Point x is at 2/3 on a number line. on the same number line, point y is at the same distance from 0 as a point x, but has a numerator of 8 . what is the denominator of the fraction at point y? draw a number line to model the problem

The distance of the point x and y are given same. This fact can be used to derive the denominator of the fraction y:

The denominator of the fraction at point y is 12 and thus y = .

Given that:

Point x is at 2/3 on a number line.

Point y is at same distance as of the x from the point O but has numerator y.

Let the denominator of y be d. Then point x and y are at equal distance form the origin, thus we have:

Thus, the denominator of the fraction at point y is 12 and thus y = .

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The denominator is 12

Step-by-step explanation:

The Number Line

We can represent any real number in a properly segmented line, where the zero-mark is the separation between positive numbers to its right side and negative numbers to the left side.

We are given the number x = 2/3. Since it's positive, its location lies to the right of the zero but before the 1 as shown in the figure below.

We want to locate a second point y at the same distance from 0 as the point x, so we have two options: y is the same as x, or y is negative at the same distance from zero. We chose the last option.

Its numerator must be 8, so we need to multiply it by 4. But we cannot alter the value of x, so we must also multiply the denominator by 4, which gives us the fraction 8/12, but recall it must be negative.  

The denominator is 12

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: