So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:
<em>(Note that synthetic division can only be used when the divisor is a 1st degree binomial)</em>
- -10 | 1 + 2 - 82 - 28
- ---------------------------
Now firstly, drop the 1:
- -10 | 1 + 2 - 82 - 28
- ↓
- -------------------------
- 1
Next, you are going to multiply -10 and 1, and then combine the product with 2.
- -10 | 1 + 2 - 82 - 28
- ↓ - 10
- -------------------------
- 1 - 8
Next, multiply -10 and -8, then combine the product with -82:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80
- -------------------------
- 1 - 8 - 2
Next, multiply -10 and -2, then combine the product with -28:
- -10 | 1 + 2 - 82 - 28
- ↓ -10 + 80 + 20
- -------------------------
- 1 - 8 - 2 - 8
Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).
<u>Putting it together, the quotient is
</u>
Step-by-step explanation:
(b) If
then
Note that
cancel out so we get

Solving for
we get

(c) I'm not sure what the problem is asking for but here goes. As r doubles,
becomes

Answer:
Amount invested at 8% is $9000 and amount invested at 18% is $21000.
Step-by-step explanation:
Let amount invested at 8% be x.
Let amount invested at 18% be y.
We get the 1st equation as:
........(1)
We get the second equation as:

=> 
or getting rid of the decimal by multiplying by 100 on both sides.
........(2)
Multiplying (1) by 8 and subtracting from (2) we get
So, y = 21000
And 

So, x = 9000
Therefore, amount invested at 8% is $9000 and amount invested at 18% is $21000.
Answer:
steps below
Step-by-step explanation:
2ⁿ⁺¹ +2ⁿ⁻¹ = 2ⁿ⁻¹ (2² + 1) = 5*2ⁿ⁻¹
Answer:
Daddy
Step-by-step explanation:
Chill