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gavmur [86]
3 years ago
7

Consider this set of fractions. 2/3 , negative 2/3, 1, -1, 1/3, negative 1/3 Explain the order and placement of these numbers on

a number line.​
Mathematics
2 answers:
valkas [14]3 years ago
6 0

Answer:

<u>Summarizing, we place the fractions provided in this order from left to right:</u>

<u>-1 < -2/3 < - 1/3 < 1/3 < 2/3 < 1</u>

<u>or in order from right to left on the number line:</u>

<u>1 > 2/3 > 1/3 > -1/3 > -2/3 > -1</u>

Step-by-step explanation:

1. Let's place the set of fraction numbers given on a number line. We'll place the lowest on the extreme left and we'll continue to place the rest until we place the highest on the extreme right, this way:

On the extreme left:

Negative 1 (It is the lowest number)

The next one from the left to right is:

Negative 2/3

- 2/3 > - 1

The next one, to the right of - 2/3 is:

Negative 1/3

- 1/3 > - 2/3

The fourth from left to right is:

1/3

Positive numbers are always bigger than negative numbers and 1/3 is the lowest positive number we have in this set.

The fifth from left to right is:

2/3

Finally, the highest number in this set and in the extreme right of the number lines is;

1

<u>Summarizing, we place the fractions provided in this order from left to right:</u>

<u>-1 < -2/3 < - 1/3 < 1/3 < 2/3 < 1</u>

<u>or in order from right to left on the number line:</u>

<u>1 > 2/3 > 1/3 > -1/3 > -2/3 > -1</u>

In-s [12.5K]3 years ago
4 0

Answer:

Sample Response: The negative numbers go to the left of zero, and the positive ones go to the right. Numbers get larger as you move to the right.  

The correct order is −1, −  2 /3 , −  1 /3 ,   1 /3 ,   2 '3 , 1.

or

The correct order is Negative 1, negative two-thirds, negative one-third, one-third, two-thirds, 1..

Positive numbers are to the right of zero.

Negative numbers are to the left of zero.

Numbers increase from left to right.

place ^^ any of these and you will get them correct on :)

Step-by-step explanation

good luck everyone :)

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Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK
lesantik [10]
Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2

==============================================

Explanation:

For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval

In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ] 
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank

-------------------------------------------

To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.

-------------------------------------------

Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4

This is why f(-4) = -3

-------------------------------------------

We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.

From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]

We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3

Doing those replacements and simplifying leads to...

[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2

So the average rate of change is 2

Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.

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How does the volume of the larger cube compare to the volume of the smaller cube? Use pencil and
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Answer:

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the volume of the larger would be 7.8^3 = 474.55

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