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>
Solving a system of equations, we can see that:
- Speed of the private jet: 168 mi/h
- Speed of the commercial jet: 192mi/h
<h3>How to find the speeds of each jet?</h3>
Let's define the variables:
- P = speed of the private jet.
- C = speed of the commercial jet.
With the given information, we can write:
P*8h = D
C*7h = D
C = 2*P - 144mi/h
So we have a system of 3 equations, where D is the distance in the problem.
With the first and second equations we can write:
P*8h = D = C*7h
Isolating P, we get:
P = C*(7/8)
Now we can replace that in the last equation:
C = 2*P - 144mi/h
C = 2*C*(7/8) - 144mi/h
And now we can solve that for C.
C - 2*(7/8)*C = - 144mi/h
C*(1 - 14/8) = -144mi/h
C*(8/8 - 14/8) = - 144mi/h
C*(6/8) = 144mi/h
C = (8/6)*144mi/h = 192mi/h
Now that we know the speed of the commercial jet, we can find the speed of the private jet.
P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h
If you want to learn more about systems of equations:
brainly.com/question/13729904
#SPJ1
Answer: x = 40.81 or 41
Step-by-step explanation:
A = B = 21
C = 35
Hypotenuse = x
Calculating Hypotenuse:
21^2 + 35^2 = x^2
=> 441 + 1225 = x^2
=> x^2 = 1666
=> x = 40.81 or 41
Answer: Option (3)
Step-by-step explanation:
The slope of the given line is
Thus, the answer must be Option (3)
