Answer:
(n ≤ -3) ∪ (-1 ≤ n)
Step-by-step explanation:
I like to "unfold" the absolute value expression by copying the right-side expression to the left side (with the same comparison symbol) and negating its value. I do it this way because I find it easier to work the problem "all at once".
-1 ≥ n +2 ≥ 1
Obviously, -1 ≥ 1 is not true, which means the solution to this inequality will be disjoint sections of the number line. A compound inequality of this nature is generally interpreted to mean the AND of the two inequalities. So, technically, this is an incorrect step. I choose to overlook that, and consider the expression to represent the two inequalities ...
-1 ≥ n +2 . . . OR
n +2 ≥ 1
Subtracting 2 from the above compound inequality gives ...
-3 ≥ n ≥ -1
So, the solution is ...
(n ≤ -3) ∪ (-1 ≤ n)
_____
Further explanation
The inequality symbol negates its content if that content is negative. So, the expression ...
|n+2| ≥ 1
means ...
±(n +2) ≥ 1
This resolves to two cases:
n +2 ≥ 1
and
-(n +2) ≥ 1
The latter case is equivalent to ...
n +2 ≤ -1
which can also be written as ...
-1 ≥ n +2
A more technically correct solution process would identify the two cases and work them separately.
__
In the graph, the red shading (with the solid edge) shows the solution with respect to the numbers on the x-axis. If you were to graph this on a number line, you would put solid dots at -3 and -1, and shade the line to their left and right, respectively. The blue curve shows the absolute value, and the green line shows y=1, so you can see that the shaded areas correspond to the absolute value being greater than or equal to 1.
+
9
To add or subtract fractions, their denominators
must be the same. We can get a common
denominator by multiplying the second fraction
by 3/3.
6
-
(-}).
What number belongs in the green box?
Enter
A.56
B.6720
C.960
D.40
Using, binomial coefficient, the value of 8C5 is 56, which corresponds to option A.
To calculate the value of 8C5 (8 choose 5), we use the binomial coefficient formula:
nCr = n! / (r! * (n - r)!)
where n is the total number of items, r is the number of items chosen.
In this case, n = 8 and r = 5.
8C5 = 8! / (5! * (8 - 5)!)
Now, let's calculate the factorials:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
5! = 5 * 4 * 3 * 2 * 1 = 120
3! = 3 * 2 * 1 = 6
Now, substitute these values back into the formula:
8C5 = 40,320 / (120 * 6)
8C5 = 40,320 / 720
8C5 = 56
Therefore, the value of 8C5 is 56, which corresponds to option A.
To know more about binomial coefficient:
#SPJ6
Answer: The answer would be 56!
Step-by-step explanation:
6x7x8 / 3! =56
Answer:
it is 5 to figure 9 you move 8 units and 2 units
A. 12
B. 10
C. 9
D. 11