Question

3. Изобразите на координатной прямой и запишите в виде числовых промежутков объединение и пересечение промежутков ( — бесконечность ; 7] и [-6; 9)Пожалуйста ​

Answer 1

Ответ:

Пошаговое объяснение:

(-∞; 7]∩[-6; 9)=[-6; 7]

(-∞; 7]∪[-6; 9)=(-∞; 9)

             /////////////////////

------------.-------------------.------------------°------------------>x

            -6                    7                    9

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

Answer 2

Representation on a Number Line

To represent the intervals and find their union and intersection, let's first plot them on a number line:

- Interval A: (-∞, 7] - Interval B: [-6, 9)

The number line would look like this:

   -∞        -6        7         9
    |---------|---------|---------|
    A                   B

Union of Intervals

The union of two intervals is the set of all numbers that are in either of the intervals. To find the union of intervals A and B, we need to determine the range that covers both intervals.

Looking at the number line, we can see that the union of A and B would be from -∞ to 9, including 7 but excluding -6. Therefore, the union of intervals A and B can be represented as (-∞, 9).

Intersection of Intervals

The intersection of two intervals is the set of all numbers that are common to both intervals. To find the intersection of intervals A and B, we need to determine the overlapping range.

Looking at the number line, we can see that the intersection of A and B would be from -6 to 7, including -6 but excluding 7. Therefore, the intersection of intervals A and B can be represented as [-6, 7).

In summary:

- Union of intervals A and B: (-∞, 9) - Intersection of intervals A and B: [-6, 7)

Please let me know if there's anything else I can help you with!