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Eleven more than a number squared, decreased by six; evaluate when [tex] t = 5 [/tex].

Key Words | Replace With
------------|--------------
eleven | 11
more than | +
a number | [tex] t [/tex]
squared | exponent of 2
decreased by| -
six | 6

Write and evaluate the expression.

1. Write the expression as [tex] 11 + t^2 - 6 [/tex].

The value when [tex] t = 5 [/tex] is:
- 16
- 30
- 7.5

Answer :

To solve the given problem, we need to translate the phrases into a mathematical expression and then evaluate it when [tex]\( t = 5 \)[/tex].

We start with the key phrases:

1. "eleven more than": This translates to [tex]\( 11 + \)[/tex].
2. "a number squared": If the number is [tex]\( t \)[/tex], then squared means [tex]\( t^2 \)[/tex].
3. "decreased by six": This translates to subtracting 6, or [tex]\( - 6 \)[/tex].

Now combining these:

- "eleven more than a number squared" is [tex]\( 11 + t^2 \)[/tex].
- "decreased by six" results in [tex]\( 11 + t^2 - 6 \)[/tex].

So, the expression is:
[tex]\[ 11 + t^2 - 6 \][/tex]

Let's evaluate this expression when [tex]\( t = 5 \)[/tex]:

1. Substitute [tex]\( t = 5 \)[/tex] into the expression:
[tex]\[ 11 + 5^2 - 6 \][/tex]

2. Calculate [tex]\( 5^2 \)[/tex] (which is [tex]\( 25 \)[/tex]):
[tex]\[ 11 + 25 - 6 \][/tex]

3. Add [tex]\( 11 \)[/tex] and [tex]\( 25 \)[/tex]:
[tex]\[ 36 \][/tex]

4. Subtract [tex]\( 6 \)[/tex] from [tex]\( 36 \)[/tex]:
[tex]\[ 30 \][/tex]

Therefore, the expression [tex]\( 11 + t^2 - 6 \)[/tex] evaluates to [tex]\( 30 \)[/tex] when [tex]\( t = 5 \)[/tex].

Now, let's check the possible answers mentioned:

- Expression [tex]\( 11 + t^2 - 6 \)[/tex]: Correct
- Expression [tex]\( 11 + 2t - 6 \)[/tex]: This is incorrect based on the phrase translation.
- Expression [tex]\( 11 + \frac{t}{2} - 6 \)[/tex]: This is also incorrect based on the phrase translation.

For the values when [tex]\( t = 5 \)[/tex]:

- The value when [tex]\( t = 5 \)[/tex] is [tex]\( 16 \)[/tex]: Incorrect
- The value when [tex]\( t = 5 \)[/tex] is [tex]\( 30 \)[/tex]: Correct
- The value when [tex]\( t = 5 \)[/tex] is [tex]\( 7.5 \)[/tex]: Incorrect

Thus, the correct expression is [tex]\( 11 + t^2 - 6 \)[/tex] and the value when [tex]\( t = 5 \)[/tex] is [tex]\( 30 \)[/tex].

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