Question

Tina wrote mathematical expressions for five statements. Her work is shown. ​ Statement​ ​Tina's Expressions A​ ​The product of a number and seven. ​7n ​B ​The sum of three consecutive numbers. n+(n+1)+(n+2) ​C ​The square of a number times three. ​3n2 ​D ​Twice the sum of a number and 8. ​2n+8 E ​The cube of a number divided by two. ​n3÷2 Did Tina write the correct expressions? Select Correct or Incorrect for each expression. Select Linear or Nonlinear to correctly identify each of Tina's expressions.

Answer 1

See explanation

Explanation:

Linear expression is usually an expression of 1st degree.

A. The product of a number and seven
`=7\cdot n=7n`

Correct, linear

B. The sum of three consecutive numbers.

Let the smallest number be n, the next number is n + 1 and the last number is n + 2. Then their sum is

`n+(n+1)+(n+2)`

Correct, linear

C. ​The square of a number times three.

Let the number be n, then its square is
`n^2` and the square of a number times three is

`n^2\cdot 3=3n^2`

Correct, nonlinear

D. ​Twice the sum of a number and 8.

If the number is n, then the sum of the number anf 8 is n + 8. Twice the sum is

`2\cdot (n+8)=2(n+8)`

Incorrect, linear

E. The cube of a number divided by two.

If the number is n, then its cube is
`n^3.` The cube of the number divided by 3 is

`n^3/ 3`

Correct, nonlinear