A1 = first term = 8
<u>Plug in a1 = 8:</u>
an = 8 + (n - 1)d
<u>FInd d:</u>
Given that a2 = 5
5 = 8 + (2-1)d
5 = 8 + d
d = -3
<u>Plug in d = -3:</u>
an = 8 -3(n - 1)
Answer: an = 8 -3(n - 1) ; <span>n ≥ 1</span>
Answer:
False
Step-by-step explanation:
The sum of the smaller two sides must be larger than the third side
8+7 > 15
15 >15
This is not true so the three sides cannot form a triangle
29.9, 30.0,30.1,30.5,30.7,30.08,31.0,31.0
the number of data is 8 elements so the medium will be the 3rd and 4th number
so the medium is 30.5 and 30.7
Answer:
a.
<u>Increasing:</u>
x < 0
x > 2
<u>Decreasing:</u>
0 < x < 2
b.
-1 < x < 2
x > 2
c.
x < -1
Step-by-step explanation:
a.
Function is increasing when it is going up as we go rightward
Function is decreasing when it is going down as we go rightward
We can see that as we move up (from negative infinity) until x = 0, the function is increasing. Also, as we go right from x = 2 towards positive infinity, the function is going up (increasing).
So,
<u>Increasing:</u>
x < 0
x > 2
The function is going down, or decreasing, at the in-between points of increasing, that is from 0 to 2, so that would be:
<u>Decreasing:</u>
0 < x < 2
b.
When we want where the function is greater than 0, we basically want the intervals at which the function is ABOVE the x-axis [ f(x) > 0 ].
Looking at the graph, it is
from -1 to 2 (x axis)
and 2 to positive infinity
We can write:
-1 < x < 2
x > 2
c.
Now we want when the function is less than 0, that is basically saying when the function is BELOW the x-axis.
This will be the other intervals than the ones we mentioned above in part (b).
Looking at the graph, we see that the graph is below the x-axis when it is less than -1, so we can write:
x < -1
