Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
Answer:
m=9
Step-by-step explanation:
11-9m=-70
-11 -11
-9m = -81
divide both sides by -9 and you get m=9
Answer:
y = (5/2)x + 20
Step-by-step explanation:
Since the bus and train are both at the station at time 0, the y-intercept for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The existing graph shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So another point on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the slope. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another point on the line.
All you need to write an equation is the slope, m and the y-intercept, b and fill those two numbers into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get
y=(5/2)x +20
we conclude that the point on this line that is apparent from the given equation is (-6, 6)
<h3>
Which point is on the line, only by looking at the equation?</h3>
Remember that a general linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
Here we have the linear equation:
y - 6= (-23)*(x + 6)
Now, for a linear equation with a slope a and a point (h, k), the point slope form of the linear equation is:
(y - k) = a*(x - h)
Now we can compare that general form with our equation, we will get:
(y - k) = a*(x - h)
(y - 6) = (-23)*(x + 6)
Then we have: k = 6 and h = -6.
Thus, we conclude that the point on this line that is apparent from the given equation is (-6, 6).
If you want to learn more about linear equations:
brainly.com/question/1884491
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It depends on how many sides it has
If it has 2 then 50 percent
If it has 4 then 25 percent
If it has 5 then 20 percent
You divide the amount of sides by 100
x / 100 = percent
Example 2 / 100 = 50.
Hope This Helps!
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