Is the equation 13/4−3=1/4 true or false? Enter 1 if the statement is true. Enter 2 if the statement is false.(1 point)

Question

Is the equation 13/4−3=1/4 true or false? Enter 1 if the statement is true. Enter 2 if the statement is false.(1 point)

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9 answers
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Answer 1

Bot GPT 4-o mini answered
25 days ago

To determine if the equation \( \frac{13}{4} - 3 = \frac{1}{4} \) is true or false, let's simplify the left side:

1. Convert \( 3 \) to a fraction with a denominator of \( 4 \):
\[
3 = \frac{12}{4}
\]

2. Substitute this into the equation:
\[
\frac{13}{4} - \frac{12}{4} = \frac{1}{4}
\]

3. Now subtract the fractions:
\[
\frac{13 - 12}{4} = \frac{1}{4}
\]
\[
\frac{1}{4} = \frac{1}{4}
\]

Since both sides are equal, the equation is true.

Thus, the answer is \( 1 \).

Answer 2

Finally Some Answers answered
25 days ago

Consider the following expressions: −34+6⋅216−−√ _____ 4(2+6)÷2−6 . Which operator ( > , < , or =) should be inserted into the blank space to make the statement true? (1 point)

()

Answer 3

Bot GPT 4-o mini answered
25 days ago

To compare the two expressions in the statement \(-34 + 6 \cdot \sqrt{216} \, \_\_ \, 4(2 + 6) \div 2 - 6\), we need to calculate both sides.

### Left Side: \(-34 + 6 \cdot \sqrt{216}\)

1. Calculate \(\sqrt{216}\):
\[
\sqrt{216} = \sqrt{36 \times 6} = 6\sqrt{6} \approx 6 \times 2.45 \approx 14.7
\]
2. Now compute \(6 \cdot \sqrt{216}\):
\[
6 \cdot \sqrt{216} \approx 6 \cdot 14.7 \approx 88.2
\]
3. Now, compute \(-34 + 6 \cdot \sqrt{216}\):
\[
-34 + 88.2 \approx 54.2
\]

### Right Side: \(4(2 + 6) \div 2 - 6\)

1. Calculate \(2 + 6\):
\[
2 + 6 = 8
\]
2. Now compute \(4 \cdot 8 \div 2\):
\[
4 \cdot 8 = 32
\]
\[
32 \div 2 = 16
\]
3. Finally, compute \(16 - 6\):
\[
16 - 6 = 10
\]

### Comparison:

Now we compare the two results:
- Left Side: \(\approx 54.2\)
- Right Side: \(10\)

So we have:
\[
54.2 \, \_\_ \, 10
\]

Since \(54.2 > 10\), the operator that should be inserted is \(>\).

Thus, the answer is \(>\).

Answer 4

Finally Some Answers answered
25 days ago

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 5

Bot GPT 4-o mini answered
25 days ago

To determine if the value \( b = 3.5 \) makes the inequality \( 5b - 2 > 13 \) a true statement, we can substitute \( b \) into the inequality and simplify:

1. Substitute \( b = 3.5 \):
\[
5(3.5) - 2 > 13
\]

2. Calculate \( 5(3.5) \):
\[
5(3.5) = 17.5
\]

3. Now substitute back into the inequality:
\[
17.5 - 2 > 13
\]

4. Simplify the left side:
\[
17.5 - 2 = 15.5
\]

5. Now check the inequality:
\[
15.5 > 13
\]

Since this statement is true, the value of \( 3.5 \) for \( b \) makes the inequality a true statement.

Thus, the answer is \( 1 \).

Answer 6

Finally Some Answers answered
25 days ago

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

x=()

Answer 7

Bot GPT 4-o mini answered
25 days ago

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

1. Subtract 2 from both sides:
\[
\sqrt{x} = 7 - 2
\]
\[
\sqrt{x} = 5
\]

2. Now, square both sides to eliminate the square root:
\[
x = 5^2
\]
\[
x = 25
\]

Now we check the given options: **20, 25, or 30**.

The value that makes the equation true is:
\[
\boxed{25}
\]

So, the answer is \(x = 25\).

Answer 8

Finally Some Answers answered
25 days ago

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)

The value of z that makes the equation true is()

Answer 9

Bot GPT 4-o mini answered
25 days ago

To solve the equation \( \sqrt{2z - 2} = 5 \), we will first isolate the square root and then square both sides to eliminate it.

1. Square both sides of the equation:
\[
(\sqrt{2z - 2})^2 = 5^2
\]
\[
2z - 2 = 25
\]

2. Add 2 to both sides:
\[
2z = 25 + 2
\]
\[
2z = 27
\]

3. 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**.

The value that makes the equation true is:
\[
\boxed{13.5}
\]

So, the answer is \( z = 13.5 \).

Is the equation 13/4−3=1/4 true or false? Enter 1 if the statement is true. Enter 2 if the statement is false.(1 point)

To determine if the equation \( \frac{13}{4} - 3 = \frac{1}{4} \) is true or false, let's simplify the left side:

Consider the following expressions: −34+6⋅216−−√ _____ 4(2+6)÷2−6 . Which operator ( > , < , or =) should be inserted into the blank space to make the statement true?​ (1 point)

To compare the two expressions in the statement \(-34 + 6 \cdot \sqrt{216} \, \_\_ \, 4(2 + 6) \div 2 - 6\), we need to calculate both sides.

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)

To determine if the value \( b = 3.5 \) makes the inequality \( 5b - 2 > 13 \) a true statement, we can substitute \( b \) into the inequality and simplify:

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 need to isolate \(\sqrt{x}\):

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 will first isolate the square root and then square both sides to eliminate it.

Consider the following expressions: −34+6⋅216−−√ _____ 4(2+6)÷2−6 . Which operator ( > , < , or =) should be inserted into the blank space to make the statement true? (1 point)