Evaluate the expression "eleven more than a number squared, decreased by six" when [tex]t = 5[/tex].

Key Terms:
- Eleven: 11
- More than: +
- A number: [tex]t[/tex]
- Squared: exponent of 2
- Decreased by: -
- Six: 6

Tasks:
1. Write the expression as [tex]11 + t^2 - 6[/tex].
2. Evaluate the expression for [tex]t = 5[/tex].

The value of the expression when [tex]t = 5[/tex] is 30.

Let's analyze the wording step by step:

1. The phrase “eleven more than a number squared” tells us to start with the square of a number and then add 11. In mathematical terms, if the number is [tex]$t$[/tex], then “a number squared” is [tex]$t^2$[/tex] and “eleven more than” means add [tex]$11$[/tex] to that. This gives:
[tex]$$
t^2 + 11.
$$[/tex]

2. Next, the phrase “decreased by six” indicates that we subtract 6 from the previous expression:
[tex]$$
t^2 + 11 - 6.
$$[/tex]

3. When [tex]$t = 5$[/tex], substitute [tex]$5$[/tex] for [tex]$t$[/tex]. Since [tex]$t^2$[/tex] means [tex]$5^2$[/tex], we have:
[tex]$$
5^2 + 11 - 6.
$$[/tex]
Calculate [tex]$5^2 = 25$[/tex], so the expression becomes:
[tex]$$
25 + 11 - 6.
$$[/tex]

4. Now, perform the arithmetic:
[tex]$$
25 + 11 = 36, \quad\text{and then}\quad 36 - 6 = 30.
$$[/tex]

Thus, when [tex]$t = 5$[/tex], the expression evaluates to [tex]$30$[/tex].

To summarize:
- The expression is written as: [tex]$$11+t^2-6.$$[/tex]
- The value of the expression when [tex]$t = 5$[/tex] is [tex]$$30.$$[/tex]