Answer:
Step-by-step explanation:
A standard polynomial in factored form is given by:
Where <em>p</em> and <em>q</em> are the zeros.
We want to find a third-degree polynomial with zeros <em>x</em> = 2 and <em>x </em>= -8i and equals 320 when <em>x </em>= 4.
First, by the Complex Root Theorem, if <em>x</em> = -8i is a root, then <em>x </em>= 8i must also be a root.
Therefore, we acquire:
Simplify:
Expand the second and third factors:
Hence, our function is now:
It equals 320 when <em>x</em> = 4. Therefore:
Solve for <em>a</em>. Evaluate:
So:
Our third-degree polynomial equation is:
Subtract 16 to get
x^2 -25 = 0
Factor this as
(x -5)(x +5) = 0
The zero product property tells you the product will be zero when one of the factors is zero.
For x-5 = 0
x = 5
For x+5 = 0
x = -5
The appropriate choice is
3) x=-5 or x=5
Option ( C ) is the correct answer.
Option A:
I and III only the answers.
Solution:
Let white vases be "w" and red vases be "r".
Cost of total flower = $336
Cost of each vase = $11
Total cost of the centerpieces
= Cost of (white vases + red vases) + Cost of flowers
= 11(w + r) + 336
= 11w + 11r + 336
Total cost of the centerpieces = 11w + 11r + 336 = 11(w + r) + 336
Therefore I and III only the answers.
Option A is the correct answer.
<h3>5 gallons of 50 % alcohol solution is used</h3>
<em><u>Solution:</u></em>
Let "x" is the gallons of 50 % alcohol solution
Then, 10 gallons is 35 % solution
The, 10 + x is the gallons of 40 % solution
Then, according to question,
"x" gallons of 50 % solution is mixed with 10 gallons of 35 % solution to get 10 + x gallons of 40 % solution
Therefore,
Thus 5 gallons of 50 % alcohol solution is used
