Answer:
a[n] = a[n-1]×(4/3)
a[1] = 1/2
Step-by-step explanation:
The terms of a geometric sequence have an initial term and a common ratio. The common ratio multiplies the previous term to get the next one. That sentence describes the recursive relation.
The general explicit term of a geometric sequence is ...
a[n] = a[1]×r^(n-1) . . . . . where a[1] is the first term and r is the common ratio
Comparing this to the expression you are given, you see that ...
a[1] = 1/2
r = 4/3
(You also see that parenthses are missing around the exponent expression, n-1.)
A recursive rule is defined by two things:
- the starting value(s) for the recursive relation
- the recursive relation relating the next term to previous terms
The definition of a geometric sequence tells you the recursive relation is:
<em>the next term is the previous one multiplied by the common ratio</em>.
In math terms, this looks like
a[n] = a[n-1]×r
Using the value of r from above, this becomes ...
a[n] = a[n-1]×(4/3)
Of course, the starting values are the same for the explicit rule and the recursive rule:
a[1] = 1/2
9+6= 15
15+5=20
20+15=35
35 is the answer.
Answer:
A
Step-by-step explanation:
If you want to figure out all you have to do is divide 465 by 16.5.
The only equation that shows that is the first one. In equations you need to get the X by itself so you'll have to divide to do that.
It's same if you say something like "You have 4 apples but need to divide them in 2 groups."
The green one is a 1:4 Scale. Or the blue one is 4x larger.
-WarriorGT
Answer:
17. D
18. C
Step-by-step explanation:
For both of these questions, you only need a general understanding of what rotation, translation, and dilation do. That is sufficient to let you choose the correct answer.
<h3>17.</h3>
The coordinates of Y are both negative, so it is a point in quadrant III on the graph. Rotating a point in quadrant III 270° clockwise will rotate it through quadrants II and I to quadrant IV, where it will be to the right and below the origin. Translation 9 units right and 5 units down will put it farther to the right and farther below the origin, still in quadrant IV.
As you know, translation right 9 units adds 9 to the x-coordinate. Translation down 5 units subtracts 5 from the y-coordinate. That means the coordinates of Y' must have x > 9 and y < -5. There is only one answer choice like that:
D. Y'(11, -8)
__
<h3>18.</h3>
Dilation about the origin multiplies each coordinate by the scale factor. It does not change the quadrant of a point on the graph. The original coordinates of R are (negative, positive), so it is in quadrant II. The dilated point will still be in quadrant II, but will be closer to the origin. Both coordinate values will change.
R' = (1/3)R = (1/3)(-2, 3) = (-2/3, 3/3)
R' = (-2/3, 1) . . . . . matches choice C