Question

Consider the following expressions:
−6+3⋅5
______ 16−−√+32÷8
.

Which operator can be inserted to make the statement true?

(1 point)
Responses

≤
less-than-or-equal-to

=
equals

<
less than

>

..

Answer 1

When the value of r is 23, the equation 3r−47.5=21.5
is a true statement. Which of the following values of r makes the inequality 3r−47.5>21.5
a true statement? (1 point)
Responses

23.5
23.5

22
22

22.5
22.5

23

Answer 2

To determine which operator can be inserted to make the statement true, we first need to evaluate both sides of the expression:

**Left Side:**
\(-6 + 3 \cdot 5\)

Calculating:
1. First, compute \(3 \cdot 5 = 15\).
2. Then, add \(-6 + 15 = 9\).

So, the left side equals \(9\).

**Right Side:**
\(\sqrt{16} + 32 \div 8\)

Calculating:
1. First, compute \(32 \div 8 = 4\).
2. Next, calculate \(\sqrt{16} = 4\).
3. Finally, add \(4 + 4 = 8\).

So, the right side equals \(8\).

Now, we compare the results:
- Left side: \(9\)
- Right side: \(8\)

Now we look at the potential operators:
1. **≤** (less than or equal to): \(9 \leq 8\) - false
2. **=** (equals): \(9 = 8\) - false
3. **<** (less than): \(9 < 8\) - false
4. **>** (greater than): \(9 > 8\) - true

Thus, the operator that can be inserted to make the statement true is **> (greater than)**.

Answer 3

To find which value of \( r \) makes the inequality \( 3r - 47.5 > 21.5 \) a true statement, we can start by solving the inequality itself.

1. Start with the inequality:
\[
3r - 47.5 > 21.5
\]

2. Add \( 47.5 \) to both sides:
\[
3r > 21.5 + 47.5
\]
\[
3r > 69
\]

3. Divide both sides by \( 3 \):
\[
r > 23
\]

Now, we need to determine which of the provided options is greater than \( 23 \):

- **23.5**: Yes, it is greater than \( 23 \).
- **22**: No, it is less than \( 23 \).
- **22.5**: No, it is less than \( 23 \).
- **23**: No, it is equal to \( 23 \).

The only value that makes the inequality \( 3r - 47.5 > 21.5 \) a true statement is:

**23.5**.