1. What are the non-negative values among the given numbers -36, -0, -0.7, and 10.3? 2. Identify the true statements

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Sure! Here are the detailed and step-by-step solutions for each problem:

1. To determine the non-negative values among the given numbers (-36, -0, -0.7, and 10.3), we need to find the values that are greater than or equal to zero. Among the given numbers, we can identify that -0 and 10.3 are non-negative because they are greater than or equal to zero. Therefore, the non-negative values among the given numbers are -0 and 10.3.

2. Let"s evaluate each statement one by one:

1) 4.87 is a non-negative number.
This statement is true because 4.87 is greater than zero.

2) -4.87 is a rational number.
This statement is true because -4.87 can be expressed as a ratio of two integers (-487/100).

3) 4.87 is a non-positive number.
This statement is false because 4.87 is greater than zero, so it is not non-positive.

4) -4.87 is an integer.
This statement is false because -4.87 is a decimal number and not a whole number.

The true statements are 1) and 2).

3. To find the number with the largest absolute value among -35.5, 0, 7, and -29, we need to compare the absolute values of each number. The absolute value of a number represents its distance from zero on the number line without considering its sign.

The absolute values are as follows:
|-35.5| = 35.5
|0| = 0
|7| = 7
|-29| = 29

From the given numbers, the number with the largest absolute value is -35.5, as its absolute value (35.5) is greater than the absolute values of the other numbers.

For the pairs of numbers 26, 5.3 and 3.5, -15 and 15, and - and 37, the opposite numbers are as follows:
26 and -26
5.3 and -5.3
3.5 and -3.5
-15 and 15
- and 37 (No opposite number is given)

4. The pair of opposite numbers for 20 is (-20, 20). Opposite numbers have the same magnitude but opposite signs.

5. To find the value of the expression 126.4| + -0.6, we need to evaluate the absolute value of 126.4 and subtract 0.6 from it.
The absolute value of a number is always positive or zero. Therefore, |126.4| = 126.4.
So the expression becomes: 126.4 + (-0.6)
Adding these numbers together gives us: 125.8

6. In the expression |16, 1:... = -4.1|, we need to determine what value should replace the "..." to make the equation true.
For the given equation, |16, 1:... = -4.1|, the symbol "|" represents the absolute value of a number.
To find the value that satisfies the equation, let"s evaluate each side of the equation separately:

Left side: |16, 1:...
The absolute value of a number represents its distance from zero on the number line. Since 16 is positive, the absolute value of 16 is 16.
So the left side of the equation becomes: 16, 1:...

Right side: -4.1
We already have the right side of the equation as -4.1.
So the right side remains the same.

To make the equation true, the value on the left side should be equal to the value on the right side. Therefore, the value that replaces "..." is -4.1.

I hope this explanation helps! If you have any further questions, feel free to ask.