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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)

11 answers

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 \( \boxed{1} \).

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

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.

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)

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.

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

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.

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

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?

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

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 \( \frac{4}{3} \)).