Describe what happens to the graph of y=3x + 4 when the slope is changed 1/3 one over three
1 answer:
Answer:
see the explanation
The graph in the attached figure
Step-by-step explanation:
we have
This is a linear equation (the graph is a line)
The y-intercept is the point (0,4) ---> value of y when the value of x is equal to zero)
The x-intercept is the point (-4/3,0) ---> value of x when the value of y is equal to zero)
The slope is m=3
If the slope is changed to m=1/3
we have
This is a linear equation too (the graph is a line)
The y-intercept is the point (0,4) ---> is the same
The x-intercept is the point (-12,0) ---> the x-intercept is different
The slope is m=1/3
The second line becomes a lot less steep
Remember that the slope is the ratio between the rise and the run
In the first line the ratio rise/run is 4/1
In the second line the ratio rise/run is 1/3
see the attached figure to better understand the problem
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Answer:
22.5
Step-by-step explanation:
If you expand the series, you can see the first few terms of the series:
- Putting 1 in
,
- Putting 2 in
- Putting 3 in
- Putting 4 in
We can see the series is 0, 0.5, 1, 1.5, ....
This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.
We know formula for sum of arithmetic series:
Where,
denotes the nth partial sum
is the first term (in our case it is 0)
is the common difference (difference in term and the previous term) (in our case it is 0.5)
Substituting these into the formula, we get the 10th partial sum to be:
So the sum of the first 10 terms is 22.5. Third answer choice is right.