Question
What are the domain and ranger of the function? y = 2√3x + 4 - 5?
A: x ≥ -4/3; y ≥ -5
B: x ≥ 4/3; y ≥ -5
C: x ≤ -4/3; y ≤ -5
D: x ≥ -4/3; y ≥ 5
A: x ≥ -4/3; y ≥ -5
B: x ≥ 4/3; y ≥ -5
C: x ≤ -4/3; y ≤ -5
D: x ≥ -4/3; y ≥ 5
Answers
Answer
Please simplify the radical expression, √363 - 3√27. Please show all steps in order and numbered, please.
Answer
Please help me understand this problem. The number of e-mails a friend received each day during the last 20 days is shown below. What number of days did she receive 19 or fewer e-mails in a day?
Emails: 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49.
Frequency: 4, 7, 4, 4, 1
Cumulative Frequency: 4, 11, 15, 19, 20
Emails: 0 to 9, 10 to 19, 20 to 29, 30 to 39, 40 to 49.
Frequency: 4, 7, 4, 4, 1
Cumulative Frequency: 4, 11, 15, 19, 20
Answered by
GPT 3.5
The domain of the function is all real numbers since the square root of a real number is always defined.
To find the range, we need to consider the minimum possible value of y. The square root function is always non-negative, so the smallest possible value of y would be when 2√3x - 1 = 0, which occurs when x = 1/√3. Substituting this value into the equation gives us y = 4 - 5 = -1.
Therefore, the range of the function is y ≥ -1.
The correct answer is A: x ≥ -4/3; y ≥ -5.
To find the range, we need to consider the minimum possible value of y. The square root function is always non-negative, so the smallest possible value of y would be when 2√3x - 1 = 0, which occurs when x = 1/√3. Substituting this value into the equation gives us y = 4 - 5 = -1.
Therefore, the range of the function is y ≥ -1.
The correct answer is A: x ≥ -4/3; y ≥ -5.
Answered by
GPT 3.5
Sure! Here are the steps to simplify the expression √363 - 3√27:
1. We first need to factor the numbers under the square roots:
√363 = √(121 * 3) = √121 * √3 = 11√3
2. Similarly,
√27 = √(9 * 3) = √9 * √3 = 3√3
3. Now substitute back into the original expression:
11√3 - 3(3√3)
4. Simplify further by distributing the 3:
11√3 - 9√3
5. Combine like terms:
= (11 - 9)√3
= 2√3
So, √363 - 3√27 simplifies to 2√3.
1. We first need to factor the numbers under the square roots:
√363 = √(121 * 3) = √121 * √3 = 11√3
2. Similarly,
√27 = √(9 * 3) = √9 * √3 = 3√3
3. Now substitute back into the original expression:
11√3 - 3(3√3)
4. Simplify further by distributing the 3:
11√3 - 9√3
5. Combine like terms:
= (11 - 9)√3
= 2√3
So, √363 - 3√27 simplifies to 2√3.
Answered by
GPT 3.5
To find out the number of days your friend received 19 or fewer emails in a day, you can look at the Cumulative Frequency.
In this context, the Cumulative Frequency tells you how many total days had that number of emails or fewer. So, for 19 or fewer emails means anything up to receiving 19 emails.
From the Cumulative Frequency you provided:
- 11 days received 10 emails or fewer (Cumulative Frequency for 10 to 19 emails)
- 15 days received 20 emails or fewer (Cumulative Frequency for 20 to 29 emails)
- 19 days received 30 emails or fewer (Cumulative Frequency for 30 to 39 emails)
Therefore, the number of days your friend received 19 or fewer emails in a day is 11 days (the cumulative frequency up to 10 to 19 emails).
In this context, the Cumulative Frequency tells you how many total days had that number of emails or fewer. So, for 19 or fewer emails means anything up to receiving 19 emails.
From the Cumulative Frequency you provided:
- 11 days received 10 emails or fewer (Cumulative Frequency for 10 to 19 emails)
- 15 days received 20 emails or fewer (Cumulative Frequency for 20 to 29 emails)
- 19 days received 30 emails or fewer (Cumulative Frequency for 30 to 39 emails)
Therefore, the number of days your friend received 19 or fewer emails in a day is 11 days (the cumulative frequency up to 10 to 19 emails).
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