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Chapter 0: Problem 44

Write each statement using symbols. The sum of 3 and \(y\) is the sum of 2 and 2 .

Short Answer

Expert verified
3 + y = 2 + 2

Step by step solution

01

Identify Key Components

First, determine the important elements of the statement. The statement talks about the sum of 3 and y, and the sum of 2 and 2.
02

Express in Mathematical Terms

Write the sums using mathematical symbols. The sum of 3 and y can be written as 3 + y. The sum of 2 and 2 can be written as 2 + 2.
03

Set Up the Equality

Combine both expressions into an equation. According to the statement, these two sums are equal. Therefore, write the equation as 3 + y = 2 + 2.

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Key Concepts

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

mathematical symbols
Mathematical symbols help us express complex ideas with simplicity and precision. They serve as a universal language in math! When you see a plus sign (+), it means addition 鈥� combining two or more numbers, variables, or expressions. In the given exercise, we use the plus sign to denote the sum of numbers.
Here, we take the 'sum' as a key word to translate the text into symbols. For example, saying 'the sum of 3 and y' is translated to '3 + y'. Using symbols makes it easier to manipulate and solve math problems.
equations
An equation is a statement that asserts the equality of two expressions. It consists of two sides, usually separated by an equals sign (=).
In the given exercise, we set up the equation by equating 'the sum of 3 and y' to 'the sum of 2 and 2', which are represented as '3 + y' and '2 + 2' respectively. Then, we write the equation as follows:
\(3 + y = 2 + 2\).
This equation tells us that whatever value 'y' holds, when added to 3, it equals 4 (since 2 + 2 equals 4). Equations are pivotal in expressing relationships between variables and constants.
basic algebra
Basic algebra involves using symbols and variables to solve problems. A variable, like 'y' in our example, represents an unknown value that we want to find.
Let's recap the steps:
  • Identify the key components: Here, we identify the sums mentioned in the statement.
  • Express in mathematical terms: Convert 'the sum of 3 and y' to '3 + y' and 'the sum of 2 and 2' to '2 + 2'.
  • Set up the equation: Combine them into one equation: \(3 + y = 2 + 2\).
These steps are fundamental to solving algebraic expressions, where you often translate words into mathematics, set up equations, and find the unknown.

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Most popular questions from this chapter

The final velocity \(v\) of an object in feet per second (ft/s) after it slides down a frictionless inclined plane of height \(h\) feet is $$v=\sqrt{64 h+v_{0}^{2}}$$ where \(v_{0}\) is the initial velocity (in \(\mathrm{ft} / \mathrm{s}\) ) of the object. (a) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 4 feet? Assume that the initial velocity is \(0 .\) (b) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 16 feet? Assume that the initial velocity is \(0 .\) (c) What is the final velocity \(v\) of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of \(4 \mathrm{ft} / \mathrm{s} ?\)

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{5}{\sqrt{2}-1}$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{2}{\sqrt{3}}$$

Simplify each expression. Assume that all variables are positive when they appear. $$6 \sqrt{5}-4 \sqrt{5}$$

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$2 x\left(x^{2}+1\right)^{1 / 2}+x^{2} \cdot \frac{1}{2}\left(x^{2}+1\right)^{-1 / 2} \cdot 2 x$$
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