The factoring of the polynomial x^4+4x^3+7x^2+16x+12 = 0, considering it's linear factors, is given as follows:
(x² + 5.4x + 11.29)(x + 1)(x + 3).
How to factor the polynomial?The polynomial for this problem is defined as follows:
x^4+4x^3+7x^2+16x+12 = 0.
We want to factor the polynomial according to it's linear factors, hence the Factor Theorem is used.
The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
The coefficients of the polynomial in this problem are given as follows:
a = 1, b = 4, c = 7, d = 16, e = 12.
Inserting these coefficients into a 4th degree equation solver, the roots are given as follows:
x = -2.7 + 2i.x = -2.7 - 2i.x = -1.x = -3.Hence the polynomial is factored as follows:
(x + 2.7 - 2i)(x + 2.7 + 2i)(x + 1)(x + 3).
Applying the subtraction of perfect squares for the first two linear factors, considering that i² = -1, we have that:
(x + 2.7 - 2i)(x + 2.7 + 2i) = (x + 2.7)² - (2i)²
(x + 2.7 - 2i)(x + 2.7 + 2i) = (x² + 5.4x + 11.29).
Hence the factored polynomial is of:
(x² + 5.4x + 11.29)(x + 1)(x + 3).
Missing informationThe problems asks to factor the polynomial according to it's linear factors.
More can be learned about the Factor Theorem at https://brainly.com/question/30213721
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please answer this question
Answer:
activity2
1. ( 14.4) adn
2.(0.616) adn
3.( 5-36) adn
Write an equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3
Important things you need to know:
1. x intercept = solution of the equation
2. parabola = the highest power is x²
3. "passes through" is important because you have the y intercept (it is the c in ax² + bx + c = 0)
The intercept form is y = a(x-r)(x-s), where r and s are the x intercepts (solutions) of the graph
Substitite the numbers and values you know:
y = a(x-r)(x-s)
0.05 = a(-2-(-7)) × (-2-(-3))
Then you should find a.
Rewrite the equation in the form of y = a ( x+7 )( x+3 ) where the value of a is found.
Please help! Complete answers please.
Answer:
m3 = 103 degrees
m4 = 77 degrees
Step-by-step explanation:
comment if you want me to explain please :)
The interior angles of ∆AUL (or any triangle for that matter) sum to 180°, so
∠3 + 20° + 57° = 180°
===> ∠3 = 103°
Angles ∠3 and ∠4 occur on the same ray LP, so they are supplementary to one another. In other words,
∠3 + ∠4 = 180°
so that
∠4 = 180° - 103° = 77°
Item 4 Find the distance between the two points. (4, −5), (−1, 7)
Answer:
yes , the distance between the two points is 13 units
Finding a percentage of o total amount without a calculator...
An item is regularly priced at $35. It is on sale for 40% off the regular price. How much (In dollars) Is discounted from the regular price?
Amount discounted: si
х
5
?
9514 1404 393
Answer:
$14
Step-by-step explanation:
Computing 40% can be done a couple of ways.
40% = 40/100 = 4/10 = 2/5
40% of 35 = (2/5)(35) = 2(35/5) = 2(7) = 14
__
40% = 4/10 = 2(2(1/10))
40% of 36 = 2(2(1/10)(35)) = 2(2(3.5)) = 2(7) = 14
The amount discounted is $14.
How many tons are equal to 36,000 pounds? With work!
Answer:
18 tons
Step-by-step explanation:
1 pound = 0.0005 ton
Therefore,
36,000 pounds
= 36000*0.0005
= 18 tons
Help me plz., ,, ,, ,, ,,,
Answer:
1. 100000
2. 16777216
3. x7
4.64
5.1/64 (Decimal: 0.015625)
Step-by-step explanation:
A quantity with an initial value of 720 decays continuously at a rate of 9% per hour. What is the value of the quantity after 69 hours, to the nearest hundredth?
Answer:
1.45
Step-by-step explanation:
f(t)=720e^rt
f(t)=720e
rt
Continuously uses Pe^(rt)
r\text{: decays }9\% \
r: decays 9%→−0.09
per hour
f(t)=720e^{-0.09t}
f(t)=720e
−0.09t
(where t is in hours)
69\text{ hours: no time conversion necessary}
69 hours: no time conversion necessary
hours are the only units in the problem.
\text{Plug in }t=69
Plug in t=69
f(69)=720e^{-0.09(69)}
f(69)=720e
−0.09(69)
1.44665097413
1.44665097413
\approx 1.45
≈1.45
Round to the nearest hundredth
HELP meeeeeeeeeeeeeeeeeeeee
Answer:
first:
a)
second:
b)
Step-by-step explanation:
Which number line shows all the values of that make the inequality -3 +1 < 7 true?
Answer:
Number line D is true
Step-by-step explanation:
Given
[tex]-3x + 1 < 7[/tex]
See attachment for number lines
Required
Which number line makes the inequality true
First, we solve for x in [tex]-3x + 1 < 7[/tex]
[tex]-3x < 7 - 1[/tex]
[tex]-3x < 6[/tex]
Divide through by -3
[tex]\frac{-3x}{-3} < \frac{6}{-3}[/tex]
[tex]x > -2[/tex]
The inequality means x is greater than -2.
This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened
Number line D is true
You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Write a function that represents the balance y (in dollars) after x years.
Answer:
f(x)=.65+y
Step-by-step explanation:
.
The function for compound interest is A = 500 ( 1.065 )ˣ
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the compound interest amount be represented as A
Now , the interest rate r = 6.5 %
The number of times the interest is applied = yearly
The principal amount P = $ 500
n = 1 ( compounded yearly )
t = x ( number of years )
So, the function that represents the balance y (in dollars) after x years is:
y ( x ) = 500 ( 1 + 0.065/1 )ˣ
On simplifying , we get
y ( x ) = 500 ( 1.065 )ˣ
Hence , the function is A = 500 ( 1.065 )ˣ
To learn more about compound interest click :
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Szklanka ma pojemnóść 250ml czyli 250cm³. Ile szklanek można napełnić wodą z litrowej butelkki
Answer:
75cm
Step-by-step explanation:
A coin lands on heads 300 times. The relative frequency of heads is 0.6. How many times was the coin flipped?
Answer: Number of times the coin is flipped =500
Step-by-step explanation:
Relative frequency of head = [tex]\dfrac{\text{Number of times heads occur}}{\text{Total number of times coin is flipped}}[/tex]
Let x= Number of times the coin is flipped, then
[tex]0.6=\dfrac{300}{x}\\\\\Rightarrow\ x=\dfrac{300}{0.6}\\\\\Rightarrow\ x=\dfrac{3000}{6}\\\\\Rightarrow\ x=500[/tex]
Hence, Number of times the coin is flipped =500
A human heart beats an average of 80 beats per minute. How many beats is this in an hour?
Answer:
4800 beats an hour
Step-by-step explanation:
there are 60 minutes in and hour
the heart beats 80 times per minute( that is actually a very high heart rate)
80*60=4800 per hour
1/3a = -5. Solve each equation
Answer:
1/3a = -5
1=3a×-5
1=-15a
a=-1/15
Answer:
a=-15
Step-by-step explanation:
1/3a = -5
1/3(*3)a=-5*3
a=-15
What is additive inverse of the check?
please help
7x -3
-7x + 3
-7x - 3
7x - 3
Answer:
pretty sure it would be 7x-3
Kelly works at her own nail
salon. Today, she did 11
manicures and received $52.25
overall in tips. If x represents the
cost of each manicure, which of
the following equations can be
used to find the total amount of
money she earned, including
tips, for her nail salon today?
A. y = 11(x + 52.25)
B. y = 52.25x + 11
c. y = 52.25(x + 11)
D. y = 11x + 52.25
Answer:
(x×11)÷52.25
Step-by-step explanation:
if 11=52.25 and y=x then x11÷52.25 i think that is the answer
Ava pours 3 gallons of paint equally into 5 cans. How many gallons of paint will there be in each can?
Answer:
0.6
Step-by-step explanation:
first you well have a 3 and then dived it by 5 and after you dived them to you well get the answer 0.6
Find the radius of a circle in which an inscribed square has a side of 8 inches.
Answer:
r = 4
Step-by-step explanation:
side of square is the same as the diameter of the circle
if diameter is 8 then radius is 4
3 unit right
3 unit left
3 unit up
3 unit down
8 unit right
8 unit left
8 unit up
8 unit down
A student was given the following instructions:
"Given f(x) = 6x + 4, find f(4)."
How do you list all of the rational zeros of g(x)=x^4-3x^3-53x^2-9x?
I only know how to list them for when the last number doesn’t have the variable x.
Answer:
No lo se
Step-by-step explanation:
Please I need formula and faces
Answer:
+3[36 hahahahhh Sana all mag hanap ka nlg sa iba
is a rectangle a plane shape
Answer:
A plane shape with four straight sides and four right angles for corners is called a rectangle.
Step-by-step explanation:
Alfredo is ordering a taxi from an online taxi service. The taxi charges $3.50 just for
the pickup and then an additional $0.75 per mile driven. How much would a taxi ride
cost if Alfredo is riding for 5 miles? How much would a taxi ride cost that is m miles
long?
Is -50 greater than 2
True or false
FALSE
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
In AJKL.m._J = 40and m K = 55°. In AMNP, m M = 40° and m P = 85 A student concludes that the triangles are not similar. Do you agree or disagree? Why? (1 point)
O Disagree, by the Interior Angles Theorem, m N = 55°, so the triangles are similar by the AA similarity criterion
O Disagree, by the Interior Angles Theorem, mZN = 45°, so the triangles are similar by the AA similarity criterion
O Agree by the interior Angles Theorem, m_N = 45 Togo the triangles are not similar by the AA
O Agree, since m_K #m_P, the triangles are not similar by the AA similarity criterion
Answer: A
Step-by-step explanation:
Source: trust me bro
Please work out -80 ÷ -8
Answer:
10
Step-by-step explanation:
-80 / -8 = 10
the negatives cancel each other out
-80÷-8=10
.....................
Mrs. Dyson is making trail mix for Christmas gifts. She needs 4 cups of nuts, 6 ups of raisins, and 5 cups of chocolate chips. What percent of the trail mix are
raisins
HINT: Use Part to Whole and Reduce
A.60%
B.40%
C.6%
D.15%
Answer:
b
Step-by-step explanation:
15/6=2.5
100/2.5=40
please help me on this will give you brainliest
Answer:
2,010,000
Step-by-step explanation:
3 x 10^5
10^5= 100000
3 x 100000 = 300000
300000 x 6.7 = 2,010,000
Hope this helps
Answer:
Im not 100% sure but i think its 44,776.1194
Step-by-step explanation: What you do is multiply 3 x 100,000 because 10 to the 5th power is 100,000. Then you divide 300,000 by 6.7 and get your answer of 44,776.1194. Sorry if its incorrect