Write an algebraic expression to represent each of these 6 verbal expressions.1. 7 less than fifteen times a number
2. the difference of nine times a number and the quotient of 6 and the same number
3. the sum of 100 and four times a number
4. the product of 3 and the sum of 11 and a number
5. four times the square of a number increased by five times the same number
6. 23 more than the product of 7 and a number

Answer:

1. 15n - 7

2. 9n - (6/n)

3. 4n + 100

4. 3(11 + n)

5. 4n^2 + 5n

6. 7n + 23

Step-by-step explanation:

1. "7 less than fifteen times a number" can be represented as 15n - 7, where n represents the unknown number. This expression means that you take the number, multiply it by 15, and then subtract 7 from the result.

2. "The difference of nine times a number and the quotient of 6 and the same number" can be represented as 9n - (6 / n), where n represents the unknown number. This expression means that you take the number, multiply it by 9, and then subtract the quotient of 6 divided by the same number.

3. "The sum of 100 and four times a number" can be represented as 4n + 100, where n represents the unknown number. This expression means that you take the number, multiply it by 4, and then add 100 to the result.

4. "The product of 3 and the sum of 11 and a number" can be represented as 3(11 + n), where n represents the unknown number. This expression means that you take the number, add 11 to it, and then multiply the sum by 3.

5. "Four times the square of a number increased by five times the same number" can be represented as 4n^2 + 5n, where n represents the unknown number. This expression means that you square the number, multiply the result by 4, and then add the product of the number and 5.

6. "23 more than the product of 7 and a number" can be represented as 7n + 23, where n represents the unknown number. This expression means that you take the number, multiply it by 7, and then add 23 to the result.