The total number of roots of the given polynomial function is 6.
The given polynomial is [tex]f(x)=3x^{6}+2x^{5}+x^{4} -2x^{3}[/tex].
We need to determine the total number of roots of the given polynomial function.
What is the total number of roots of the polynomial function?
The number of roots of any polynomial is depended on the degree of that polynomial. Suppose n is the degree of a polynomial f(x), then fx) has n number of roots.
Here, the degree of the given polynomial function is 6.
Therefore, the given polynomial function will be having 6 roots.
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Given: a and b are parallel and c is a transversal.
Prove: ∠2 ≅ ∠7
Parallel lines b and a are cut by transversal c. On line b where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 5, 6, 2. On line a where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 3, 7, 8, 4.
Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent.
We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because
angles are congruent. Angles 5 and 7 are congruent because angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the
.
The missing words to complete the proof are respectively; Vertical Angles; Corresponding angles; Transitive Property
How to prove congruent angles?The image of the transversal line is attached.
1) We know that lines a and b are parallel and that line c is a transversal because that is given.
2) We can tell that angles 2 and 5 are congruent because vertical angles are congruent.
3) Angles 5 and 7 are congruent because corresponding angles by parallel lines cut by a transversal are congruent.
4) Therefore, angles 2 and 7 are congruent based on the transitive property.
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Answer: vertical, corresponding, and transitive property
Step-by-step explanation: I got the correct answer on Edge 2022. The answer is correct trust me! Proof is shown down below.
A football team carried out a report to see the impact of stretching on preventing injury. Of the 45 footballers in the squad 36 stretch regularly. Of those who stretch, 6 got injured last year. There was a total of 10 injured players last year.
The results can be presented in a frequency tree. What fraction of players who don't stretch get injured?
The fraction of players who don't stretch and get injured = 4/9.
The frequency tree is shown in the image attached.
The total number of footballers = 45.
The total number of footballers who stretch = 36.
Therefore, the number of footballers who don't stretch = 45 - 36 = 9.
The total number of injured footballers = 10.
The number of injured footballers from the players who stretch = 6.
Therefore, the number of injured footballers from the footballers who don't stretch = 10 - 6 = 4.
The total number of footballers who don't get injured = 45 - 10 = 35.
The number of footballers who stretch and don't get injured = 36 - 6 = 30.
The number of footballers who don't stretch and don't get injured = 9 - 4 = 5.
Therefore, the frequency tree can be shown in the image attached.
The fraction of players who don't stretch and get injured = 4/9.
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Suppose as part of a national study of economic competitiveness a marketing research firm randomly sampled 200 adults between the ages of 27 and 35 living in metropolitan seattle and 180 adults between the ages of 27 and 35 living in metropolitan minneapolis. each adult selected in the sample was asked, among other things, whether they had a college degree. from the seattle sample 66 adults answered yes and from the minneapolis sample 63 adults answered yes when asked if they had a college degree. based on the sample data, can we conclude that there is a difference between the population proportions of adults between the ages of 27 and 35 in the two cities with college degrees
No we cannot conclude that there is a difference between the population proportion of adults between the ages of 27 and 35 in the two cities.
How to solve for the population proportionFor Seattle
66/200 = 0.33
For Minneapolis
63/180
= 0.35
We have to form our hypothesis
H0: p1 = p2
H1: p1 ≠ p2
We solve for the test statistic
z = (p1-p2)/√(p1*(1-p1)/n1+p2x(1-p2)/n2)
The calculation is given as -0.41
The excel output is given in the attachment
=-0.41
At a significance level of 0.1, the level of acceptance is at -1.645 and 1.645. The value of the test stat can be found here.
Since Z=-0.41 is between -2.58 and 2.58, we do not reject H0.
Hence we fail to reject the null hypothesis.
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Let
f(x) = (x − 3)−2.
Find all values of c in (1, 4) such that
f(4) − f(1) = f '(c)(4 − 1).
(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
c =
Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This does not contradict the Mean Value Theorem since f is not continuous at x = 3.
This does not contradict the Mean Value Theorem since f is continuous on (1, 4), and there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This contradicts the Mean Value Theorem since there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
,
but f is not continuous at x = 3.
Nothing can be concluded.
Answer:
3/4 = -3* 2*(c-
I hope it helps!
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I need help on this question
pls help yes
The arc length of the semicircle is 5π units
Calculating length of an arcFrom the question, we are to calculate the arc length of the semicircle
Arc length of a semicircle = 1/2 the circumference of the circle
∴ Arc length of a semicircle = 1/2 × 2πr
Arc length of a semicircle = πr
Where r is the radius
From the given information,
r = 5
∴ Arc length of the semicircle = 5 × π
Arc length of the semicircle = 5π units
Hence, the arc length of the semicircle is 5π units
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Find the value of k for which the point (3k,k) lies on the line y = 3x +8.
Step-by-step explanation:
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If $5x-7=13x+17$, what is $6(x-4)$?
Answer:
0(x-4)
Step-by-step explanation:
in my working system i mean just when i try on the place of 4 any number can be inserted
$5x-7=13x+17$,here both gives -22 as a result so
$6(x-4)$=6x-24 and to give the same result or 0
$6(x-4)$=0(x-any number )
Find the product of the given polynomials. (5x + 5 - 2x) (4 + 7x -1)
Answer:
21x2 +44x +15
Step-by-step explanation:
20x + 35x2 - 5x + 20 + 35x - 5 - 8x - 14x2 +2x
35x2-14x2 +20x-5x+35x-8x+2x +15
21x2 +44x +15
A shopkeeper buys a stove for $860 what is the selling price if he makes the profit of 15%
Answer:
$989
Step-by-step explanation:
860*0.15 is = 129
129 + 860 is 989
The cost of the fruit is given by the function y=3x+1, where x is the number of fruits and y is the total cost. Find the range of the function.
4. The term containing the highest power of x in the polynomial f(x) is 4x^4. Given that f(x) = 0
has 2 roots -2 and 3, and that 2x² + 3x + 2 is a quadratic factor of f(x),
(a) express f(x) as a polynomial in descending powers of x,
We're given [tex]f(x) = 0[/tex] when [tex]x=-2[/tex] and [tex]x=3[/tex], so both [tex]x+2[/tex] and [tex]x-3[/tex] divide [tex]f(x)[/tex]
We're also told [tex]2x^2+3x+2[/tex] divides [tex]f(x)[/tex]. This quadratic does not have roots at -2 or 3, so we can factorize [tex]f(x)[/tex] as
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
where the leading coefficient is 2 because the full expansion should have a leading term of [tex]4x^4[/tex].
Now just expand [tex]f(x)[/tex] :
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (x^2 - x - 6) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (2x^4 + x^3 - 13x^2 - 20x - 12)[/tex]
[tex]f(x) = \boxed{4x^4 + 2x^3 - 26x^2 - 40x - 24}[/tex]
Use the function f(x) = 4x² - 7x - 15 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
Step-by-step explanation:
Part A:
4x² - 7x - 15
a, b, c = 4, -7, -15
ac = -60
factors that add up to -7 and multiply to -60 are (-12, 5)
rewrite equation
(4x² - 12x) + (5x - 15)
factor out GCF from both groups
4x(x - 3) + 5(x - 3)
(4x+5)(x-3)
Part B:
Using the factored form from the previous part we can set both factors equal to 0 to solve for x.
4x+5 = 0
4x = -5
x = -5/4
x-3 = 0
x = 3
the two x-intercepts are -5/4 and 3
Part C:
Since the leading coefficient is positive, the right side of the function will be going up or to positive infinity as x goes towards positive infinity. Since the degree is even both sides go in the same direction so on the left side it also goes towards positive infinity as x goes towards negative infinity.
help this homework and it geometry
1) Given
2) Segment addition postulate
3) Substitution property
4) Segment addition postulate
5) Transitive property of equality
R
53°
1
2
T
S
47°
What are the measures of angles 1 and 2?
mz1 =
mz2 =
Answer:
m∠1 = 50°
m∠2 = 130°
Step-by-step explanation:
There is a formula:
[tex]\text{angle} = \frac{1}{2} (\text{intercepted arc}_1 + \text{intercepted arc}_2)[/tex]
[tex]\text{m} \angle 1 = \frac{1}{2} (53^\circ + 47^\circ)[/tex]
[tex]\text{m} \angle 1 = \frac{1}{2} (100^\circ)[/tex]
[tex]\text{m} \angle 1 = 50^\circ[/tex]
Angle 1 and angle 2 together form a straight angle, which measures 180°. Angle 1 and angle 2 are suplementary angles.
[tex]\text{m} \angle 1 + \text{m} \angle 2 = 180^\circ[/tex]
[tex]50^\circ + \text{m} \angle 2 = 180^\circ[/tex]
[tex]\text{m} \angle 2 = 180^\circ - 50^\circ[/tex]
[tex]\text{m} \angle 2 = 130^\circ[/tex]
Can you help me graph and list the (Zeros, Maximums, Minimums, Asymptotes)
The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.
What is a Function ?A function is a law that relates a dependent variable and an independent variable with each other
It is given that
y = 2tan (x - π/2) +3
To find the zeroes of a function that function has to be equated to zero.
2tan (x - π/2) +3 = 0
2tan (x - π/2) = -3
tan (x - π/2) = -3/2
x - 90 = -56.31
x = 33.69 degree
The zero of the function is at 33.69 degree
For finding the maxima /minima
the derivative is
dy/dx = 2 sec² (x - π/2)
the point at which the slope is zero is substituted in the second derivative to find maxima/minima
d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)
if the value is negative then it is a maxima and if it is positive it is a minima.
The vertical asymptote is found by finding the values that make the function undefined
x = 0+ πn
No horizontal or oblique asymptote
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Determine if the sequence 4, 10, 19, 31,... is arithmetic. If it is, determine the first term a and the common difference d
Answer:
It is not arithmetic, so therefore there is no common difference
Step-by-step explanation:
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. There is no constant term in the above pattern.
Answer:
not an arithmetic sequence
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers that have a common difference. That is, the difference between any term and the previous term is constant for the sequence. Other kinds of sequences have other relationships between the differences.
DifferencesThe "first" differences of this sequence are ...
10-4 = 619-10 = 931 -19 = 12The first differences are not constant. However, we notice the "second" differences are constant. These are the differences of successive first differences.
9 -6 = 312 -9 = 3 . . . . . . constant 2nd differencesSequence typeThe first differences are not constant, so this sequence is not an arithmetic sequence.
For polynomial sequences, the level of constant difference tell you the degree of the polynomial describing the sequence. This sequence has constant 2nd-level differences, so can be described by a 2nd degree (quadratic) polynomial:
f(n) = 1.5n² +1.5n +1 . . . . . a quadratic sequence
__
Additional comment
Sequences that are exponential have differences that have a common ratio. That ratio is the same at every level. It is the base of the exponential function.
Solve ly + 21 > 6
() {yly <-8 or y> 4]
O (yly<-4 or y> 4}
(yly <-6 or y> 6}
[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]
Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [
PLEASE GIVE BRAINLIEST
Which of the following statements correctly describes this expression? 2x + 4
A. 4 less than 2 times a number
B. 2 times a number more than 4
C. The difference of 2x and 4
D. 4 times a number added to 2
Answer:
2 times a number more than 4
Answer:B
Step-by-step explanation:
Mara found the length of time of an investment. The principal of the investment was $4,300, the interest rate was 6.2 percent, and the interest was $2,666. Mara made an error in her work.
I = p r t. 2666 = (4300) (0.062) t. 2666 = (266.6) t. StartFraction 266.6 over 2666 EndFraction = t. 0.1 = t.
What was Mara’s error?
Mara did not substitute the values from the problem into the formula correctly.
Mara did not multiply correctly.
Mara did not divide correctly.
Mara divided when she should have multiplied.
The error that Maria made is that she did not divide correctly.
What error did Maria make?The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.
Simple interest = principal x time x interest rate
2666 = 4300 x 0.062 x t
2666 = 266.60t
t = 2666 / 266.60
t = 10 years
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Evaluate:
2/3 + 4/5 x 7/5 - 8/3
Step-by-step explanation:
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Answer:
-0.88
Explanation:
2/3 + 4/5 x 7/5 - 8/3
2/3 + 28/25 - 8/3
2/3 - 8/3 + 28/25
-6/3 + 28/25
-2 + 28/25
-50/25 + 28/25
-22/25
-0.88
In the figure below, what is the value of x°?
Answer:
1
Step-by-step explanation:
x to the zeroth power is always 1
Answer:
Step-by-step explanation:
90 - 20 = 70
So now do 5 times x and that's also equal to 70
70.x =11
Simplify -3/2÷9/6
○-4
O-1
04
01
Answer:
-1
Step-by-step explanation:
the answer snis negative One
True OR False
---------------------
x + 65 = 87, x = 27?
Answer:
False
Step-by-step explanation:
27+65=92, so false
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: False[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x + 65 = 87[/tex]
[ subtract 65 on both sides ]
[tex]\qquad \tt \rightarrow \: x + 65 - 65 = 87 - 65[/tex]
[tex]\qquad \tt \rightarrow \: x = 22[/tex]
but according to the statement it says, x = 27
which is proved wrong.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A ray has an endpoint.?
Answer:
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.
Please explain the bottom two the ones with the explanation box
First we must solve the bottom situations.
___________________________________________ (2A and 2B)
First expression (2A): 2v+8.3+2v-6.1
⇒ Collect like terms
(2v + 2v) + (8.3 - 6.1)
⇒ Simplify
4b + 2.2
Second expression (2B): 3v+14.4-v
⇒ Collect like terms
(3v - v) + 14.4
⇒ Simplify
2v + 14.4
They are not equivalent because when simplified they both have different coefficients and constants each of different values.
_____________________________________________ (4A and 4B)
First expression (4A): 10 + 3 (1/3x + 2)
⇒ Simplify 1/3x to x/3.
10 + 3(x/3 + 2)
⇒ Expand by distributing terms.
10 + x + 6
⇒ Collect like terms.
x + (10 + 6)
⇒ Simplify.
x + 16
Second expression: x + 16
This expression can not be simplified any further. This is because it is a simplified version of another expression.
These expressions are equivalent because expression 4B is the simplified version of expression 4A.
______________________________________
Level: 7th Grade
Unit: Distributing and Combing Like Terms
how do I do this, i am doing this and i need full points
Answer:
D is correct ...
nind d d find her r d d d f FBI f
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
[tex]\sqrt{69}[/tex]
Step-by-step explanation:
from the pythagorean theorem:
[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]
Find the range of the data in the box plot below. \text{ cm} cmstart text, space, c, m, end text A horizontal boxplot titled Amount of rain in Vietnam cities, in centimeters, is plotted along a horizontal axis marked from 0 to 10, in increments of 0.5. A left whisker extends from 3.5 to 5.5. The box extends from 5.5 to 7 and is divided into 2 parts by a vertical line segment at 6. The right whisker extends from 7 to 7.5. All values estimated.
7978978
Step-by-step explanation:
What are the soultions of the equation x^4 - 9x^2 + 8 = 0? Use u substitution to solve.
Step-by-step explanation:
Let u=x^2.
Notice that
[tex] {x}^{4} - 9 {x}^{2} + 8 = 0[/tex]
[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8 = 0[/tex]
[tex]u {}^{2} - 9u + 8 = 0[/tex]
[tex](u - 8)(u - 1) = 0[/tex]
[tex]u = 8[/tex]
[tex]u = 1[/tex]
Replace x^2= u
[tex] {x}^{2} = 8[/tex]
[tex]x = ±2 \sqrt{2} [/tex]
[tex] {x}^{2} = 1[/tex]
[tex]x = ±1[/tex]
So our answer is
[tex]±1 \: [/tex]
and
[tex]±2 \sqrt{2} [/tex]
What’s the answer here? Answer ASAP please.
Answer:
6
Step-by-step explanation:
f(6) is the y-value when x = 6
From inspection of the graph, f(6) = -6
g(5) is the y-value when x = 5
From inspection of the graph, g(5) = -5
Substitute the found values into the given equation:
4 · f(6) - 6 · g(5)
= 4 · (-6) - 6 · (-5)
= -24 - (-30)
= -24 + 30
= 6
