Find the third degree polynomial function that has an output of 40 when x=1, and has zeros −19 and −i?
Answer:
[tex]f(x) = (x + 19)(x^2 + 1)[/tex]
Step-by-step explanation:
Complex numbers:
The following relation is important for complex numbers:
[tex]i^2 = -1[/tex]
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Has zeros −19 and −i
If -i is a zero, its conjugate i is also a zero. So
[tex]f(x) = a(x - (-19))(x - (-i))(x - i) = a(x+19)(x+i)(x-i) = a(x+19)(x^2 - i^2) = a(x + 19)(x^2 + 1)[/tex]
Output of 40 when x=1
This means that when [tex]x = 1, f(x) = 40[/tex]. We use this to find the leading coefficient a. So
[tex]f(x) = a(x + 19)(x^2 + 1)[/tex]
[tex]40 = a(20)(2)[/tex]
[tex]40a = 40[/tex]
[tex]a = 1[/tex]
The polynomial is:
[tex]f(x) = (x + 19)(x^2 + 1)[/tex]
What is the answer
How do you solve it
Answer:
-50y+(-80)
Step-by-step explanation:
I'm lost on this please help
Answer:
Y=1/4x+33/4
Step-by-step explanation:
Y=1/4x+b
9=1/4(3)+b
9=3/4+b
8.25=33/4=b
Y=1/4x+33/4
Jill collected a total of 19 gallons of honey. If she distributes all of the honey equally between 7 jars, how much honey will be in each jar?
The linear function f(x) = 0 5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function 9(x) represents the average test score in your science
class, where x is the number of the test taken.
x 0x)
1 81
283
3 85
Part A: Determine the test average for your math class after completing test 2.
Part B: Determine the test average for your science class after the completing test 2.
Part C: Which class had a higher average after completing test 4? Show work to support your answer
Answer:
more information
Step-by-step explanation:
the parallelogram height is 1 and 1/2 times the base length and the base length is 6
-4x - 4(6x-14) +8(6x-10) - (20x -18)
Answer:
I believe it is -6
Step-by-step explanation:
Which expresses shows another way to write 36+16?
4(9 + 4), because :
4 * 9 + 4 * 4 = 36 + 16
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
53 and 17
Step-by-step explanation:
If you add 53 and 17, you get 70.
If you subtract 17 from 53, you get 36. Hope this helps!
Help me please I give brainliest and be serious
Answer:
15, y = 1/2x + 3.75
Step-by-step explanation:
Am not 100% sure but for #15
cuz I graphed it & it looks alike
What is the surface are of the box in square meters that Elizabeth decorates
Answer:
Step-by-step explanation:
C(x)=4x; R(x) = 6X-.001x²
Marginal cost?
Answer:
the answer is to commit uninstall
Step-by-step explanation:
gg wp
ce este un numar rational?
Answer:
ratio
Step-by-step explanation:
slove this plzzz plzzz
Answer:
an equilateral triangle have equal angles and equal sides.
so, side x and side bc are 12.
Answer:
It's going to be 12, so is the other size.
Step-by-step explanation:
You can see that in each corner, it shows the triangle is the same, which means it is equilateral, so the answer is 12 :D
What is the area of the top AND bottom faces?
Answer:
Top : 24cm²
Bottom : 24cm²
Step-by-step explanation:
Surface area : Base × Height
Top :
3 × 8 = 24
Bottom :
3 × 8 = 24
Which of the following gives a valid reason for using the given solution method to solve the system of equations shown?
Equation 1: 4x - 5y = 4
Equation Il: 2x + 3y = 2
A. Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
B
Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I
0
Substitution: Equation I can be solved for x in one step by dividing both sides by 4.
D.
Substitution: Equation Il can be solved for x in one step by subtracting 3y from both sides.
Answer:
C
Step-by-step explanation:
Factor completely
12n^3 + 15n^2 + 4n + 5
*NEED HELP QUICKLY*
my son is doing a math assignment and he needs this done within the hour. i tried to help with it but math isn’t my strong suit.
Answer: undefined
Step-by-step explanation:
I think im not sure tho
|x+3 , if x = 2. Plz help I will pick brainlist
Answer:
1(2)+3=5
Step-by-step explanation:
What is the answer to this
What is the equation ( y = mx + b) of the line that passes through (2,5) and (6, 13)
Answer:
y=2x+1
Step-by-step explanation:
y=mx+b
m=(13-5)/(6-2)
m=8/4
m=2
b=y-mx
b=5-2*2
b=5-4
b=1
y=2x+1
Answer:
y=2x+1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(13-5)/(6-2)
m=8/4
m=2
y-y1=m(x-x1)
y-5=2(x-2)
y-5=2x-4
y=2x-4+5
y=2x+1
Pleaseeeee helppppppp
Answer:
TIK TOK
Step-by-step explanation:
ON THE CLOCK
please help me solve this problem!!
Answer:
here's the link to the answer
Step-by-step explanation:
WWW.math.com/int.etg
Which equation is another way to show
5/4?
A. 1/5x1/4=
B. 4x1/5=
C. 4 divided by 5=
D. 5 divided by 4=
E. 5+1/4=
Answer:
D
Step-by-step explanation:
5 divided by 4 is just 5/4 written out
Two claimants place calls simultaneously to an insurer's claims call center. The times X and Y, in minutes, that elapse before the respective claimants get to speak with call center representatives are independently and identically distributed. The moment generating function of each random variable is
M(t)= (1/11.5t)^2 , t < 2/3
Required:
Calculate the standard deviation of X + Y.
The moment generating function of each random variable is;
M(t) = (1/(1 - 1.5t))^(2), t < 2/3
Answer:
SD[X + Y] = 3
Step-by-step explanation:
For ease of differentiation, let's rewrite the M(t) function as;
M(t) = (1 - (3/2)t)^(-2)
Let's find the first derivative of the function;
M'(t) = 3(1 - (3/2)t)^(-3)
To get E[X], we will put 0 for t to get;
E[X] = 3(1 - (3/2)0)^(-3)
E[X] = 3
Now,let's find the second derivative of M(t)
M"(t) = (27/2)(1 - (3/2)t)^(-4)
At,t = 0, we will get E[X²]
Thus;
E[X²] = 27/2
Now, Var[X] = E[X²] - (E[X])²
Var[X] = (27/2) - 3²
Var[X] = 9/2
We are told that the times X and Y are independently and identically distributed. Thus, the sum of their variances is equal to the variance of their sum. This is expressed as;
Var[X + Y] = 9/2 + 9/2
Var[X + Y] = 9
Now,we know that square root of variance is standard deviation. Thus;
SD[X + Y] = √9
SD[X + Y] = 3
15, 16, 21 determine wether the triangle is acute
Answer:
no they don't because you could not use those numbers
X + (x+1) + (x+2) = -21
Answer:
x= - 8
Step-by-step explanation: Are you solving for X if so here is the answer
Andrew bought 3 boxes of granlla bars. There are 13 granola bars in each box. choose the expression that shows how many granola bars Andrew brought.
13+b
13b
b÷13
13÷b
Answer:
13b
Step-by-step explanation:
Answer:
The correct Answer is B: 13B
Step-by-step explanation:
Have A Nice Day.
For this cylinder the radius = 6.8 inches and the height L = 14.2 inches. Which is the BEST estimate for the surface area?Use 3.14 what is this answer
Answer:
896.784
Step-by-step explanation:
Comment if you want the explanation
CAN SOMEONE HELP ME PLZZZ
Answer:2440
Step-by-step explanation: