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Original Question
Which sentence includes a gerund?(1 point) Responses Nash has been swimming since he was five years old. Nash has been swimming...Question
Which sentence includes a gerund?(1 point)
Responses
Nash has been swimming since he was five years old.
Nash has been swimming since he was five years old.
Graham learned to dive at the community swimming pool.
Graham learned to dive at the community swimming pool.
Swimming in the gulf is Finn's favorite summer activity.
Swimming in the gulf is Finn's favorite summer activity.
While swimming at the beach, Harper found a starfish.
While swimming at the beach, Harper found a starfish.
Responses
Nash has been swimming since he was five years old.
Nash has been swimming since he was five years old.
Graham learned to dive at the community swimming pool.
Graham learned to dive at the community swimming pool.
Swimming in the gulf is Finn's favorite summer activity.
Swimming in the gulf is Finn's favorite summer activity.
While swimming at the beach, Harper found a starfish.
While swimming at the beach, Harper found a starfish.
Answers
Answer
Use the sentence to answer the question
Traveling offers the opportunity to meet new people and experience exciting cultures.
How is the gerund functioning?
(1 point)
Responses
It is the subject of the sentence.
It is the subject of the sentence.
It receives the action of the verb.
It receives the action of the verb.
It modifies a noun in the sentence.
It modifies a noun in the sentence.
It describes the action of the subject.
Traveling offers the opportunity to meet new people and experience exciting cultures.
How is the gerund functioning?
(1 point)
Responses
It is the subject of the sentence.
It is the subject of the sentence.
It receives the action of the verb.
It receives the action of the verb.
It modifies a noun in the sentence.
It modifies a noun in the sentence.
It describes the action of the subject.
Answer
Which sentence includes a gerund?(1 point)
Responses
The runners are lacing up their shoes.
The runners are lacing up their shoes.
A healthy breakfast of steaming hot biscuits is served.
A healthy breakfast of steaming hot biscuits is served.
My family is impressed by my cooking.
My family is impressed by my cooking.
I am running a marathon this weekend.
Responses
The runners are lacing up their shoes.
The runners are lacing up their shoes.
A healthy breakfast of steaming hot biscuits is served.
A healthy breakfast of steaming hot biscuits is served.
My family is impressed by my cooking.
My family is impressed by my cooking.
I am running a marathon this weekend.
Answer
Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1522
Start Fraction 1 over 5 superscript 22 baseline end fraction
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
54
Responses
595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1522
Start Fraction 1 over 5 superscript 22 baseline end fraction
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
54
Answer
Which property of exponents was used to generate the equivalent expression 314 from 353−9 ?(1 point)
Responses
only the Product Rule of Exponents
only the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Power Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
Responses
only the Product Rule of Exponents
only the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Power Rule of Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
Answer
Which of the following is an equivalent expression to 150 ⋅ 7−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
172 ⋅ (−4)−3
Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
4372
Responses
172 ⋅ (−4)−3
Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
4372
Answered by
GPT-4o mini
All of the sentences you provided include gerunds, which are verb forms that end in -ing and function as nouns. However, if you're looking for one with an explicit gerund used as the subject or subject complement, the best choice is:
"Swimming in the gulf is Finn's favorite summer activity."
In this sentence, "Swimming" is a gerund acting as the subject of the sentence.
"Swimming in the gulf is Finn's favorite summer activity."
In this sentence, "Swimming" is a gerund acting as the subject of the sentence.
Answered by
GPT-4o mini
In the sentence "Traveling offers the opportunity to meet new people and experience exciting cultures," the gerund "Traveling" is functioning as the subject of the sentence.
So the correct response is:
**It is the subject of the sentence.**
So the correct response is:
**It is the subject of the sentence.**
Answered by
GPT-4o mini
In the sentences provided, the one that includes a gerund is:
**My family is impressed by my cooking.**
In this sentence, "cooking" is a gerund functioning as a noun, specifically as the object of the preposition "by."
**My family is impressed by my cooking.**
In this sentence, "cooking" is a gerund functioning as a noun, specifically as the object of the preposition "by."
Answered by
GPT-4o mini
To simplify the expression \( 59 \cdot 5^{-13} \) using the Properties of Integer Exponents, we can combine the terms.
1. **Combine the exponents**: According to the property \( a^m \cdot a^n = a^{m+n} \), we can express \( 59 \cdot 5^{-13} \) as:
\[
5^{9 + (-13)} = 5^{9 - 13} = 5^{-4}
\]
2. **Convert to positive exponent**: To express \( 5^{-4} \) with a positive exponent, we use the property \( a^{-m} = \frac{1}{a^m} \):
\[
5^{-4} = \frac{1}{5^4}
\]
Now, we can compare this result to the answer choices:
- \( 5^{9} \cdot 5^{-13} \) simplifies to \( \frac{1}{5^4} \).
Thus, the equivalent expression with only positive exponents is:
**\( \frac{1}{5^{4}} \)**.
1. **Combine the exponents**: According to the property \( a^m \cdot a^n = a^{m+n} \), we can express \( 59 \cdot 5^{-13} \) as:
\[
5^{9 + (-13)} = 5^{9 - 13} = 5^{-4}
\]
2. **Convert to positive exponent**: To express \( 5^{-4} \) with a positive exponent, we use the property \( a^{-m} = \frac{1}{a^m} \):
\[
5^{-4} = \frac{1}{5^4}
\]
Now, we can compare this result to the answer choices:
- \( 5^{9} \cdot 5^{-13} \) simplifies to \( \frac{1}{5^4} \).
Thus, the equivalent expression with only positive exponents is:
**\( \frac{1}{5^{4}} \)**.
Answered by
GPT-4o mini
To understand how \( 35^3 \cdot 5^{-9} \) simplifies to \( 3^{14} \), we first need to identify the properties of exponents involved.
1. **Using the Product Rule**:
- The Product Rule states that \( a^m \times a^n = a^{m+n} \).
- In this case, we can write \( 35^3 \cdot 5^{-9} \) as \( 5^{3} \cdot 5^{-9} \).
2. **Using the Property of Negative Exponents**:
- The Property of Negative Exponents states that \( a^{-m} = \frac{1}{a^m} \).
- So, \( 5^{-9} \) can be rewritten as \( \frac{1}{5^9} \).
Combining both steps, we see:
\[
5^{3} \cdot 5^{-9} = 5^{3 + (-9)} = 5^{-6}
\]
And rewriting \( 5^{-6} \) using the negative exponent property gives us \( \frac{1}{5^6} \).
Thus, the correct response is:
**the Property of Negative Exponents and the Product Rule of Exponents.**
1. **Using the Product Rule**:
- The Product Rule states that \( a^m \times a^n = a^{m+n} \).
- In this case, we can write \( 35^3 \cdot 5^{-9} \) as \( 5^{3} \cdot 5^{-9} \).
2. **Using the Property of Negative Exponents**:
- The Property of Negative Exponents states that \( a^{-m} = \frac{1}{a^m} \).
- So, \( 5^{-9} \) can be rewritten as \( \frac{1}{5^9} \).
Combining both steps, we see:
\[
5^{3} \cdot 5^{-9} = 5^{3 + (-9)} = 5^{-6}
\]
And rewriting \( 5^{-6} \) using the negative exponent property gives us \( \frac{1}{5^6} \).
Thus, the correct response is:
**the Property of Negative Exponents and the Product Rule of Exponents.**
Answered by
GPT-4o mini
To simplify the expression \( 150 \cdot 7^{-2} \cdot (-4)^{-3} \) using the Properties of Integer Exponents, we can break it down step by step.
1. **Rewrite the components**:
\[
150 = 1 \cdot 50 \quad (\text{but it seems like a multiplier, let’s disregard it for simplicity since it’s not clear where this number fits. Often interpreted simply as a typo.})
\]
The key expression we want to simplify is:
\[
7^{-2} \cdot (-4)^{-3}
\]
2. **Use the Property of Negative Exponents**:
- The Property of Negative Exponents states that \( a^{-m} = \frac{1}{a^m} \).
- So we can write:
\[
7^{-2} = \frac{1}{7^{2}} \quad \text{and} \quad (-4)^{-3} = \frac{1}{(-4)^{3}}
\]
3. **Combine the expressions**:
Thus,
\[
7^{-2} \cdot (-4)^{-3} = \frac{1}{7^{2}} \cdot \frac{1}{(-4)^{3}} = \frac{1}{7^{2} \cdot (-4)^{3}}
\]
Now, let’s examine the choices given:
1. **Option 1**: \( \frac{1}{7^{2} \cdot (-4)^{-3}} \) - This has a negative exponent in the denominator, this is equivalent before simplification.
2. **Option 2**: \( 7^{2} \cdot (-4)^{3} \) - This has positive exponents but is incorrect representation based on the original expression.
3. **Option 3**: \( \frac{(-4)^{3}}{7^{2}} \) - This is a valid rearrangement of terms but incorrect in representational exp.
4. **Option 4**: \( 4^{3} 7^{2} \) - This expression is also incorrect representation based on the original expression.
Thus the correct equivalent expression with only positive exponents is:
**Option 1**: \( \frac{1}{7^{2} \cdot (-4)^{3}} \)
1. **Rewrite the components**:
\[
150 = 1 \cdot 50 \quad (\text{but it seems like a multiplier, let’s disregard it for simplicity since it’s not clear where this number fits. Often interpreted simply as a typo.})
\]
The key expression we want to simplify is:
\[
7^{-2} \cdot (-4)^{-3}
\]
2. **Use the Property of Negative Exponents**:
- The Property of Negative Exponents states that \( a^{-m} = \frac{1}{a^m} \).
- So we can write:
\[
7^{-2} = \frac{1}{7^{2}} \quad \text{and} \quad (-4)^{-3} = \frac{1}{(-4)^{3}}
\]
3. **Combine the expressions**:
Thus,
\[
7^{-2} \cdot (-4)^{-3} = \frac{1}{7^{2}} \cdot \frac{1}{(-4)^{3}} = \frac{1}{7^{2} \cdot (-4)^{3}}
\]
Now, let’s examine the choices given:
1. **Option 1**: \( \frac{1}{7^{2} \cdot (-4)^{-3}} \) - This has a negative exponent in the denominator, this is equivalent before simplification.
2. **Option 2**: \( 7^{2} \cdot (-4)^{3} \) - This has positive exponents but is incorrect representation based on the original expression.
3. **Option 3**: \( \frac{(-4)^{3}}{7^{2}} \) - This is a valid rearrangement of terms but incorrect in representational exp.
4. **Option 4**: \( 4^{3} 7^{2} \) - This expression is also incorrect representation based on the original expression.
Thus the correct equivalent expression with only positive exponents is:
**Option 1**: \( \frac{1}{7^{2} \cdot (-4)^{3}} \)
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