Decide whether the following statement is true or false.Every polynomial function of degree 3 with real coefficients has exactly three real zeros.
Answers
Consider the next polynomial function,
\(\begin{gathered} f(x)=(x+1)(x^2+1) \\ \Rightarrow f(x)=(x+1)(x-i)(x+i) \end{gathered}\)Notice that f(x) has one real zero and two complex zeros.
However, the expanded form of f(x) is
\(f(x)=x^3+x^2+x+1\)Therefore, f(x) is a polynomial of degree 3 with real coefficients that has exactly 1 real zero and 2 complex zeros.
This is a counterexample of the statement. The answer is False.
Related Questions
The sphere shown below is placed in a full overflow cup and sinks to the bottom. How much water is displaced by the sphere?Lector inmersivo
(1 Punto)
A. 51.0 mL
Option 2
C. 88.6 mL
D. 407.7 mL
B. 66.5 mL
the sphere is 4.6cm
Answers
Answer:
a resposta é a letra c elll
Cassie has a total of 110 coins in her piggy bank. All the coins are quarters and dimes. The coins have a total value of $20.30. How many quarters and how many dimes are in the piggy bank?
Answers
Answer:
48 dimes and 62 quarters
Step-by-step explanation:
Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
Learn more on a Ferris wheel here;
https://brainly.com/question/30524034
#SPJ1
the second third and fourth terms in the expansion of (a + b)^n are 12, 60 and 160 respectively. calculate the values of a b and n
Answers
The values of a, b, and n are: a = (3/4)^(1/7), b = (3/4)^(1/7) and n = 8/3.
What is the values of a b and n?We know that the general formula for the binomial expansion of (a + b)ⁿ is:
(a + b)ⁿ = nC₀aⁿb⁰ + nC₁aⁿ⁻¹b¹ + nC₂aⁿ⁻²b² + ... + nCₖaⁿ⁻ᵏbᵏ + ... + nCₙa⁰bⁿ
where;
nCk is the binomial coefficient given by:nCk = n! / (k!(n-k)!)
where;
! denotes the factorial function.We are given that the second, third, and fourth terms in the expansion are 12, 60, and 160 respectively. Therefore, we have:
nC₁aⁿ⁻¹b¹ = 12
nC₂aⁿ⁻²b² = 60
nC₃aⁿ⁻³b³ = 160
We can solve for a and b by dividing the second equation by the first and the third equation by the second. This gives:
nC₂/nC₁ = (n-1)a/b = 5 ...(1)
nC₃/nC₂ = (n-2)a/b = 8/3 ...(2)
Now, we can solve for a and b by solving the system of equations (1) and (2) simultaneously.
We can start by multiplying equation (1) by b and equation (2) by 3b, which gives:
(n-1)a = 5b ...(3)
(n-2)a = 8b ...(4)
Subtracting equation (4) from equation (3), we get:
a = 13b
Substituting this into equation (4), we get:
11b = 8b/n
Solving for n, we get:
n = 8/3
Substituting this value of n into equation (1), we get:
5 = (8/3 - 1)a/b = 5a/b
Therefore, a = b.
Substituting a = b into any of the equations for the terms in the expansion, we get:
nC₁aⁿ⁻¹b¹ = n(a + b)ⁿ⁻¹ = 12
Substituting n = 8/3, a = b, and simplifying, we get:
2a⁷ = 12/8
Solving for a, we get:
a = (3/4)^(1/7)
Therefore, the values of a, b, and n are:
a = (3/4)^(1/7)
b = (3/4)^(1/7)
n = 8/3
Learn more about binomial expansion here: https://brainly.com/question/13602562
#SPJ1
A curve has equation y = 2x + 1/(x-1)² Verify that the curve has a stationary point at x=2 and determine its nature.
Answers
There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.
To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.
Given the equation:
y = 2x + 1/(x-1)²
Let's find the derivative dy/dx:
dy/dx = d/dx [2x + 1/(x-1)²]
To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:
For the first term, 2x, the derivative is 2.
For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:
d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)
Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:
-2(x-1)^(-3) * 1 = -2/(x-1)^3
Now, let's set dy/dx equal to zero and solve for x:
-2/(x-1)^3 = 0
This equation is satisfied when the numerator is equal to zero:
-2 = 0
However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.
For more question on stationary point click on
https://brainly.com/question/28978328
#SPJ11
On the basis of a survey of 25 random typists, a confidence interval for the mean time needed to complete typing a page was (5.588; 6.412). Knowing that the distribution of the time needed to type a page is normal, and the sample standard deviation was equal to 1, determine the confidence level used for the calculations
Answers
Answer:
95%
Step-by-step explanation:
Confidence interval:
Mean (m) ± Tcrit * s/sqrt (n)
s = standard deviation = 1
Lower boundary = m - Tcrit * s/sqrt (n) - - - (1)
Upper boundary = m + Tcrit * s/sqrt (n) - - - (2)
m - Tcrit * s/sqrt (n) = 5.588 - - - (1)
m + Tcrit * s/sqrt (n) = 6.412 - - (2)
Subtracting (1) and (2)
-2Tcrit * s/sqrt (n) = - 0.824
Tcrit = [0.824 * sqrt(n)] / 2 * s
Recall:
s = 1
[0.824 * sqrt(n)] / 2 * 1
Sample size = n = 25
[0.824 * sqrt(25)] / 2
[0.824 * 5] ÷ 2
Tcrit = 2.06
Hence, we use the t table to obtain the significance level which gives a t value of 2.06 at (n-1) = (25 - 1) = 24 degrees of freedom.
Significance level α = 0.05
(1 - 0.05) * 100%
0.95 * 100% = 95%
You rent an apartment that costs $1000 per month during the first year, but the rent
is set to go up 12% per year. What would be the rent of the apartment during the 11th
year of living in the apartment? Round to the nearest tenth (if necessary).
Answer:
Submit Answer
Answers
Answer:
2320
Step-by-step explanation:
12% of 1000 is 120 so you multiple that time 11 which equals 1320 and then you add 1000 which gives you 2320
slope of the line with points (4,-2) and (24,-17)
Answers
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1
-17+2 divided by 24-4
-15/20
-3/4
Answer:
-3/4
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (-17- -2)/(24-4)
= (-17+2)/(20)
= -15/20
=-3/4
Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.
Answers
Answer:
Step-by-step explanation:
The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000, 3,983 rounded to the nearest thousand is 4,000, 13,560 rounded is 14,000.
7,000 + 4,000+ 14,000 = 25,000
I NEED HELP WITH STATISTICS
Answers
A. The null hypothesis H₀ and the alternative hypothesis H₁ are:
H₀: μ = 35 minutes H₁: μ > 35 minutes
B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.
C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.
What is a Type II error?A Type II error occurs when the null hypothesis is false, but the test does not reject it.
In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.
Find more exercises on Type II error;
https://brainly.com/question/29689920
#SPJ1
PLEASE HELP!!
the variables x and y have a proportional relationship and y=40 when x=30 what is the value of x when y=50
Answers
Refer to the given image
HELP!! ILL MARK BRRAINLIST
Answers
Answer:
I think answer is D but it could be wrong not sure
What are the zeros of the function
Answers
Answer: i think c
Step-by-step explanation:
Mr.Kermshner has 168 bandages march through June. How much is it if each bandage is 3 cents
Answers
504 bandages if it is each bandage is 3 cents.
Given,
Mr. Kermshner has 168 bandages march through June.
To find the how much is it if each bandage is 3 cents ?
Now, According to the question,
Based on the given conditions,
Formulate:
Total bandage is 168
and, each bandage is 3 cents
= 168 x 3
= 504
Alternative form = 5.04 x 10^2
Hence, 504 bandages if it is each bandage is 3 cents.
Learn more about Bandages Questions at:
https://brainly.com/question/13653524
#SPJ1
the sum of 8 and 7 double
Answers
Answer: 30
Step-by-step explanation:
(8+7) x 2
= 15 x 2
= 30
Please help thank you all so much
Answers
The domain of the composite functions:
a). (f + g)(-2) = 23
b). (f - g) (-2) = 1
c). f(x) - g(x) = x² - 5x - 13
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:
a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13
(f + g)(-2) = 4 + 8 - 2 + 13
(f + g)(-2) = 23
b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13
(f - g)(-2) = 4 + 8 + 2 - 13
(f - g) (-2) = 1
c). f(x) - g(x) = x² - 4x - x - 13
f(x) - g(x) = x² - 5x - 13
Therefore, the domain of the composite functions:
a). (f + g)(-2) = 23
b). (f - g) (-2) = 1
c). f(x) - g(x) = x² - 5x - 13
Read more about composite function here:https://brainly.com/question/10687170
#SPJ1
Tania has a roll of cloth that is
52.5
52.5 feet long. She uses the cloth to make scarves that are each
3.75
3.75 feet long. How many scarves can Tania make?
Answers
Answer:
Tania can make 14 scarves.
Step-by-step explanation:
You get this answer by dividing 52.5 by 3.75.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
cot²θ = 1/tan²θ
plug this in to get
1/(1/tan²θ + 1)
1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ
we then have
1/((1+tan²θ)/tan²θ)
1/(x/y) = y/x, so this is equal to
tan²θ/(1+tan²θ)
tan²θ = sin²θ/cos²θ, so plug this in to get
(sin²θ/cos²θ)/(1+sin²θ/cos²θ)
1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ
sin²θ + cos²θ = 1, so we have
(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get
(sin²θ/cos²θ)/(1/cos²θ)
(a/b)/(c/d) = (d/c) * (a/b), so we have
(sin²θ/cos²θ)/(1/cos²θ) = cos²θ/1 * sin²θ/cos²θ = sin²θ
Assume that you have a total of 14 people on the board: 5 out-of-state seniors, 3 in-state seniors, 1 out-of-state non-senior, and 5 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists. In how many ways can the officers be chosen while still conforming to University rules?
Answers
Answer:
The appropriate solution is "570". The further explanation is given below
Step-by-step explanation:
There's a whole average of 14 committee members of trustees, including 5 out-of-state leaders, 5 in-state senior citizens, 1 out-of-state semi-senior, and 3 semi-senior in-state elderly. Out of those 14 members, 3 members must be chosen. According to the required specifications, the 3 members chosen should also include at least a single in-state member as well as at least 1 longtime leader.We may establish the executive committee in two distinct ways, in compliance with us even. One is about choosing the in-state participant from either the five seniors throughout the state, which follows the university's two requirements. As well as the other option is to choose an in-state participant from either the three non-senior in-state students.The 2nd incarnation should also be chosen from either the 5 out-of-state leaders throughout the second scenario. Across each circumstance, we can determine the multitude of scenarios, and afterward, the amount of the two can provide the maximum range of things the board can indeed be chosen.(1)
Choosing the right 1 member out of 5 seniors throughout the state.
The remaining 2 candidates would be chosen from some of the other 13 committee members within a week of choosing 1 member from either the 5 in-state representatives.
So, throughout this case, the number among approaches p is supplied by:
⇒ \(p=5C_1\times 13C_2\)
\(=5\times 78\)
\(=390\)
(2)
Choosing the right one person of the legislature out of three non-senior members of the state
In this scenario, as already mentioned, the second participant needs to be chosen from the 5 qualified out-of-state citizens. Currently that we would have chosen 2 members out of 14 members in all, the 3rd member should be chosen out of another leftover 12 people.
Therefore, the amount of forms, throughout this case q, seems to be:
⇒ \(q=3C_1\times 5C_1\times 12C_1\)
\(=3\times 5\times 12\)
\(=180\)
So that the total no. of ways will be:
⇒ \(p+q\)
⇒ \(390+180\)
⇒ \(570\)
Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one producer to another. In May 2013, the author went to a certain website, randomly selected 10 zinfandels from among the 325 available, and obtained the following values of alcohol content (%).
14.9 14.5 16.2 14.3 15.9
13.7 16.2 14.6 13.9 15.1
A. Calculate the interpret several measures of center.
B. Calculate the sample variance using the defining formula.
Answers
Answer:
Kindly check explanation
B) 0.829
Step-by-step explanation:
Given the data :
% Alcohol content of 10 zindafel wine
14.9 14.5 16.2 14.3 15.9
13.7 16.2 14.6 13.9 15.1
Sorted value : 13.7, 13.9, 14.3, 14.5, 14.6, 14.9, 15.1, 15.9, 16.2, 16.2
Range = maximum - minimum
Range = 16.1 - 13.7
n = number of samples = 10
Median = 1/4(n + 1)th term
Median = 1/4(10+1)th term = 11/4 = 2.75 th term
(14.3 + 14.5) / 2 = 28.8 /2 = 14.40
Mode = 16. 2 ( most occurring observation)
Mean(m) = (13.7 + 13.9 + 14.3 + 14.5 + 14.6 + 14.9 + 15.1 + 15.9 + 16.2 + 16.2) / 10
= 149.3 / 10
= 14.93
I need help quickly A committee is to consist of two members if there are seven men and five women available to serve on the committee and you need to choose 1 man and 1 woman how many different committees can be formed?
Answers
Answer:
35
Step-by-step explanation:
You want to know the number of 2-person committees that can be formed from 7 men and 5 women if one of each is on the committee.
NumberAny of 7 men can be chosen. For each of those, any of 5 women can be chosen. The number of possible committees is ...
7 × 5 = 35
35 different committees can be formed.
<95141404393>
i really need helpl lol pleasehelppppppppppppplplplppplplpl ?
Answers
Answer:
1,050
Step-by-step explanation:
3.5x
12x
25
=
1,050
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
Answers
The value of x in the direct and indirect varoation is calculated as: x = 2.
What is Direct and Indirect Variation?If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.
With the information stated, we would have the following:
z = kx/y³
Find k, by plugging in the values of x, y, and z:
12 = k(8/2³)
12 = k(8/8)
12 = k
k = 12
Find x when y = 1 and z = 24:
24 = 12(x)/1³
24 = 12x
24/12 = x
x = 2.
Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.
Learn more about direct and indirect varoationon:
https://brainly.com/question/493649
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
Which equation is represented by the graph below
Answers
Answer:
y=in ×-3
it's the answer
9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Answers
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Sebastian programs his calculator to cvaluate a linear
function, but he doesn't say what the function is. When
8 is entered, the calculator displays the value 6. When
12 is entered, the calculator displays the value 9.
Which of the following expressions explains what the
calculator will display when any number, n, is entered?
Answers
Answer: y = 3/4x
Step-by-step explanation:
Each y-value output is 3/4 of the x-value inputted.
8 x 0.75 = 6
12 x 0.75 = 9
CE and FH are parallel lines.
Which angles are supplementary angles?
Answers
Answer:
<CDG and <CDB are supplementary angles.
Answer:
hff
Step-by-step explanation:
< CDG and <CDB are supplementary angles.
msm555 is correct
hope it is helpful to you ☺️☺️☺️
I need help. I have this question and it says express your answer as a simplified mixed number 8 4/7 - 3 2/7 =
Answers
Answer:
5 3/7 or 37/7
5 2/7 simplified mixed number
Please help thank you
Answers
I can't see the whole paper the sentences is cut