Question
Use graphs to find the set.
left parenthesis negative 5 comma 2 right parenthesis intersect left bracket negative 3 comma 9 right bracket
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The set is
enter your response here. (Type your answer in interval notation.)
B.
The set is the empty set.
left parenthesis negative 5 comma 2 right parenthesis intersect left bracket negative 3 comma 9 right bracket
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The set is
enter your response here. (Type your answer in interval notation.)
B.
The set is the empty set.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the intersection of the set \((-5, 2)\) and the interval \([-3, 9]\), we need to determine the values that are common to both sets.
1. **Interval \((-5, 2)\)**: This is an open interval that includes all numbers greater than \(-5\) and less than \(2\). It does not include \(-5\) or \(2\).
2. **Interval \([-3, 9]\)**: This is a closed interval that includes all numbers greater than or equal to \(-3\) and less than or equal to \(9\). It includes the endpoints \(-3\) and \(9\).
To find the intersection, we look for numbers that are in both intervals.
- The interval \([-3, 9]\) starts at \(-3\), which is less than the upper bound of the first interval, \(2\).
- The first interval ends at \(2\), which is also included in the second interval.
In graphical terms, we can visualize:
- The first interval from \(-5\) to \(2\) (excluding \(-5\) and \(2\)).
- The second interval from \(-3\) to \(9\) (including \(-3\) and \(9\)).
The intersection of these intervals is \([-3, 2)\), which means:
- The left endpoint is \(-3\) (included since it is in the closed interval).
- The right endpoint is \(2\) (not included since it is an open interval).
So, the intersection can be expressed in interval notation.
**Thus, the correct choice is:**
A. The set is \([-3, 2)\).
If you need to fill in the answer box:
**Answer: \([-3, 2)\)**.
1. **Interval \((-5, 2)\)**: This is an open interval that includes all numbers greater than \(-5\) and less than \(2\). It does not include \(-5\) or \(2\).
2. **Interval \([-3, 9]\)**: This is a closed interval that includes all numbers greater than or equal to \(-3\) and less than or equal to \(9\). It includes the endpoints \(-3\) and \(9\).
To find the intersection, we look for numbers that are in both intervals.
- The interval \([-3, 9]\) starts at \(-3\), which is less than the upper bound of the first interval, \(2\).
- The first interval ends at \(2\), which is also included in the second interval.
In graphical terms, we can visualize:
- The first interval from \(-5\) to \(2\) (excluding \(-5\) and \(2\)).
- The second interval from \(-3\) to \(9\) (including \(-3\) and \(9\)).
The intersection of these intervals is \([-3, 2)\), which means:
- The left endpoint is \(-3\) (included since it is in the closed interval).
- The right endpoint is \(2\) (not included since it is an open interval).
So, the intersection can be expressed in interval notation.
**Thus, the correct choice is:**
A. The set is \([-3, 2)\).
If you need to fill in the answer box:
**Answer: \([-3, 2)\)**.
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