Question
Find the square root of 81: 81−−√ .(1 point)
Responses
−9
negative 9
9, −9
9, negative 9
9
9
40.5
40.5
Responses
−9
negative 9
9, −9
9, negative 9
9
9
40.5
40.5
Answers
Answer
Find the square root of 100: 100−−−√ .(1 point)
Responses
10
10
10,−10
10 comma negative 10
−10
negative 10
50
Responses
10
10
10,−10
10 comma negative 10
−10
negative 10
50
Answer
Find the cube root of 512: 512−−−√3 .(1 point)
Responses
−8
negative 8
8
8
170.666...
170.666...
8, −8
Responses
−8
negative 8
8
8
170.666...
170.666...
8, −8
Answer
Find the cube root of −343 : −343−−−−√3 (1 point)
Responses
−7
negative 7
−114.333...
negative 114.333...
7, −7
7 comma negative 7
7
Responses
−7
negative 7
−114.333...
negative 114.333...
7, −7
7 comma negative 7
7
Answer
Recognize which of the following statements is true.(1 point)
Responses
When k is negative, x3=k has one solution, which is negative.
When k is negative, x cubed equals k has one solution, which is negative.
When k is negative, x2=k has one solution, which is negative.
When k is negative, x squared equals k has one solution, which is negative.
When k is positive, x3=k has one positive solution and one negative solution.
When k is positive, x cubed equals k has one positive solution and one negative solution.
When k is positive, x2=k has one solution, which is positive.
Responses
When k is negative, x3=k has one solution, which is negative.
When k is negative, x cubed equals k has one solution, which is negative.
When k is negative, x2=k has one solution, which is negative.
When k is negative, x squared equals k has one solution, which is negative.
When k is positive, x3=k has one positive solution and one negative solution.
When k is positive, x cubed equals k has one positive solution and one negative solution.
When k is positive, x2=k has one solution, which is positive.
Answer
u sure?
Answered by
GPT-4o
The square root of 81 is 9. Therefore, the correct response is:
9
9
Answered by
GPT-4o
The square roots of 100 are 10 and -10. Therefore, the correct response is:
10, −10
10, −10
Answered by
GPT-4o
The cube root of 512 is 8. Therefore, the correct response is:
8
8
Answered by
GPT-4o
The cube root of -343 is -7. Therefore, the correct response is:
−7 (negative 7)
−7 (negative 7)
Answered by
GPT-4o
Let's analyze each statement:
1. "When k is negative, x³ = k has one solution, which is negative."
- True: A cubic equation with a negative k has one real negative solution.
2. "When k is negative, x² = k has one solution, which is negative."
- False: A quadratic equation with a negative k has no real solutions because the square of a real number is always non-negative.
3. "When k is positive, x³ = k has one positive solution and one negative solution."
- False: A cubic equation with a positive k has only one real positive solution and two complex (non-real) solutions.
4. "When k is positive, x² = k has one solution, which is positive."
- False: A quadratic equation with a positive k has two real solutions (one positive and one negative): \( x = \sqrt{k} \) and \( x = -\sqrt{k} \).
Hence, the correct statement is:
"When k is negative, x³ = k has one solution, which is negative."
1. "When k is negative, x³ = k has one solution, which is negative."
- True: A cubic equation with a negative k has one real negative solution.
2. "When k is negative, x² = k has one solution, which is negative."
- False: A quadratic equation with a negative k has no real solutions because the square of a real number is always non-negative.
3. "When k is positive, x³ = k has one positive solution and one negative solution."
- False: A cubic equation with a positive k has only one real positive solution and two complex (non-real) solutions.
4. "When k is positive, x² = k has one solution, which is positive."
- False: A quadratic equation with a positive k has two real solutions (one positive and one negative): \( x = \sqrt{k} \) and \( x = -\sqrt{k} \).
Hence, the correct statement is:
"When k is negative, x³ = k has one solution, which is negative."
Answered by
GPT-4o
Let's review all of the statements again carefully:
1. "When k is negative, \( x^3 = k \) has one solution, which is negative."
- True: A cubic equation with a negative k indeed has one real negative solution and two complex solutions.
2. "When k is negative, \( x^2 = k \) has one solution, which is negative."
- False: A quadratic equation with a negative k has no real solutions because the square of any real number is non-negative.
3. "When k is positive, \( x^3 = k \) has one positive solution and one negative solution."
- False: A cubic equation with a positive k has one real positive solution and two complex solutions, not an additional real negative solution.
4. "When k is positive, \( x^2 = k \) has one solution, which is positive."
- False: A quadratic equation with a positive k has two real solutions: \( x = \sqrt{k} \) and \( x = -\sqrt{k} \), one positive and one negative.
Therefore, my previous analysis is correct. The true statement is:
"When k is negative, \( x^3 = k \) has one solution, which is negative."
1. "When k is negative, \( x^3 = k \) has one solution, which is negative."
- True: A cubic equation with a negative k indeed has one real negative solution and two complex solutions.
2. "When k is negative, \( x^2 = k \) has one solution, which is negative."
- False: A quadratic equation with a negative k has no real solutions because the square of any real number is non-negative.
3. "When k is positive, \( x^3 = k \) has one positive solution and one negative solution."
- False: A cubic equation with a positive k has one real positive solution and two complex solutions, not an additional real negative solution.
4. "When k is positive, \( x^2 = k \) has one solution, which is positive."
- False: A quadratic equation with a positive k has two real solutions: \( x = \sqrt{k} \) and \( x = -\sqrt{k} \), one positive and one negative.
Therefore, my previous analysis is correct. The true statement is:
"When k is negative, \( x^3 = k \) has one solution, which is negative."