QuestionWrite algebraic expressions for these phrases: a. 2 times the quantity $y$ plus 11 b. $n$ cubed increased by 5 Check: 18 increased by the product of 3 and $d$ . Identify operations: increased by, product of. Write the expression.

Studdy Solution

STEP 1

Assumptions1. The verbal expressions are to be translated into algebraic expressions. . The words "times", "quantity", "plus", "cubed", "increased by", "product of" are to be interpreted as mathematical operations.
3. The variables used in the expressions are $y$ , $n$ , and $d$ .

STEP 2

Let's start with the first verbal expression "2 times the quantity $y$ plus11". The word "times" implies multiplication, "quantity" implies a group of terms, and "plus" implies addition.

STEP 3

Translate the verbal expression into an algebraic expression. The phrase "2 times the quantity $y$ plus11" can be written as $2(y +11)$

STEP 4

Now, let's move to the second verbal expression " $n$ cubed increased by". The word "cubed" implies a power of3, and "increased by" suggests addition.

STEP 5

Translate the verbal expression into an algebraic expression. The phrase " $n$ cubed increased by5" can be written as $n^3 +5$

STEP 6

Now, let's analyze the verbal phrase "18 increased by the product of3 and $d$ ". The key verbal phrases in the expression are "increased by" and "product of". The phrase "increased by" implies addition, and "product of" implies multiplication.

STEP 7

Translate the verbal phrase into an algebraic expression. The phrase "18 increased by the product of3 and $d$ " can be written as $18 +3d$ So, the algebraic expressions for the given verbal expressions are $2(y +11)$ , $n^3 +5$ , and $18 +3d$ .

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QuestionWrite algebraic expressions for these phrases: a. 2 times the quantity $y$ plus 11 b. $n$ cubed increased by 5 Check: 18 increased by the product of 3 and $d$ . Identify operations: increased by, product of. Write the expression.

Studdy Solution

STEP 1

Assumptions1. The verbal expressions are to be translated into algebraic expressions. . The words "times", "quantity", "plus", "cubed", "increased by", "product of" are to be interpreted as mathematical operations.
3. The variables used in the expressions are $y$ , $n$ , and $d$ .

STEP 2

Let's start with the first verbal expression "2 times the quantity $y$ plus11". The word "times" implies multiplication, "quantity" implies a group of terms, and "plus" implies addition.

STEP 3

Translate the verbal expression into an algebraic expression. The phrase "2 times the quantity $y$ plus11" can be written as $2(y +11)$

STEP 4

Now, let's move to the second verbal expression " $n$ cubed increased by". The word "cubed" implies a power of3, and "increased by" suggests addition.

STEP 5

Translate the verbal expression into an algebraic expression. The phrase " $n$ cubed increased by5" can be written as $n^3 +5$

STEP 6

Now, let's analyze the verbal phrase "18 increased by the product of3 and $d$ ". The key verbal phrases in the expression are "increased by" and "product of". The phrase "increased by" implies addition, and "product of" implies multiplication.

STEP 7

Translate the verbal phrase into an algebraic expression. The phrase "18 increased by the product of3 and $d$ " can be written as $18 +3d$ So, the algebraic expressions for the given verbal expressions are $2(y +11)$ , $n^3 +5$ , and $18 +3d$ .

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QuestionWrite algebraic expressions for these phrases: a. 2 times the quantity yyy plus 11 b. nnn cubed increased by 5 Check: 18 increased by the product of 3 and ddd. Identify operations: increased by, product of. Write the expression.

Studdy Solution

STEP 1

Assumptions1. The verbal expressions are to be translated into algebraic expressions. . The words "times", "quantity", "plus", "cubed", "increased by", "product of" are to be interpreted as mathematical operations.3. The variables used in the expressions are yyy, nnn, and ddd.

STEP 2

Let's start with the first verbal expression "2 times the quantity yyy plus11". The word "times" implies multiplication, "quantity" implies a group of terms, and "plus" implies addition.

STEP 3

Translate the verbal expression into an algebraic expression. The phrase "2 times the quantity yyy plus11" can be written as2(y+11)2(y +11)2(y+11)

STEP 4

Now, let's move to the second verbal expression "nnn cubed increased by". The word "cubed" implies a power of3, and "increased by" suggests addition.

STEP 5

Translate the verbal expression into an algebraic expression. The phrase "nnn cubed increased by5" can be written asn3+5n^3 +5n3+5

STEP 6

Now, let's analyze the verbal phrase "18 increased by the product of3 and ddd". The key verbal phrases in the expression are "increased by" and "product of". The phrase "increased by" implies addition, and "product of" implies multiplication.

STEP 7

Translate the verbal phrase into an algebraic expression. The phrase "18 increased by the product of3 and ddd" can be written as18+3d18 +3d18+3dSo, the algebraic expressions for the given verbal expressions are 2(y+11)2(y +11)2(y+11), n3+5n^3 +5n3+5, and 18+3d18 +3d18+3d.

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QuestionWrite algebraic expressions for these phrases: a. 2 times the quantity $y$ plus 11 b. $n$ cubed increased by 5 Check: 18 increased by the product of 3 and $d$ . Identify operations: increased by, product of. Write the expression.

Assumptions1. The verbal expressions are to be translated into algebraic expressions. . The words "times", "quantity", "plus", "cubed", "increased by", "product of" are to be interpreted as mathematical operations.
3. The variables used in the expressions are $y$ , $n$ , and $d$ .

Let's start with the first verbal expression "2 times the quantity $y$ plus11". The word "times" implies multiplication, "quantity" implies a group of terms, and "plus" implies addition.

Translate the verbal expression into an algebraic expression. The phrase "2 times the quantity $y$ plus11" can be written as $2(y +11)$

Now, let's move to the second verbal expression " $n$ cubed increased by". The word "cubed" implies a power of3, and "increased by" suggests addition.

Translate the verbal expression into an algebraic expression. The phrase " $n$ cubed increased by5" can be written as $n^3 +5$

Now, let's analyze the verbal phrase "18 increased by the product of3 and $d$ ". The key verbal phrases in the expression are "increased by" and "product of". The phrase "increased by" implies addition, and "product of" implies multiplication.

Translate the verbal phrase into an algebraic expression. The phrase "18 increased by the product of3 and $d$ " can be written as $18 +3d$ So, the algebraic expressions for the given verbal expressions are $2(y +11)$ , $n^3 +5$ , and $18 +3d$ .