Question

eleven more than a number squared, decreased
by six;

evaluate when t = 5

A 2-column table with 6 rows. Column 1 is labeled Key Words with entries eleven, more than, a number, squared, decreased by, six. Column 2 is labeled Replace With entries 11, +, t, exponent of 2, minus, 6.

Write and evaluate the expression.Check all that apply.
Write the expression as 11 +t2 -6
Write the expression as 11 +2t -6
Write the expression as 11 +StartFraction t Over 2 EndFraction -6
The value when t = 5 is 16.
The value when t = 5 is 30.
The value when t = 5 is 7.5.

Answer 1

To evaluate the expression "eleven more than a number squared, decreased by six" when \( t = 5 \), we can follow the provided keywords to create the mathematical expression.

1. **Identify the Keywords**:
- Eleven
- More than
- A number (let's denote it as \( t \))
- Squared
- Decreased by
- Six

2. **Replace the Keywords**:
- Eleven = 11
- More than = +
- A number = \( t \)
- Squared = exponent of 2 (which would be \( t^2 \))
- Decreased by = minus (-)
- Six = 6

3. **Write the Expression**:
The expression can be constructed as:
\[
11 + t^2 - 6
\]

4. **Simplify the Expression**:
This simplifies to:
\[
t^2 + 5
\]
(since \( 11 - 6 = 5 \))

5. **Evaluate When \( t = 5 \)**:
Now, substituting \( t = 5 \) into \( 11 + t^2 - 6 \):
\[
11 + (5)^2 - 6 = 11 + 25 - 6
\]
\[
= 11 + 25 - 6 = 30
\]

Now, we can evaluate the options:

- Write the expression as \( 11 + t^2 - 6 \) ✅
- Write the expression as \( 11 + 2t - 6 \) ❌ (This is incorrect because it's not the correct representation of the given phrase)
- Write the expression as \( 11 + \frac{t}{2} - 6 \) ❌ (This is incorrect because it misrepresents the problem)
- The value when \( t = 5 \) is 16. ❌
- The value when \( t = 5 \) is 30. ✅
- The value when \( t = 5 \) is 7.5. ❌

So the correct statements are:
- "Write the expression as \( 11 + t^2 - 6 \)"
- "The value when \( t = 5 \) is 30."