this chapter

Determine whether the ordered pair is a solution of the system. $$ \begin{aligned} &(24,12) \\ &-7 x+8 y \geq-200 \\ &x+2 y \geq 57 \\ &y \geq-6 x+45 \end{aligned} $$

The cost to make a product is $$\$ 9.50$$. The fixed overhead costs per month to make the product are $$\$ 2400$$. The price of each product is $$\$ 15.75$$. Find the break-even point for this product.

Graph. Label the solution region. $$ \begin{aligned} &-3 x+4 y \leq 20 \\ &-3 x+4 y \geq 4 \\ &y \geq 0 \\ &y \leq 4 \end{aligned} $$

A timber bolt with a diameter of \(\frac{1}{2} \mathrm{in}\). weighs \(0.9 \mathrm{lb}\) and costs $$\$ 3.73$$. A hex bolt with a diameter of 1 in. weighs \(3 \mathrm{lb}\) and costs $$\$ 7.82$$. The total weight of 30 bolts is \(69 \mathrm{lb}\). Find the number of timber bolts and the number of hex bolts.

A karat describes the percent gold in an alloy (a mixture of metals). $$ \begin{array}{|c|c|} \hline \text { Name of alloy } & \text { Percent gold } \\ \hline \text { 10-karat gold } & 41.7 \% \\ \text { 14-karat gold } & 58.3 \% \\ \text { 18-karat gold } & 75 \% \\ \text { 20-karat gold } & 83.3 \% \\ \text { 24-karat gold } & 100 \% \\ \hline \end{array} $$ Find the amount of 10-karat gold and 20 -karat gold to combine to make 3 g of 14-karat gold. Round to the nearest hundredth.
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