The polynomial function of degree 7 with the given zeros and multiplicities is: f(x) = x³(x + 2)³(x - 2)
To find a polynomial function with the specified zeros and multiplicities, we can construct it using the factors that correspond to each zero and multiplicity.
Since -2 has a multiplicity of 3, it means it appears three times as a zero. Similarly, 0 has a multiplicity of 3, and 2 has a multiplicity of 1.
A polynomial function with these zeros and multiplicities can be written as:
f(x) = (x + 2)³ × x³ × (x - 2)
To make it a polynomial of degree 7, we can multiply it by an additional linear factor:
f(x) = (x + 2)³ × x³ × (x - 2) × (x - r)
Where "r" is a constant representing the last factor. This factor ensures the degree of the polynomial is 7.
Now, we need to find the value of "r" to complete the polynomial. Since we already have three factors with multiplicity 3 and one factor with multiplicity 1, the polynomial has already reached its degree of 7.
Therefore, we don't need to include the "x - r" factor, and the final polynomial is:
f(x) = (x + 2)³ × x³ × (x - 2)
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The polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 2 as a zero of multiplicity 1 is f(x) = x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2.
To find a polynomial function of degree 7 with the given zeros and multiplicities, we can start by constructing the factors of the polynomial.
Since -2 is a zero of multiplicity 3, we have the factor (x + 2)^3. Similarly, since 0 is a zero of multiplicity 3, we have the factor x^3. Lastly, since 2 is a zero of multiplicity 1, we have the factor (x - 2).
Multiplying these factors together, we obtain:
(x + 2)^3 * x^3 * (x - 2)
Expanding this expression, we get:
(x^3 + 6x^2 + 12x + 8) * x^3 * (x - 2)
To simplify further, we multiply the terms:
(x^6 + 6x^5 + 12x^4 + 8x^3) * (x - 2)
Expanding again, we obtain:
x^7 - 2x^6 + 6x^6 - 12x^5 + 12x^4 - 24x^3 + 8x^3 - 16x^2
Combining like terms, we get:
x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2
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Which exponential equation correctly rewrites this logarithmic equation? log6 18=x
Given:
The logarithmic equation is:
[tex]\log_618=x[/tex]
To find:
The exponential equation of this logarithmic equation.
Solution:
According to the properties of logarithm:
[tex]\log_bm=x\Leftrightarrow m=b^x[/tex]
We have,
[tex]\log_618=x[/tex]
Here, [tex]b=6, m=18[/tex]. Using the above property of logarithm, we get
[tex]18=6^x[/tex]
Therefore, the required exponential equation is [tex]18=6^x[/tex].
Answer:
the awnser is acctully 6^x =18
Step-by-step explanation:
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Step-by-step explanation:
1) [tex](-4)^2{\cdot}(-4)[/tex]
We know that, [tex]a^x{\cdot}a^y=a^{x+y}[/tex]
[tex](-4)^2{\cdot}(-4)=(-4)^{2+1}\\\\=(-4)^3\\\\=64[/tex]
2) [tex](-2)^5{\cdot} (-2)^3[/tex]
Again using above property,
[tex](-2)^5{\cdot} (-2)^3=(-2)^8\\\\=256[/tex]
3) [tex]5^{-3}[/tex]
We know that,
[tex]a^{-x}=\dfrac{1}{a^x}[/tex]
So,
[tex]5^{-3}=\dfrac{1}{5^3}\\\\=\dfrac{1}{125}[/tex]
4) [tex]2.5^2=2.5\times 2.5\\\\=6.25[/tex]
Hence, this is the required solution.
which value from the set{2,14,16,63}makes the equation n-7=9 true
Answer:
16.
Step-by-step explanation:
n - 7 = 9
Add 7 to both sides
n = 9 + 7 = 16.
Answer:
16
Step-by-step explanation:
Given
n - 7 = 9 ( add 7 to both sides )
n = 16
A cylindrical flower vase has a diameter of 6cm and a volume of 171cm^(3)
Determine the height of the vase.
Answer:
h = 6.05 cm
Step-by-step explanation:
Volume of a cylinder = πr²h
Where,
Pi, π = 3.14
Radius, r = diameter/2 = 6 cm/2
= 3 cm
Height, h = ?
Volume if the cylinder = 171 c ³
Volume of a cylinder = πr²h
171 = 3.14 * 3² * h
171 = 3.14 * 9 * h
171 = 28.26 * h
171 = 28.26h
h = 171/28.26
h = 6.0509554140127
Approximately,
h = 6.05 cm
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A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices - a, b, c, d - and
only one correct answer. What is the probability that she answered neither of the problems correctly?
Write your answer as a fraction in simplest forme
Answer:
3/4
Step-by-step explanation:
2 problems consist 8 choices of answers.
the events for the correct answer are 2
and the events for incorrect answer are 6
so, the probability that she answered neither of the problems correctly = 6/8 = 3/4
Cecily claims that the equation y = mx + b, where b is a real number,
represents a function whose graph is a line. Which statement BEST
classifies this claim?
Cecily's claim is true only when b is zero.
Cecily's claim is true for all values of b.
Cecily's claim is not true for any value of b.
Cecily's claim is true only when b is not zero
Answer:
Cecily's claim is true for all values of b.
Step-by-step explanation:
Cecily's claim is true for all values of b.
If she graphs y = mx, and then y = mx + b, and then y = mx + c, and so on, she will find that her graphs are all straight lines that are parallel to each other (as they will all have the same slope, m).
A circular tabletop has an approximate circumference of 47.1 inches. What is its diameter?
Answer: 14.99
Step-by-step explanation:C=2πr
d=2r
Solving ford
d=C
π=47.1
π≈14.9924
Write the expanded form of the given expression.
(x^4)(x^4)
Answer:
[tex]x^{8}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex]x^{4}[/tex] × [tex]x^{4}[/tex] = [tex]x^{(4+4)}[/tex] = [tex]x^{8}[/tex]
In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the total percent decrease.
Answer: 237,500 total decrease
Step-by-step explanation:
HELPPPP Trigonometry QUESTIONS
Answer:
Step-by-step explanation:
for the right side :
its a triangular prism and the volume is 4 x 8 x 10 = 320.
the SA is 10x4 divided by 2 x 2which is just 40.
8x5x2= 80 and
10x10= 100, so
the SA of the right figure is 220 in^2
PLEASE HELP ASAP IM TIMED!!
What is the standard form of y=2(x-3)(x+5) and show your work
Answer:
o really sis/bro hsgsmhsndjd
What is the solution to the system of equations graphed below?
(1, 2) because that's where the lines intersect!
Answer: (1, 2)
Step-by-step explanation:
The solution of the systems of equations graphed can be found where the two linear lines intersect. In this graph, the lines intersect at 1 in the x-axis (the line with arrows that runs from left to right" and at 2 in the y-axis (the line with arrows that runs north to south).
A ladder 30m long rest against a vertical wall. If the ladder makes an angle of 63° with the wall ,find the distance between the foot of the ladder and the wall
Answer:
13.62 m
Step-by-step explanation:
We are to determine the value of the adjacent side given the value of the hypotenuse
we would use cos to determine this value
cos 63 = adjacent / hypotenuse
0.45399 = x / 30
x = 30 x 0.45399 = 13.62
A motor has an internal resistance of 12.1 Ω. The motor is in a circuit with a current of 4.0 A
What is the voltage?
HELP PLEASE
Answer:
48.4 volts
Step-by-step explanation:
by using the formula :
V = I × R, we get :
V = 4.0 × 12.1 = 48.4 volts
Question 10 of 10 To find the inverse of f(x) = 2x - 1, Patel begins by replacing f(x) with y. He then switches x and y. What is the next step? A. Replace y with f-1(x). B. Subtract 1 from both sides of the equation. C. Solve the equation for y. O D. Solve the equation for x. SUBMIT
Answer:
f⁻¹(x) = (x+1)/2
Step-by-step explanation:
Given the function f(x) = 2x - 1, we are to find its inverse;
Let y = f(x)
y = 2x - 1
Replace y with x
x = 2y - 1
Make y the subject of the formula
2y = x + 1
Divide both sides by 2
2y/2 = (x+1)/2
y = (x+1)/2
Replace y with f⁻¹(x)
f⁻¹(x) = (x+1)/2
Hence the required inverse is (x+1)/2
Which is the value of 2c2d if c = 0.5 and d = 3?
A. 0.15
B. 1.5
C.33
D. 6
E 15
Answer:
The answer is D (6).
hope this helps!
Someone help I have been stuck on this for 30 min
Answer:
fcuck off nobdy caresd XD
Step-by-step explanation:
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Which is the x-intercept of f(x) = log6(2x) – 1?
Answer:
Hope this helps!
Please mark brainliest!
x-intercept(s):
(1/log(36),0)
y-intercept(s):
(0,−1)
Ok if I have 159 booklets to do and I do 12 in a year how many years will it take to finish all the booklets?
Answer:
13.25 years
Step-by-step explanation:
Take the number of booklets and divide by the number of booklets per year
159/12
13.25 years
Consider the function and its inverse.
f(x) = x2 + 4 and f-1(x) = -x - 4
When comparing the functions using the equations, which conclusion can be made?
The domain of f(x) is restricted to x 20, and the domain of f'(x) is restricted to x2 0.
The domain of f(x) is restricted to x 20, and the domain off(x) is restricted to xs 0.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x2 4.
O The domain of f(x) is restricted to x s 0, and the domain off'(x) is restricted to x s 4.
Step-by-step explanation:
it might be the last one
may it helped u
Please Help. It would be very helpful to me
Answer:
A) 2 inches
Step-by-step explanation:
What is the vaule of tan-240 degrees?
What is 39,800,000 in scientific notation PLS HELP
Answer:
3.98 x 10^7
Step-by-step explanation:
Answer:
3.98x10^7Step-by-step explanation:
Determine the equation of the circle graphed below.
( help me please. )
Answer:
________________________________
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A king rules a small mountain kingdom which is in the form of a square of length 4 kilometers. The square is described by the coordinate system0≤≤4,0≤≤4. The king has four adult children, each of which has a luxury palace located at the points (1,1),(3,1),(1,3),(3,3). Each child owns all the land that is nearer their palace than any other palace.
Sketch a Voronoi diagram to represent this information.
Answer:
i can not get the answer
What is the percent decrease when the balance in a bank account goes from $300 to $60?
The percent decrease is 20%.
The percent decrease is 25%.
The percent decrease is 80%.
Answer:
The percent decrease is 80%. or C.
Step-by-step explanation:
Hope this helps! (:
FIND BD !!!!!!!!!!!!!!!!!!!!
BD = 2x-4
But it's also BE - CE + CD
BE is 3x-1
CE is 2x-3
CD is 2
so
BD = 3x-1 -(2x-3) +2
simplified
BD = 1x +4
since BD = BD (obviously), we can also say that the righthand sides of the two equation must be equal
2x -4 = 1x +4
let's solve for x and that put it into either of the 2 equations.
2x -4 = 1x +4
subtract 1x on both sides
x -4 = 4
add 4 on both sides
x = 8
substitute x for its value in 2x -4 = 1x +4
(this way we double check BD in two expressions at once. the equation should come out true, meaning same value for BD in each expression. both sides should be equal).
2*8 -4 = 1*8 +4
12 = 12
seems true
BD is safely 12
The base of triangle M is four times the base of tri-
angle N, while the height of triangle N is half the
height of triangle M. The area of triangle M is how
many times that of triangle N ?
Answer:
two times
Step-by-step explanation:
ΔM: let 'h' = height; let '4b' = base
ΔN: let 'h/2' = height; let 'b' = base
Area (ΔM) = 2bh
Area (ΔN) = bh
7 pens and 2 pencils cost 22
3 pens and 4 pencils cost 11
Find the cost of a pen
find the cost of a pencil
Pen : $3
Pencil : $0.50
what is the first 50 digitizes of PI
Answer:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196
Step-by-step explanation:
1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9