Answer:
First choice: m = -4
Step-by-step explanation:
The second equation is already solved for n, so lets's use the substitution method and substitute m - 2 for n in the first equation.
m - 2n = 8
m - 2(m - 2) = 8
m - 2m + 4 = 8
-m + 4 = 8
-m = 4
m = -4
As
, the sequence
converges to zero.
If you're talking about the infinite series
well we've shown by comparison that this series must also converge because we know any geometric series
will converge as long as
.
Answer:
y=53x-7
Step-by-step explanation:
5x-3y=21
-3y=-5x+21
divide by 3
y=5/3x-7
Answer:
8 days
Step-by-step explanation:
On day 8, Isabella will save 256 nickels, bringing her total to 510.
_____
The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.
_____
The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.
__
The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...
an = a1·r^(n-1) = 2·2^(n-1) = 2^n
The sum of n terms of the sequence is ...
S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)
S = 2^(n+1) -2
__
We want S > 500, so ...
500 < 2^(n+1) -2
502 < 2^(n+1)
251 < 2^n
log(251) < n·log(2)
n > log(251)/log(2)
n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels
Answer:
Step-by-step explanation:
First, begin by multiplying 
by its reciprocal.
To do this, flip the fraction upside-down.
The resulting equation looks like this: 
Cancel out the two 27's and you are left with 
, which you can simplify to q.
Next, multiply -3 by 
. Remember, what you do on one side, you must do on the other.
Your equation should look like this:
The final answer is .
Have a nice day!
