Answer:
x = -6/11
Step-by-step explanation:
-6(-4x + 3) = 2(10x + 3)
-6 * -4x = -24x
-6 * 3 = -18
2 * 10x = 20x
2 * 3 = 6
-24x - 18 = 20x + 6
-20x -20x
-44x - 18 = 6
+18 +18
-44x = 24
------- ------
-44 -44
24/-44 = -24/44
-24/44 = -6/22
x = -6/11
Answer:
Periodic
Step-by-step explanation:
Because the terms repeat, this is a periodic sequence.
Answer:
2. 1 / a^2
3, 1
4. - 1
Step-by-step explanation:
Formulas : -
x^y / x^z = x^( y - z )
x^-y = 1 / x^y
x^y / x^y = 1
2.
a^2 / a^4
= a^( 2 - 4 )
= a^-2
= 1 / a^2
3.
m^6 / m^6 = 1
4.
- 8^4 / 8^4
= - 1 x 8^4 / 7^4
= - 1
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
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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
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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.
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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
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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.
