Question

Use the number line below to determine which lf the following answer choices has statements that are all true

Answer 1

The correct answer is B, as it correctly identifies the points on the number line and their relationship.

The image shows a number line with certain points labeled, and the task is to determine the true statements about the locations of points A and D, as well as the relationships between certain values.

From the number line, we can see the following:

- Point A is located at -4.

- Point D is located at a position greater than 1 but less than 2, which corresponds to
`\(1(1)/(2)\)` or 1.5.

Now, we need to determine the truth of the inequalities given in the answer choices related to these points.

Given this information, let's evaluate the answer choices:

A. Point A represents -4, Point D represents
`\(1(1)/(2)\), and \(1(1)/(2) < -4\)`

- This statement is incorrect because
`\(1(1)/(2)\)` is greater than -4, not less.

B. Point A represents -4, Point D represents
`\(1(1)/(2)\)`, and
`-4 < \(1(1)/(2)\)`

- This statement is correct. Point A is indeed -4, Point D is indeed
`\(1(1)/(2)\)`, and -4 is indeed less than
`\(1(1)/(2)\)`.

C. Point A represents 4, Point D represents
`\(1(1)/(3)\)`, and
`4 > \(1(1)/(3)\)`

- This statement is incorrect. Point A does not represent 4, it represents -4, and Point D does not represent
`\(1(1)/(3)\)`; it represents
`\(1(1)/(2)\)`.

D. Point A represents -4, Point D represents
`\(1(1)/(3)\), and \(1(1)/(3)\) > -4`

- This statement is incorrect because Point D does not represent
`\(1(1)/(3)\)`; it represents
`\(1(1)/(2)\).`

The correct answer is B, as it correctly identifies the points on the number line and their relationship.

Answer 2

Given,

The number line is given above in the question.

Here, point A is lies left of the 0 in the given number line.

It is also seen that point A is at 4.

Hence, it is cleared that point A is lies at point -4 in the number line.

The point D is lies between the point C and 2.

It is clearly seen that the D is not mid point of C and 2.

It is bit right of mid point.

Hence, the point D is at 1 3/4 of the number lies.

As known that, always negative value is less than the positive value.

So,

`-4<1(3)/(4)`

Hence, option (d) is correct.