V + 9 over 3= 8 what is v?
2 answers:
You might be interested in
Answer:
Recursive:
Explicit:
And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:
Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:
Explicit Rule:
The standard format for the explicit rule is:
Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:
Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:
Evaluate:
Hence, the 20th term is 225.
Problem 4
<h3>Answer:</h3>------------------
Work Shown:
The left line goes through (-2,0) and (0,4)
The slope of this line is
m = (y2-y1)/(x2-x1)
m = (4-0)/(0-(-2))
m = (4-0)/(0+2)
m = 4/2
m = 2
The y intercept is b = 4
Since m = 2 and b = 4, this means y = mx+b turns into y = 2x+4. This portion is only done when x < 1. Note the open circle at the endpoint of this portion. So we do not include x = 1 as part of this piece.
---
The line on the right side goes through (1,-2) and (2,-1)
Slope
m = (y2-y1)/(x2-x1)
m = (-1-(-2))/(2-1)
m = (-1+2)/(2-1)
m = 1/1
m = 1
The y intercept is b = -3. You can see this if you extend the line until it crosses the y axis.
Alternatively, plug in (x,y) = (1,-2) and m = 1 into y = mx+b to find that b = -3
So y = mx+b turns into y = 1x+(-3) or just y = x-3
We combine both parts to end up with
This is only graphed when (note the closed or filled in circle for the endpoint of this portion).
===================================================
Problem 5
Answer:
<h3>------------------
Work Shown:
y = |x| .... parent function
y = |x+3| ... shift 3 units to the left
y = (1/2)*|x+3| .... vertically compress by factor of 1/2
f(x) = (1/2)*|x+3|
------
Break that down into a piecewise function
when x < -3, then y = -(1/2)(x+3)
when , then y = (1/2)(x+3)
I'm using the rule that y = |x| turns into y = -x when x < 0 and y = x when
So that is how we get as the piecewise function.