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
Step-by-step explanation:
you can't use a calculator ?
that is all that is needed.
the original price $312.
it is $145 off.
so, the actual sales price is : 312 - 145 = $167
Answer:
(x, y+6) will vertically move 6 units up.
Step-by-step explanation:
If we move vertically 6 units up, 6 is added to the y-coordinate.
so
(x, y+6) will vertically move 6 units up.
For example, let suppose the point P(-2, 3). When we apply a translation of (x, y+6) to the point P(-2, 3), the coordinates of point P after the translation will be:
(x, y) → (x, y+6)
P(-2, 3) → P(-2, 9) ∵ P(-2, 3+6)
Therefore, (x, y+6) will vertically move 6 units up.
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
First, add all of the minutes together. You would get 75 minutes of practice per day.
Then you multiply 75 by 7, and you get 525 minutes.
He practices 525 minutes (or 8.75) hours per week
