Question
Which of the following is developed to result in the answer of 1?(1 point)
Responses
3(80)
3
(
8
0
)
3 left parenthesis 8 superscript 0 baseline right parenthesis
13−(7.42)0
13
−
(
7.42
)
0
13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline
(−2.97)0
(
−
2.97
)
0
left parenthesis negative 2.97 right parenthesis superscript 0 baseline
50+90
Responses
3(80)
3
(
8
0
)
3 left parenthesis 8 superscript 0 baseline right parenthesis
13−(7.42)0
13
−
(
7.42
)
0
13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline
(−2.97)0
(
−
2.97
)
0
left parenthesis negative 2.97 right parenthesis superscript 0 baseline
50+90
Answers
Answer
Which of the following shows the correct process of solving −30+4.5
−
3
0
+
4.5
?(1 point)
Responses
−30+4.5=−3+4.5=1.5
−
3
0
+
4.5
=
−
3
+
4.5
=
1.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5
−30+4.5=(−3)0+4.5=1+4.5=5.5
−
3
0
+
4.5
=
(
−
3
)
0
+
4.5
=
1
+
4.5
=
5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5
−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
−
3
0
+
4.5
=
−
1
⋅
3
0
+
4.5
=
−
1
⋅
1
+
4.5
=
−
1
+
4.5
=
3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5
−30+4.5=−3⋅0+4.5=0+4.5=4.5
−
3
0
+
4.5
=
−
3
⋅
0
+
4.5
=
0
+
4.5
=
4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.
−
3
0
+
4.5
?(1 point)
Responses
−30+4.5=−3+4.5=1.5
−
3
0
+
4.5
=
−
3
+
4.5
=
1.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5
−30+4.5=(−3)0+4.5=1+4.5=5.5
−
3
0
+
4.5
=
(
−
3
)
0
+
4.5
=
1
+
4.5
=
5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5
−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
−
3
0
+
4.5
=
−
1
⋅
3
0
+
4.5
=
−
1
⋅
1
+
4.5
=
−
1
+
4.5
=
3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5
−30+4.5=−3⋅0+4.5=0+4.5=4.5
−
3
0
+
4.5
=
−
3
⋅
0
+
4.5
=
0
+
4.5
=
4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.
Answer
Which of the following is an equivalent expression to 7(−5.3)0+4⋅9
7
(
−
5.3
)
0
+
4
⋅
9
when applying the Zero Power Rule? (1 point)
Responses
71+4⋅9
7
1
+
4
⋅
9
Start Fraction 7 over 1 End Fraction plus 4 times 9
70+4⋅9
7
0
+
4
⋅
9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.3+4⋅9
7
5.3
+
4
⋅
9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
75.30+36
7
(
−
5.3
)
0
+
4
⋅
9
when applying the Zero Power Rule? (1 point)
Responses
71+4⋅9
7
1
+
4
⋅
9
Start Fraction 7 over 1 End Fraction plus 4 times 9
70+4⋅9
7
0
+
4
⋅
9
Start Fraction 7 over 0 End Fraction plus 4 times 9
75.3+4⋅9
7
5.3
+
4
⋅
9
Start Fraction 7 over 5.3 End Fraction plus 4 times 9
75.30+36
Answer
Which of the following is an equivalent expression to 12(9−70)+(−29)0
1
2
(
9
−
7
0
)
+
(
−
29
)
0
? (1 point)
Responses
12(9−0)+0
1
2
(
9
−
0
)
+
0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
12(2)+1
1
2
(
2
)
+
1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1
12(9−1)−1
1
2
(
9
−
1
)
−
1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(9−1)+1
1
2
(
9
−
7
0
)
+
(
−
29
)
0
? (1 point)
Responses
12(9−0)+0
1
2
(
9
−
0
)
+
0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
12(2)+1
1
2
(
2
)
+
1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1
12(9−1)−1
1
2
(
9
−
1
)
−
1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(9−1)+1
Answer
Which of the following shows the correct process of solving −4(3+120)+150
−
4
(
3
+
12
0
)
+
15
0
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(15)+1=−60+1=−59
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
1
=
−
60
+
1
=
−
59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
15
=
−
60
+
15
=
−
45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
3
+
1
)
+
1
=
−
4
(
3
+
12
0
)
+
15
0
by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150=−4(15)+1=−60+1=−59
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
1
=
−
60
+
1
=
−
59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
15
)
+
15
=
−
60
+
15
=
−
45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
−
4
(
3
+
12
0
)
+
15
0
=
−
4
(
3
+
1
)
+
1
=
Answered by
GPT-4o mini
To determine which of the provided responses results in the answer of 1, let's evaluate each option:
1. **3(80)**: This equals \(3 \times 80 = 240\).
2. **13 − (7.42)0**: The expression \((7.42)^0 = 1\) (any non-zero number raised to the power of 0 is 1), so this evaluates to \(13 - 1 = 12\).
3. **(−2.97)0**: Here \((-2.97)^0 = 1\) (again, any non-zero number raised to 0 is 1).
4. **50 + 90**: This equals \(50 + 90 = 140\).
Now, let's summarize the results:
- 3(80) = 240
- 13 − (7.42)^0 = 12
- (−2.97)^0 = 1
- 50 + 90 = 140
The only expression that results in 1 is **(−2.97)0**.
1. **3(80)**: This equals \(3 \times 80 = 240\).
2. **13 − (7.42)0**: The expression \((7.42)^0 = 1\) (any non-zero number raised to the power of 0 is 1), so this evaluates to \(13 - 1 = 12\).
3. **(−2.97)0**: Here \((-2.97)^0 = 1\) (again, any non-zero number raised to 0 is 1).
4. **50 + 90**: This equals \(50 + 90 = 140\).
Now, let's summarize the results:
- 3(80) = 240
- 13 − (7.42)^0 = 12
- (−2.97)^0 = 1
- 50 + 90 = 140
The only expression that results in 1 is **(−2.97)0**.
Answered by
GPT-4o mini
Let's evaluate the expressions in each of the provided options step by step to determine which shows the correct process for solving \( -3^0 + 4.5 \).
1. **Option 1:**
\(-30 + 4.5 = -3 + 4.5 = 1.5\)
- This is incorrect because \(-30 + 4.5\) does not equal \(-3\).
2. **Option 2:**
\(-30 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
- Evaluating \((-3)^0\) gives 1, so this part is correct, but \(-30 + 4.5\) does not equal \((-3)^0\).
3. **Option 3:**
\(-30 + 4.5 = -1 \cdot 30 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)
- This option is incorrect. The calculations do not follow the original problem.
4. **Option 4:**
\(-30 + 4.5 = -3 \cdot 0 + 4.5 = 0 + 4.5 = 4.5 \)
- This option is incorrect as \(-3 \cdot 0\) equals 0 but doesn’t represent \(-3^0\).
We need to clarify that the expression \(-3^0\) (if interpreted without parentheses) generally evaluates as \(-(3^0)\):
- \( 3^0 = 1\) thus, \(-3^0 = -1\).
Based on this reasoning, the evaluation is:
\[ -3^0 + 4.5 = -1 + 4.5 = 3.5. \]
None of the provided options present the correct solving process using the original expression, \( -3^0 + 4.5 \). But option **3** correctly results in \(3.5\), aligning with our computation despite the misleading notation. Thus, the best option from the given responses is **option 3**.
1. **Option 1:**
\(-30 + 4.5 = -3 + 4.5 = 1.5\)
- This is incorrect because \(-30 + 4.5\) does not equal \(-3\).
2. **Option 2:**
\(-30 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
- Evaluating \((-3)^0\) gives 1, so this part is correct, but \(-30 + 4.5\) does not equal \((-3)^0\).
3. **Option 3:**
\(-30 + 4.5 = -1 \cdot 30 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)
- This option is incorrect. The calculations do not follow the original problem.
4. **Option 4:**
\(-30 + 4.5 = -3 \cdot 0 + 4.5 = 0 + 4.5 = 4.5 \)
- This option is incorrect as \(-3 \cdot 0\) equals 0 but doesn’t represent \(-3^0\).
We need to clarify that the expression \(-3^0\) (if interpreted without parentheses) generally evaluates as \(-(3^0)\):
- \( 3^0 = 1\) thus, \(-3^0 = -1\).
Based on this reasoning, the evaluation is:
\[ -3^0 + 4.5 = -1 + 4.5 = 3.5. \]
None of the provided options present the correct solving process using the original expression, \( -3^0 + 4.5 \). But option **3** correctly results in \(3.5\), aligning with our computation despite the misleading notation. Thus, the best option from the given responses is **option 3**.
Answered by
GPT-4o mini
To evaluate the expression \(7(-5.3)^0 + 4 \cdot 9\) using the Zero Power Rule, we need to apply the rule that any non-zero number raised to the power of 0 equals 1.
Here's how we compute it step by step:
1. **Applying the Zero Power Rule:**
\((-5.3)^0 = 1\), because any non-zero number raised to the power of 0 equals 1.
2. **Substituting back into the expression:**
\[7(-5.3)^0 + 4 \cdot 9 = 7(1) + 4 \cdot 9 = 7 + 36\]
Now, let's look at the available response options:
1. **71 + 4⋅9:**
\[ 7(1) + 4 \cdot 9\]
This expression simplifies to \(7 + 36\), which is correct.
2. **70 + 4⋅9:**
This implies \(7(0) + 36\), which is incorrect because it doesn't apply the Zero Power Rule accurately.
3. **75.3 + 4⋅9:**
This doesn't make logical sense in the context of the Zero Power Rule since it involves a misinterpretation of the terms.
4. **75.30 + 36:**
This is also incorrect as it does not simplify correctly based on the Zero Power Rule.
From the evaluations, **the correct equivalent expression is:**
**71 + 4 ⋅ 9** (which simplifies correctly to \(7 + 36\)).
Here's how we compute it step by step:
1. **Applying the Zero Power Rule:**
\((-5.3)^0 = 1\), because any non-zero number raised to the power of 0 equals 1.
2. **Substituting back into the expression:**
\[7(-5.3)^0 + 4 \cdot 9 = 7(1) + 4 \cdot 9 = 7 + 36\]
Now, let's look at the available response options:
1. **71 + 4⋅9:**
\[ 7(1) + 4 \cdot 9\]
This expression simplifies to \(7 + 36\), which is correct.
2. **70 + 4⋅9:**
This implies \(7(0) + 36\), which is incorrect because it doesn't apply the Zero Power Rule accurately.
3. **75.3 + 4⋅9:**
This doesn't make logical sense in the context of the Zero Power Rule since it involves a misinterpretation of the terms.
4. **75.30 + 36:**
This is also incorrect as it does not simplify correctly based on the Zero Power Rule.
From the evaluations, **the correct equivalent expression is:**
**71 + 4 ⋅ 9** (which simplifies correctly to \(7 + 36\)).
Answered by
GPT-4o mini
To find an equivalent expression to the given expression \(12(9 - 7^0) + (-29)^0\), we'll first simplify it step by step.
1. **Evaluate \(7^0\)**:
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Thus, \(7^0 = 1\).
2. **Evaluate \((-29)^0\)**:
Similarly, \((-29)^0 = 1\) because any non-zero number raised to the power of 0 is also 1.
3. **Substituting back into the expression**:
We can substitute \(7^0\) and \((-29)^0\) into the original expression:
\[
12(9 - 1) + 1
\]
This simplifies to:
\[
12(8) + 1 = 96 + 1 = 97.
\]
Now let's examine the response options:
1. **Option 1: \(12(9 - 0) + 0\)**
This simplifies to \(12(9) + 0 = 108\). Not equivalent.
2. **Option 2: \(12(2) + 1\)**
This simplifies to \(24 + 1 = 25\). Not equivalent.
3. **Option 3: \(12(9 - 1) - 1\)**
This simplifies to \(12(8) - 1 = 96 - 1 = 95\). Not equivalent.
4. **Option 4: \(12(9 - 1) + 1\)**
This simplifies to \(12(8) + 1 = 96 + 1 = 97\). This is equivalent.
Based on the calculations, the correct equivalent expression is **Option 4: \(12(9 - 1) + 1\)**.
1. **Evaluate \(7^0\)**:
According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Thus, \(7^0 = 1\).
2. **Evaluate \((-29)^0\)**:
Similarly, \((-29)^0 = 1\) because any non-zero number raised to the power of 0 is also 1.
3. **Substituting back into the expression**:
We can substitute \(7^0\) and \((-29)^0\) into the original expression:
\[
12(9 - 1) + 1
\]
This simplifies to:
\[
12(8) + 1 = 96 + 1 = 97.
\]
Now let's examine the response options:
1. **Option 1: \(12(9 - 0) + 0\)**
This simplifies to \(12(9) + 0 = 108\). Not equivalent.
2. **Option 2: \(12(2) + 1\)**
This simplifies to \(24 + 1 = 25\). Not equivalent.
3. **Option 3: \(12(9 - 1) - 1\)**
This simplifies to \(12(8) - 1 = 96 - 1 = 95\). Not equivalent.
4. **Option 4: \(12(9 - 1) + 1\)**
This simplifies to \(12(8) + 1 = 96 + 1 = 97\). This is equivalent.
Based on the calculations, the correct equivalent expression is **Option 4: \(12(9 - 1) + 1\)**.
Answered by
GPT-4o mini
To solve the expression \(-4(3 + 12^0) + 15^0\) using the Zero Power Rule, we first need to simplify it by applying the Zero Power Rule, which states that any non-zero number raised to the power of 0 equals 1.
### Steps:
1. **Calculate \(12^0\)**:
\[
12^0 = 1
\]
2. **Calculate \(15^0\)**:
\[
15^0 = 1
\]
3. **Substituting back** into the expression:
\[
-4(3 + 1) + 1
\]
4. **Now simplify**:
\[
-4(4) + 1 = -16 + 1 = -15
\]
Now, let's evaluate the response options to find which one correctly corresponds to these calculations:
1. **Option 1:**
\[
-4(3 + 12^0) + 15^0 = -4(15) + 1 = -60 + 1 = -59
\]
- This option is incorrect because \(3 + 12^0 = 4\) not \(15\).
2. **Option 2:**
\[
-4(3 + 12^0) + 15^0 = -4(15) + 15 = -60 + 15 = -45
\]
- This option is incorrect for the same reason as the first.
3. **Option 3:**
\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15
\]
- This option matches what we computed.
4. **(`Incomplete Response`):**
This doesn't show a complete expression or answer.
### Conclusion
The correct response that shows the right process is **Option 3**:
\[
-4(3+12^0) + 15^0 = -4 \cdot 4 + 1 = -16 + 1 = -15
\]
**Option 3 correctly includes the calculation process and leads to the correct equivalent expression.**
### Steps:
1. **Calculate \(12^0\)**:
\[
12^0 = 1
\]
2. **Calculate \(15^0\)**:
\[
15^0 = 1
\]
3. **Substituting back** into the expression:
\[
-4(3 + 1) + 1
\]
4. **Now simplify**:
\[
-4(4) + 1 = -16 + 1 = -15
\]
Now, let's evaluate the response options to find which one correctly corresponds to these calculations:
1. **Option 1:**
\[
-4(3 + 12^0) + 15^0 = -4(15) + 1 = -60 + 1 = -59
\]
- This option is incorrect because \(3 + 12^0 = 4\) not \(15\).
2. **Option 2:**
\[
-4(3 + 12^0) + 15^0 = -4(15) + 15 = -60 + 15 = -45
\]
- This option is incorrect for the same reason as the first.
3. **Option 3:**
\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15
\]
- This option matches what we computed.
4. **(`Incomplete Response`):**
This doesn't show a complete expression or answer.
### Conclusion
The correct response that shows the right process is **Option 3**:
\[
-4(3+12^0) + 15^0 = -4 \cdot 4 + 1 = -16 + 1 = -15
\]
**Option 3 correctly includes the calculation process and leads to the correct equivalent expression.**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.