Question

Consider this inequality: 5b−2>13
. Does the value of 3.5 for b make the inequality a true statement?

Enter 1 if the answer is yes. Enter 2 if the answer is no.

(1 point)

Answer 1

Which value of x makes the equation x−−√+2=7
true: 20, 25, or 30?(1 point)

Answer 2

Consider the equation 2z−2−−−−−√=5
. Which of the following values for z makes the equation true: 11.5, 12.5, or 13.5?(1 point)

Answer 3

Determine which of the following statements is/are true:

#1: 3⋅20=4(6+9)


#2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8


#3: 4⋅18−4⋅6=42+4⋅8


(1 point)
Responses

1 and 2
1 and 2

2 and 3
2 and 3

1
1

1 and 3

Answer 4

Which expression is A, in order to have a true equation A=5−1/13
?(1 point)
Responses

A=153+13
Start Fraction 15 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=123−13
1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=−123+13
negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=123+13

Answer 5

Which expression is A, in order to have a true equation A=5−11/3
?(1 point)
Responses

A=15/3+1/3
Start Fraction 15 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=1 2/3−1/3
1 Start Fraction 2 over 3 End Fraction minus Start Fraction 1 over 3 End Fraction

A=−1 2/3+1/3
negative 1 Start Fraction 2 over 3 End Fraction plus Start Fraction 1 over 3 End Fraction

A=1 2/3+1/3

Answer 6

To check if the value of \( b = 3.5 \) makes the inequality \( 5b - 2 > 13 \) a true statement, we can substitute \( 3.5 \) for \( b \) in the inequality:

\[
5(3.5) - 2 > 13
\]

Calculating \( 5(3.5) \):

\[
5 \times 3.5 = 17.5
\]

Now substituting that back into the inequality:

\[
17.5 - 2 > 13
\]

Calculating \( 17.5 - 2 \):

\[
17.5 - 2 = 15.5
\]

Now we check if \( 15.5 > 13 \):

This statement is true.

Thus, the value \( 3.5 \) for \( b \) makes the inequality a true statement.

The answer is \( \boxed{1} \).

Answer 7

To solve the equation \( \sqrt{x} + 2 = 7 \), we first isolate \( \sqrt{x} \):

\[
\sqrt{x} = 7 - 2
\]

\[
\sqrt{x} = 5
\]

Next, we square both sides of the equation to eliminate the square root:

\[
x = 5^2
\]

\[
x = 25
\]

Now we check the given values (20, 25, or 30) to see which makes the original equation true. The correct value is:

**25**.

Thus, the value of \( x \) that makes the equation true is **25**.

Answer 8

To solve the equation \( \sqrt{2z - 2} = 5 \), we first square both sides to eliminate the square root:

\[
2z - 2 = 5^2
\]

\[
2z - 2 = 25
\]

Next, we add 2 to both sides:

\[
2z = 25 + 2
\]

\[
2z = 27
\]

Now we divide both sides by 2 to solve for \( z \):

\[
z = \frac{27}{2} = 13.5
\]

Now, we check the provided options (11.5, 12.5, or 13.5) to see which value makes the equation true.

The correct value is **13.5**.

Thus, the value of \( z \) that makes the equation true is **13.5**.

Answer 9

Let's evaluate each statement one by one.

### Statement #1:
\[
3 \cdot 20 = 4(6 + 9)
\]

Calculating both sides:
- Left side:
\[
3 \cdot 20 = 60
\]
- Right side:
\[
4(6 + 9) = 4 \cdot 15 = 60
\]

Both sides are equal, so **Statement #1 is true.**

### Statement #2:
\[
4 \cdot 12 = 6 \cdot (8 \cdot 2)
\]
\[
12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8
\]

Calculating the left side:
- First part:
\[
4 \cdot 12 = 48
\]
- Second part:
\[
6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96
\]
Since \(48 \neq 96\), **the first part of Statement #2 is false.**

Calculating the second part:
- Left side:
\[
12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60
\]
- Right side:
\[
2 \cdot 4 \cdot 8 = 8 \cdot 8 = 64
\]
Since \(60 \neq 64\), **the second part of Statement #2 is also false.**

### Statement #3:
\[
4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8
\]

Calculating the left side:
\[
4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48
\]

Calculating the right side:
\[
42 + 4 \cdot 8 = 42 + 32 = 74
\]

Since \(48 \neq 74\), **Statement #3 is false.**

### Final Evaluation:
- Statement #1 is true.
- Statement #2 is false.
- Statement #3 is false.

The only true statement is **Statement #1**.

Thus, the correct response is: **1**.

Answer 10

Let's first compute the value of \( A \) as given in the equation:

\[
A = 5 - \frac{1}{13}
\]

To simplify \( A \), we convert 5 to a fraction with a denominator of 13:

\[
5 = \frac{65}{13}
\]

Now we can perform the subtraction:

\[
A = \frac{65}{13} - \frac{1}{13} = \frac{65 - 1}{13} = \frac{64}{13}
\]

Now, we can evaluate each of the provided expressions to see which one equals \( \frac{64}{13} \).

1. **Response A: \( \frac{15}{3} + \frac{1}{3} \)**
- Calculating:
\[
\frac{15}{3} = 5 \quad \text{and} \quad \frac{1}{3} = \frac{1}{3}
\]
- Therefore:
\[
5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
\]

2. **Response B: \( 1 \frac{2}{3} - \frac{1}{3} \)**
- Converting \( 1 \frac{2}{3} \) to an improper fraction:
\[
1 \frac{2}{3} = \frac{5}{3}
\]
- Now calculating:
\[
\frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3}
\]

3. **Response C: \( -1 \frac{2}{3} + \frac{1}{3} \)**
- Converting \( -1 \frac{2}{3} \) to an improper fraction:
\[
-1 \frac{2}{3} = -\frac{5}{3}
\]
- Now calculating:
\[
-\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3}
\]

4. **Response D: \( 1 \frac{2}{3} + \frac{1}{3} \)**
- Again converting \( 1 \frac{2}{3} \) to an improper fraction:
\[
1 \frac{2}{3} = \frac{5}{3}
\]
- Now calculating:
\[
\frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2
\]

Now we summarize the results:
- Response A: \( \frac{16}{3} \)
- Response B: \( \frac{4}{3} \)
- Response C: \( -\frac{4}{3} \)
- Response D: \( 2 \)

None of these results yield \( \frac{64}{13} \).

We need to double-check:
- Note that \( \frac{64}{13} \approx 4.92 \) and the previous values do not match.
- None of the responses provided equal \( \frac{64}{13} \).

Thus, it appears that none of the expressions for \( A \) make the equation true because none equal \( \frac{64}{13} \). Can you please confirm that the expressions provided were correct, or provide further context?

Answer 11

Let's calculate the value of \( A \) from the expression given:

\[
A = 5 - \frac{11}{3}
\]

To perform this calculation, we first convert 5 into a fraction with a denominator of 3:

\[
5 = \frac{15}{3}
\]

Now we can substitute this back into the expression for \( A \):

\[
A = \frac{15}{3} - \frac{11}{3}
\]

Now, we can subtract the two fractions:

\[
A = \frac{15 - 11}{3} = \frac{4}{3}
\]

Now, we have determined that \( A = \frac{4}{3} \).

Next, let's check each of the given expressions to see which one equals \( \frac{4}{3} \):

1. **Response A: \( \frac{15}{3} + \frac{1}{3} \)**
- Calculating:
\[
\frac{15}{3} + \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
\]

2. **Response B: \( 1 \frac{2}{3} - \frac{1}{3} \)**
- Convert \( 1 \frac{2}{3} \) to an improper fraction:
\[
1 \frac{2}{3} = \frac{5}{3}
\]
- Now calculate:
\[
\frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3}
\]

3. **Response C: \( -1 \frac{2}{3} + \frac{1}{3} \)**
- Convert \( -1 \frac{2}{3} \) to an improper fraction:
\[
-1 \frac{2}{3} = -\frac{5}{3}
\]
- Now calculate:
\[
-\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3}
\]

4. **Response D: \( 1 \frac{2}{3} + \frac{1}{3} \)**
- Again converting \( 1 \frac{2}{3} \) to an improper fraction:
\[
1 \frac{2}{3} = \frac{5}{3}
\]
- Now calculate:
\[
\frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2
\]

### Summary of Results:
- Response A: \( \frac{16}{3} \)
- Response B: \( \frac{4}{3} \) (This is correct)
- Response C: \( -\frac{4}{3} \)
- Response D: \( 2 \)

The correct expression for \( A \) that makes the equation true is:

**Response B: \( 1 \frac{2}{3} - \frac{1}{3} \)** (which equals \( \frac{4}{3} \)).