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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

>

..

3 answers

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).

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

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.