This is a geometric sequence because each term is a constant multiple, called the common ratio, of the previous term. In this case the common ratio, noted as "r", is:
8/-2=-32/8=128/-32=r=-4
The first term is -2
Any geometric sequence can be expressed as:
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.
Since we know r and a for this problem already we can say:
a(n)=-2(-4)^(n-1)
Step-by-step explanation:
4:16
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Answer: y = x/2 + 3
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
Looking at the graph,
y2 = 6
y1 = 4
x2 = 6
x1 = 2
Slope,m = (6 - 4)/(6 - 2) = 2/4 = 1/2
To determine the intercept, we would substitute x = 2, y = 4 and m= 1/2 into y = mx + c. It becomes
4 = 1/2 × 2 + c
4 = 1 + c
c = 4 - 1
c = 3
The equation becomes
y = x/2 + 3
Since both the input and the output assume only integer values, the function is classified as discrete.
<h3>What are continuous and discrete variables?</h3>
- Continuous variables: Can assume decimal values, hence they are represented by rational numbers.
- Discrete variables: Assume only countable values, such as 1, 2, 3, …, hence they are represented by whole numbers, or even integers if it can be negative.
In this problem, all values on the table assume only integer values, hence the function is classified as discrete.
More can be learned about classification of variables at brainly.com/question/16978770
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Answer:
x = 4
Step-by-step explanation:
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We can solve for x by expanding the parentheses and isolating x.
<h3>Solve for x</h3>
- 3x - 2(2x - 5) = 2(x + 3)-8
- 3x - 4x + 10 = 2x + 6 - 8
- -x + 10 = 2x - 2
- 10 = 3x - 2
- 12 = 3x
- x = 4
The value of x is 4.
