Question

Write and then evaluate the expression. Then, check all that apply. Six times the sum of a number cubed and two; evaluate when n = 3 A 2-column table with 6 rows. Column 1 is labeled Key Words with entries six, times, the sum of, a number, cubed, two. Column 2 is labeled Replace with entries 6, times, ( ), n, exponent of 3, 2. The expression is written as 6 × n3 2. The expression is written as 6(n3 2). Evaluate by substituting 3 in for the variable. Simplify by using order of operations. The value of the expression is 174. The value of the expression is 66. The value of the expression is 56.

Answer 1

The student must translate the verbal expression "six times the sum of a number cubed and two" into an algebraic one, which is 6(n^3 + 2). When evaluated with n = 3, the result is 174.

Step-by-step explanation:

The student's task involves writing an algebraic expression based on a word problem and evaluating the expression for a given value of n. The expression given is "six times the sum of a number cubed and two." We can translate this into mathematical notation as 6(n3 + 2). To evaluate when n = 3, we substitute 3 for n and simplify using the order of operations:

Next, we add 2 to the cubed value: 27 + 2 = 29.

Finally, we multiply by 6: 6 × 29 = 174.

The value of the expression when n = 3 is 174. Hence, the correct choice is "The value of the expression is 174."

Answer 2

The expression can also be written as
`6\left(n^3+2\right)`. It is important to follow the order of operations when evaluating expressions. This means that we must perform the exponentiation before the multiplication and addition.

Distribute the 6:

`6 n^3+12`

Substitute n=3:

`6\left(3^3\right)+12`

Simplify:

`\begin{aligned}&6(27)+12\\&162+12\\&174\end{aligned}`

Answer:

`6 n^3+12 ; n=3=174`