Given:
A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .
To find:
The fourth-degree polynomial function in factored form.
Solution:
The factor for of nth degree polynomial is:
[tex]P(x)=(x-a_1)(x-a_2)...(x-a_n)[/tex]
Where, [tex]a_1,a_2,...,a_n[/tex] are n zeros of the polynomial.
It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:
[tex]P(x)=(x-4)(x-(-4))(x-4i)(x-(-4i))[/tex]
[tex]P(x)=(x-4)(x+4)(x-4i)(x+4i)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2-(4i)^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
On further simplification, we get
[tex]P(x)=(x-4)(x+4)(x^2-4^2i^2)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2+16)[/tex] [tex][\because i^2=-1][/tex]
Therefore, the required fourth degree polynomial is [tex]P(x)=(x-4)(x+4)(x^2+16)[/tex].
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Polynomials can be classified based on degree as linear, quadratic, cubic, fourth degree.
Let f(x) represent the function with zeros 4, -4, 4i , and -4i. Hence:
x = 4; x = -4; x = 4i; x = -4i
x - 4 = 0; x + 4 = 0; x - 4i = 0; x + 4i = 0
f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
Find out more on polynomial at: https://brainly.com/question/2833285
How many significant figures are in 609.80
There are 5 significant figures.
6.8 x + 9.3 6.8 x + 9.3 equals -9.4 + 3.4 (2 minus 5x)
Answer:
x=-0.5
Step-by-step explanation:
6.8x + 9.3= -9.4 + 3.4 (2-5x)
6.8x + 9.3 = -9.4 + 6.8 - 17x
6.8x + 9.3 = -2.6 - 17x
22.8x = -11.9
x = -0.5
Pls help I’ll give brainliest
Answer:
5
Step-by-step explanation:
Multiply and simplify. y^3 . y^5 . y^-2 .y
A. y^-4
B. 1/y^4
C. y^-5
D. 1/ y^3
Answer:
y^7
Step-by-step explanation:
y^3 . y^5 . y^-2 . y
= y^3 . y^5 . y^-2 . y^1
= y^( 3 + 5 - 2 + 1 )
= y^( 3 + 5 + 1 - 2 )
= y^( 9 - 2 )
= y^7
What is the standard form of a trinomial?
Answer:
ax2 + bx + c
Step-by-step explanation:
the 2 is the square
Find the value of x in this equation?
-1 = x - 2
Answer:
-1=x-2
-1+2=x
x=1
Step-by-step explanation:
You have a box with 5 blue marbles, 4 red marbles, and 9 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a blue marble followed by a yellow marble?
Answer:
I think it's 45/196.
Step-by-step explanation:
Not sure though, no explanation.
The probability of pulling out a blue marble followed by a yellow marble 25% or 0.25 .
What is probability ?
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Based on the given conditions, formulate 9 ×9÷((9 + 5 + 4) ×(9 +5 +4))
Calculate the product or quotient = [tex]\frac{81}{(9 +5 + 4) * (9 + 5 + 4)}[/tex]
Calculate the sum or difference= [tex]\frac{81}{(14 + 4) * (9 +5+4)}[/tex]
Calculate the sum or difference = [tex]\frac{81}{18 * (9+5+4)}[/tex]
= [tex]\frac{81}{18 * (14 + 4)}[/tex]
=[tex]\frac{81}{18 * 18}[/tex]
Calculate the product or quotient = [tex]\frac{81}{324}[/tex]
Cross out the common factor = [tex]\frac{1}{4}[/tex]
get the result 25% or 0.25
Therefore, The probability of pulling out a blue marble followed by a yellow marble 25% or 0.25 .
Learn more about probability brainly.com/question/743546
#SPJ2
Simplify. Evaluate the numerical bases. 2^3 x ^3y ^-2 . 2^-5 xy^2
A. 4x^4
B. x^4 /4
C. x^4 / 2y^4
D. 2x^4 / y^4
9514 1404 393
Answer:
B. x^4/4
Step-by-step explanation:
[tex]2^3x^3y^{-2}\cdot 2^{-5}xy^2=2^{3-5}x^{3+1}y^{-2+2}=2^{-2}x^4\\\\=\boxed{\dfrac{x^4}{4}}[/tex]
_____
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
HELP I WILL GIVE BRAINIEST
Answer:
sorry I can only answer no.3
[tex]4x - 2 = 180 \\ 4x = 180 + 2 \\ 4x + 3x = 182 \\ \frac{7x}{7} = \frac{182}{7} \\ x = 26[/tex]
Help please I’ll mark you brainliest!!
Answer:
35 ft
Step-by-step explanation:
Sorry this took me so long, I am 99% sure it is right though
I hope this helps :)
what is 4 1/2 plus 6 2/5
Answer:
10.9
Step-by-step explanation:
4 1/2 plus 6 2/5=10.9
Answer: 10.9
Step-by-step explanation:
If a fair die is rolled 6 times, what is the probability, to the nearest thousandth, of
getting exactly 2 threes?
Answer:
The probability of rolling the die once to get a four is 1/6
Step-by-step explanation:
So we do 1/6*1/6*1/6 which is 1/216 since it's combined probabilities
Brainliest?
I will post the other reasons rn
Answer:
yeah i gotta see the others
Step-by-step explanation:
select the compound inequality shown on the graph.
Find the area of the given triangles. please and thank you
Answer:
6cm squared
Step-by-step explanation:
to find the area of a triangle, it is base x height divided by 2
4 x 3 = 12
12 divided by 2 = 6
We have a population of 200 people with a growth rate of 2%. Which equation do we use to calculate how long it will take for the population to double to 400 people? 70/.2 200/,2 200x2 400/2 70/2 70/.02 200/.02 200x.02 200/2
Answer:
70/2
Step-by-step explanation:
We have a population of 200 people
Growth rate = 2%
How long it will take for the population to double
Double the population = 2× 200 = 400
The formula for Exponential growth =
y = a(1 + r)^t
y = Value at time t = 400
a = Initial value = 200
r = 2% = 0.02
t = ?
Hence:
400 = 200 ( 1 + 0.02)^t
Divide both sides by 200
400/200 = 200 ( 1 + 0.02)^t/200
2 = (1.02)^t
Take logarithm of both sides
log 2 = log(1.02)^t
log 2 = t log 1.02
t = log 2/log 1.02
t = 35.003417942
Approximately t = 35
We have so many formula to calculate doubling time
t = 70/Growth rate
From the above question
Growth rate = 70/2%
= 35
Therefore, the equation that we use to calculate how long it will take for the population to double to 400 people is 70/2
Solve the algebraic expression , is it equivalent?
Answer:
No
Step-by-step explanation:
When you distribute the -2 you get 6x -2x+2. When you simplify it you get 4x+2 which is different than 4x-2.
A cylinder with height of 4 meters has a volume of 2,827.43 cubic meters. Find the length of the diameter.
Answer: 30 meters
Step-by-step explanation:
Volume of a cylinder = πr^2h
2,827.43 = πr^2(4)
2,827.43 = 3.14(4)r^2
2,827.43 = 12.56*r^2
2,827.43/12.56 = (12.56*r^2)/12.56
225.11 = r^2, find square root of both sides
r = 15
diameter = 30
GUYS SINCE YOU ARE SMART AND IM NOT HELP PLEASE
The volume of a cylinder is 325 pi cubic centimeters and its radius is 5 centimeters.
What is the height of the cylinder?
__cm
Answer:
13 cm
Step-by-step explanation:
just took the test
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
see explanation
Step-by-step explanation:
j - 4 ≤ 0 ( add 4 to both sides )
j ≤ 4
The graph has a closed circle at 4 on the number line with the arrow pointing left
8x−2=−11+7x +2
Please help me!!
Answer:
x=-7
Step-by-step explanation:
8x - 2 = -11 + 7x + 2
First, separate the terms: move x to one side
subtract 7x from both sides
8x -7x - 2 = -11 + 7x -7x + 2
x - 2 = -11 + 2
Now get x by itself by adding 2 to both sides
x - 2 +2 = -11 + 2 +2
x = -11 + 4
simplify
x = -7
you're welcome
Mary made 12 bracelets. 9 of those bracelets are the color blue.
What percent of bracelets are blue?
Answer:
75%
Step-by-step explanation:
We know that Mary made twelve bracelets and also that nine of them are blue, we are then asked to find the percentage of the bracelets that are blue.
To solve, first get a fraction of how many of the bracelets are blue. Since there are twelve in total, 12 will be our denominator, and since 9 are blue, 9 will be our numerator.
[tex]\frac{9}{12}[/tex]
Now to turn this into a percentage, we need to reduce this fraction to the lowest we can. Both numerator and denominator are divisible by 3, so do as followed :
[tex]\frac{9/3}{12/3}[/tex]
[tex]\frac{3}{4}[/tex]
Divide 3 by 4 :
[tex]3/4 = 0.75[/tex]
Multiply 0.75 by 100 to get our percentage :
[tex]0.75 * 100 = 75[/tex]%
Two angles which are on opposite sides of the transversal and between the parallel lines and do not share the same vertex. They are congruent.
Answer:
Interior angles are congruent.
Step-by-step explanation:
We see that angles 3,4,5,6 are between the two parallel lines . These angles are called interior angles.
Angles 3,6 are opposite and do not share the same vertex.
Similarly angles 4 and 5 do not share the same vertex.
They are congruent.
If we look closely we see that angles 3 &4 and angles 5&6 are supplementary angles.
i.e they together make up the 180 degrees on the straight line.
On the outer sides of the parallel lines angles 1&2 and angles 7 & 8 are exterior angles
which also make supplementary angles on the parallel lines.
From the diagram we see that
∠ 5= ∠7
and
∠6 = ∠ 8
as the corresponding angles are equal
∠8=∠3
∠7=∠4
As they are opposite angles
Similarly
∠1=∠6
∠2=∠5 ( opposite angles)
From above
∠5=∠7
but ∠7= ∠4
therefore
∠ 5= ∠4-----------------A
Also
∠6 = ∠ 8
but ∠8=∠3
therefore
∠6=∠8----------------------B
From An and B we conclude interior angles are congruent
Jade has tax deducted from her income at the rate of 24%.
Last month, after tax had been deducted, $1786 of her income remained.
Calculate her income last month before the tax was deducted.
Answer:
$2350
Step-by-step explanation:
Let Jade's total income be X
Therefore,the tax deducted was 24%x
Forming an equation:
X= 24%x + 1786
X = 0.24x + 1786
Collecting like terms
x - 0.24x = 1786
0.76x =1786
x= 1786 ÷0.76
X= $2350
18.6 in
Which is the best approximation for the measure of angle
EGF?
32.8°
40.2
OOO
49.8°
57.2
Answer:
The answer is "[tex]40.2^{\circ}[/tex]"
Step-by-step explanation:
Please find the graph file.
Let
[tex]\angle EGF = x\\\\\sin x = \frac{12}{18.6}\\\\\sin x = 0.6452 \\\\x = \sin^{-1} (0.64516129) \\\\x = 40.1777695^{\circ} \approx 40.2^{\circ}[/tex]
i need help asap please
Answer:
1. 1570
2. can't see properly
3. can't see properly
4. 392.5
5. 615.4
6. 6049
7. not clear can't see
8. 1589
9.:1570
I know this is in german but i really really need help...
Answer:
i would have helped u
Step-by-step explanation:
but i have forgotten the steps in solving this question
Answer:
is this Afrikaans laguage I don't understand your questions please comment it in English for me
Answer the question in the picture?
Answer:
19
Step-by-step explanation:
we know the sides of a rhombus is all equal, so:
4(2x+4)=168
8x+16=168
8x=152
x=19
x2 + 4
Select all that apply
Answer:
The first three depending on what the first one says. 2 and three are definitely correct though. If the first one says x to the second power added by 4 then it is correct.
Step-by-step explanation: