. Which of the following is an English phrase of the given mathematical expression r - 2?
2 minus r
2 less than r
2 is less than r
the sum of r and 2
Answers
Step-by-step explanation:
Recall the definition of a variable presented in Section 1.6.
Definition: Variable
A variable is a symbol (usually a letter) that stands for a value that may vary.
Let’s add the definition of a mathematical expression.
Definition: Mathematical Expression
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.
Thus,
2a, x + 5, and y2,
being formed by a combination of numbers, variables, and mathematical operators, are valid mathematical expressions. A mathematical expression must be well-formed. For example,
2 + ÷5x
is not a valid expression because there is no term following the plus sign (it is not valid to write +÷ with nothing between these operators). Similarly,
2 + 3(2
is not well-formed because parentheses are not balanced.
Translating Words into Mathematical Expressions
In this section we turn our attention to translating word phrases into mathematical expressions. We begin with phrases that translate into sums. There is a wide variety of word phrases that translate into sums. Some common examples are given in Table 3.1.1a3.1.1a , though the list is far from complete. In like manner, a number of phrases that translate into differences are shown in Table 3.1.1b3.1.1b .
Table 3.1.13.1.1 : Translating words into symbols.
sum of x and 12
x + 12
difference of x and 12
x − 12
4 greater than b
b + 4
4 less than b
b − 4
6 more than y
y + 6
7 subtracted from y
y − 7
44 plus r
44 + r
44 minus r
44 − r
3 larger than z
z + 3
3 smaller than z
z − 3
a) Phrases that are sums
b) Phrases that are differences
Let’s look at some examples, some of which translate into expressions involving sums, and some of which translate into expressions involving differences.
Example 1
Translate the following phrases into mathematical expressions:
"12 larger than x,"
"11 less than y," and
"r decreased by 9."
Solution
Here are the translations.
“12 larger than x” becomes x + 12.
“11 less than y” becomes y − 11.
“r decreased by 9” becomes r − 9.
Exercise
Translate the following phrases into mathematical expressions:
"13 more than x" and
"12 fewer than y".
Answer
Example 2
Let W represent the width of the rectangle. The length of a rectangle is 4 feet longer than its width. Express the length of the rectangle in terms of its width W.
Solution
We know that the width of the rectangle is W. Because the length of the rectangle is 4 feet longer that the width, we must add 4 to the width to find the length.
LengthLengthis=44more than+the widthW
Lengthis4more thanthe widthLength=4+W
Thus, the length of the rectangle, in terms of its width W, is 4 + W.
Exercise
The width of a rectangle is 5 inches shorter than its length L. Express the width of the rectangle in terms of its length L.
Answer
Example 3
A string measures 15 inches is cut into two pieces. Let x represent the length of one of the resulting pieces. Express the length of the second piece in terms of the length x of the first piece.
Solution
The string has original length 15 inches. It is cut into two pieces and the first piece has length x. To find the length of the second piece, we must subtract the length of the first piece from the total length.
Step-by-step explanation:
2 minus r OR also 2 deducted from r
Please mark me Brainliest and follow.