k=1; f(x)=4x^3-2x^2+2x+4; Lower bound?

Answers

Answer 1

Given:
[tex]f(x) = 4x^{3} - 2x^{2} + 2x + 4[/tex]
and,
K = 1

We would require to do the synthetic division of the above problem in order to know whether K=1 is a lower bound or not. Let's do it!

Steps of Synthetic Division:

1. Write the coefficients of the equation, and before that write 1. Like,

1 ║ 4   -2   2   4

As you can see, the coefficients of the equation are seperated by ║.

2. Drop down the first value after ║as it is. Like:
1 ║ 4   -2   2   4
:
----------------------
4

3. Multiply 4 with 1 and then place the resultant value under -2 and then add that resultant value with -2. Like
1 ║ 4   -2   2   4
: 4
----------------------
4 2

4. Repeat Step 3 until you're done.

1 ║ 4   -2   2   4
:   4   2
----------------------
4 2 4

1 ║ 4   -2   2   4
:   4   2 4
----------------------
4 2 4 8

Now every value, +4, +2, +4, +8, under the bar(---------) is positive; therefore, it means that K=1 is the upper bound, NOT lower bound.

Ans: K=1 is NOT a lower bound.
-i

Related Questions

Why does an enzyme function as a catalyst in a reaction?

A. It maintains the proper temperature needed for the reaction.

B. It decreases the amount of energy needed for the reaction.

C. It creates the right pH needed for the reaction.

D. It provides the extra energy needed for the reaction.

Answers

I believe the answer would be B. Catalysts lower the activation energy.

Answer: Less energy is required for the reaction so B

Step-by-step explanation:

Plot (−134,412) on the coordinate plane.

Answers

We are given coordinate (-1 3/4, 4 1/2).

(-1 3/4, 4 1/2) represents x-coordinate -1 3/4.

And y-coordinate 4 1/2.

First we need to go -1 and three fourth between -1 and -2.

And then for 4 1/2, we need to got 4 above on y-axis and then a half between 4 and 5.

We would draw the coordinate of intersection of vertical line of point -1 3/4 and horizontal line at 4 1/2.

The shown green point on the graph is the coordinate (-1 3/4, 4 1/2).

Answer:

I hope this helps! <3

Step-by-step explanation:

Hey, if I could get some help on this i'd really appreciate it.

QUESTION 1

What is the constant of variation for the quadratic variation?
0.1y = 3x^2

0.03

0.1

30

3

QUESTION 2

What is the constant of variation for the quadratic variation?
10y = 6x2

6

1.6

10

0.6

QUESTION 3

If f(x) varies directly with x^2, and f(x) = 96 when x = 4, find the value of f(2).

32

24

72

192

QUESTION 4

Write a quadratic variation equation if g(x) varies directly with x^2, and g(x) = 98 when x = 7.

g(x) = 2x^2

g(x) = 7x^2

g(x) = 1/2x^2

g(x) = 14x^2

Answers

1) When you rewrite the equation as
.. y = kx^2
The value of k is 3/0.1 = 30.

2) When you rewrite the equation as
.. y = kx^2
The value of k is 6/10 = 0.6.

3) f(x) = kx^2
.. k = f(x)/x^2 = 96/4^2 = f(2)/2^2
.. f(2) = 96(2/4)^2
.. f(2) = 24

4) g(x) = kx^2
.. 98 = k*7^2 = 49k
.. k = 98/49 = 2
g(x) = 2x^2

Does anybody know the answer to X

Answers

x = (66-14)/2
x = 52/2
x = 26

6) On a trip to his grandparents, Donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. How many miles did Donny drive?

Answers

60 miles an hour for 45 minutes = 45 miles
50 miles per hour for 30 minutes = 25 miles

Total =70 miles

your answer is 70 miles..... your welcome.

What is the volume of a cube whose edges each have a measure of 1.5 cm?

A)2.25 cm³

B)3.375 cm³

C)4.5 cm³

D)9 cm³

I saw this question and I realized that it had the wrong answer. The actual answer is 3.375cm

Answers

b) 3.375 [tex] cm^{3} [/tex]

Hope this helped!

The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. If in the last game he made 77 assists, how many standard deviations is that from the mean?

Answers

To get the number of standard deviation that 77 is from the mean, we get the z-score:
z-score is given by
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus the value of z from the information above is:
x=77
μ=58
σ=7
z=(77-58)/7=2.7143

What is the value of n?

Enter your answer in the box.

n = cm

Answers

The Correct answer is

(n)(4) = (7)(8)

4n = 56

n = 14

Answer:

n = 14 cm

Step-by-step explanation:

We are required to find the find the value of n.

Since, we have the lines are intersecting in the circle.

So, using the 'Intersecting Chord Theorem', which states that the product of the line segment formed by the intersecting lines are equal.

[tex]4\times n= 8\times 7[/tex]

i.e. [tex]4n=56[/tex]

i.e. n = [tex]\frac{56}{4}[/tex]

i.e. n = 14

Hence, the value of n is 14 cm.

Can someone check my answer please?

Quadrilateral ABCD is inscribed in circle O.
What is m∠B?

m∠A + m∠B = 180°
2x - 7 + 2x + 3 = 180
4x - 4 = 180
4x = 184
x = 46

m∠B = 2x + 3
m∠B = 2(46) + 3
m∠B = 92 + 3
m∠B = 95°

Answers

yes i have checked it good job! :D

Nope.
The angles A and B do not add to 180°. Rather angles A and C add to 180°, because the sum of the measures of the arcs they intercept is 360°.
.. (2x -7) +(x+4) = 180
.. 3x = 183
.. x = 61

Then ∠B = (2*61 +3)° = 125°

_____
∠A = (2*61 -7)° = 115°
∠C = (61+4)° = 65°
∠D = 180° -125° = 55°
so ABCD is NOT a trapezoid..

Medals please help

Which of the following is the statement of the triangle inequality theorem?
A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
C. The longest side of a triangle is opposite the largest angle.
D. The largest angle of a triangle is between the two longest sides.,

Answers

the triangle inequality theorem simply states, The sum of the lengths of any two sides of a triangle is greater than the length of the third side. your answer is B.

A car traveled 75% of the way from town A to town B at an average speed of 50 kmph. The car travels at an average speed of S kmph for the remaining part of the trip. The average speed for the entire trip was 40 kmph. What is S?,

Answers

the car would have been traveling at 10kmph for the remaining 25 percent of the trip. 50 times 3 (25 percent segments) is 150, use math to solve for four 25 percent segments.

In the United States the speed limit signs are in miles per hour. Unfortunately, your speedometer only reads in km/hour. How fast are you allowed to go if the speed sign says 70 mph (rounded to the nearest hundredth)

Answers

The correct answer is 112.65 kph

Answer:

The speed limit will be 112.65 kph.

Step-by-step explanation:

In order to find how fast one can go when speed sign says 70mph and the speedometer reads in km per hour we convert mph to kmph.

The conversion unit is 1mph= 1.609344kph

So 70mph = 70x1.609344=112.6541kph

Or 70mph=112.65 kph

One can travel at 112.65 kph.

Bob's carpet cleaning company uses the equation y=22x+30 to calculate cost, y, to clean x numbers of rooms. Andy's carpet cleaning company uses the table below to calculate the cost to clean rooms.

Laura needs 5 rooms cleaned. Which company charges less and by how much less?

Answers

Bob charges $140
Andy charges $135
Andy is cheaper

Identify the factors of 9x2 + 30x + 25.

A) (3x − 5)(3x − 5)
B) (3x + 5)(3x + 5)
C) (9x + 5)(x + 5)
D) (9x − 5)(x − 5)

Answers

Selection B is appropriate.

_____
The signs of the coefficients tell you the binomial factors must have both signs positive (selections B and C only). Selection B produces an x-term that is 15x+15x=30x (as we want); selection C produces an x-term that is 45x+5x=50x (not what we want).

Answer:

B is correct

Step-by-step explanation:

The signs of the coefficients tell you the binomial factors must have both signs positive (selections B and C only). Selection B produces an x-term that is 15x+15x=30x (as we want); selection C produces an x-term that is 45x+5x=50x (not what we want).

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Given a polynomial f(x) of fifth degree and g(x) such that
1. a root at 3i
2. a root at 2+4sqrt(3)
3. a root at -1/3
and that f(1)=-7520
Find polynomial f(x) as a product of its factors.

Given the three roots, we can conclude that the two other roots are the conjugates, namely -3i and 2-4sqrt(3).
Since
(x+3i)(x-3i)=x^2+9, and
(x-2+4sqrt(3))(x-2-4sqrt(3)=x^2-4x-44
We conclude that polynomial f(x) has the form
f(x)=a(x^2+9)(x^2-4x-44)(3x+1)
where a is a constant to be determined.

Knowing that f(1)=-7520, we can substitute x=1 in f(x) to get
-7520=a(1^2+9)(1^2-4(1)-44)(3+1)=a(10)(-47)(4)
=>
a=-7520/(-1880)=4

Therefore the polynomial f(x) is defined as

f(x)=4(x^2+9)(x^2-4x-44)(3x+1)
or
f(x)=4(3x+1)(x^2+9)(x^2-4x-44)

The root at -1/3 means that (3x+1) is a factor.

The root at 3i means that (x -3i)*(x +3i) = (x^2 +9) is a factor.

The root at 2 +4√3 means that (x -2 -4√3)*(x -2 +4√3) = (x^2 -4x -44) is a factor.

Evaluated at x=1, the product of these factors is (4)*(10)*(-47) = -1880, so there is an additional factor of -7520/-1880 = 4.

The intercept form of the polynomial is
.. y = 4(3x +1)*(x^2 +9)*(x^2 -4x -44)

PLEASE HELP MEEEE
Describe the relationship of input and output values for composite functions.

Answers

A COMPOSITE FUNCTION IS A COMBINATION OF TWO FUNCTIONS SUCH THAT THE OUTPUT FROM THE FIRST FUNCTION BECOMES THE INPUT FOR THE SECOND FUNCTION.
IN A COMPOSITE FUNCTION f[g(x)], SOMETIMES WRITTEN (fog) (x), THE OUTPUT OF FUNCTION G IS THE INPUT TO FUNCTION F.

Select the actual distances represented by the following scale distances if the map scale is 1 centimeter = 1 kilometer

23 centimeters =
a. 0.023 kilometers
b. 0.23 kilometers
c. 23 kilometers

0.5 centimeters =
a. 0.5 kilometers
b. 50 kilometers
c. 500 kilometers

9 centimeters =
a. 0.9 kilometers
b. 9 kilometers
c. 0.009,

Answers

23 centimeters =
We make the following rule of three:
1 centimeter ----> 1 kilometer
23 centimeter -> x kilometer
We clear x:
x = (23/1) * (1)
x = 23 kilometers
0.5 centimeters =
We make the following rule of three:
1 centimeter ----> 1 kilometer
0.5 centimeter -> x kilometer
We clear x:
x = (0.5 / 1) * (1)
x = 0.5 kilometers

9 centimeters =
We make the following rule of three:
1 centimeter ----> 1 kilometer
9 centimeter -> x kilometer
We clear x:
x = (9/1) * (1)
x = 9 kilometers

Answer:
c. 23 kilometers
a. 0.5 kilometers
b. 9 kilometers

Answer:

Correct options are:

Step-by-step explanation:

The map scale is:

1 centimeter = 1 kilometer

23 centimeters=23 kilometers

Correct option is: c

0.5 centimeters=0.5 kilometers

Correct option is: a

9 centimeters=9 kilometers

Correct option is: b

Please help asap!!! 16 points

Answers

You are given a table in which each row represents the coordinates of points. For example, in the first line, we have x=-7 and y=5. Work through the four given equations, one at a time, subbing -7 for x and 5 for y; is the equation still true? If yes, then you have found the correct answer. B is the exception; I'd suggest you check out equations A, C and D first, before focusing on B.

Example: D: (5)-5 = 2((-7) + 7) leads to 0 = 0. Is that true? If so, D is likely the correct answer.

How does a high-mass star differ from a low-mass star as both enter the final stages of their life cycle?
A. A high-mass star dies more explosively.
B. A high-mass star ends in a nova event.
C. A high-mass star ends when it runs out of hydrogen.
D. A high-mass star converts helium to carbon, whereas a low-mass star does not.,

Answers

B. A high-mass star ends in a nova event. When a high mass star gets to the end of its life, the gravity of its mass collapses upon itself, causing the collapse to accelerate and cause a nova event. On the other hand, smaller mass stars typically either become white dwarfs or red giants, depending on the particular circumstances and mass of the star.

Solve the system of equations

y=3x+30
y=8x
_______________________

x= ??

y= ??

Answers

x=6, y=48

Since both equations are set equal to y, set 3x+30=8x. Subtract 3x from each side, getting 5x=30. Divide by 5, so x=6. Then, just plug in 6 for x in any of the two equations, so y=48.

Lets get started :)

y = 3x + 30
y = 8x

Since y = both the equations, we can equate them

8x = 3x + 30 {Take 3x by subtracting to the other side in order to find the value of the variable)
We do minus, when we see plus

8x - 3x = 3x - 3x + 30
3x and -3x cancels out in the right hand side

5x = 30

Divide by 5 on either side to isolate x
We do division, when we see multiplication

[tex] \frac{5x}{5} = \frac{30}{5} [/tex]
5 and 5 cancels out

x = 6

Now, we need to substitute x by 6 in order to find y
We can substitute in either equation, we will still get the same value

y = 8(6)
= 48

y = 3(6) + 30
= 18 + 30
= 48

x = 6 , y = 48

A graphic artist earns $22 an hour, and she works 44 hours a week. What is her weekly wage?

A. $154
B. $308
C. $66
D. $968

Answers

($22/h)*(44h) = $(22*44) = $968 . . . . . matches selection D

Answer:

The answer is option D. The weekly wage is $968.

Step-by-step explanation:

The weekly salary can be found multiplying the earned money per hour and the amount of hours worked in the week:

[tex] Wweek=22\ \$/hr* 44\ hr/week[/tex]

[tex] Wweek=968\ \$/week[/tex]

the printed matter on a 14 by 18 centimeter page of a book must covor 140 square centimeters. if all margins are to be the same width, how wide should they be?

Answers

Let
x----------------> width of the margin
we know that

[Area printed matter]=140
[Area printed matter]=[(14-2x)*(18-2x)]
then
[(14-2x)*(18-2x)]=140--------> (252-28x-36x+4x²)=140
(252-64x+4x²)=140----------> 4x²-64x+112=0

using a graph tool---------> I solve the quadratic equation
see the attached figure
x1=2
x2=14----------> is not solution

the answer is
the margin should be 2 cm

Lamar has a summer job. He gets paid $7.25 an hour and a $150 bonus at the end of summer. The total Lamar earns can be modeled by the equation f(h) = 7.25h + 150, where h is the number of hours he works. In what form is the equation?

Answers

Final answer:

The equation representing Lamar's summer job earnings is in linear form with a constant rate of change represented by 7.25 and a vertical intercept of 150, which is his end-of-summer bonus.

Explanation:

The equation provided, f(h) = 7.25h + 150, is in linear form. This type of equation is used to model a relationship where the dependent variable, f(h), which represents Lamar's earnings, changes at a constant rate with respect to the independent variable, h, which represents the number of hours worked. The number 7.25 represents Lamar's hourly wage, while the 150 represents a fixed bonus amount he receives at the end of the summer, making it the constant term or vertical intercept when graphed on a coordinate plane.

Suppose you roll a special 49-sided die. what is the probability that the number rolled is a "1" or a "2"?

Answers

Final answer:

The probability of rolling a "1" or a "2" on a 49-sided die is found by adding the separate probabilities of each event, resulting in 2/49 or approximately 0.04082.

Explanation:

In probability, when you want to find the chance of one event or another occurring, you add the probabilities of each event if they cannot happen at the same time. Given a special 49-sided die, each outcome is equally likely, and every roll is an independent event. Therefore, the probability of rolling a "1" is 1 out of 49, and the probability of rolling a "2" is also 1 out of 49. To find the combined probability of rolling either a "1" or a "2", you simply add these two probabilities together.

The probability of rolling a "1" is 1/49, and the probability of rolling a "2" is 1/49. So, the combined probability (P) is:

P("1" or "2") = P("1") + P("2") = 1/49 + 1/49 = 2/49 or approximately 0.04082.

26 POINTS WILL GIVE BRAINLIEST
2. Do the sides 16, 30, and 38 form a Pythagorean Triple? Explain why or why not.

3. A triangle has sides of length 10, 14, and 22. Is the triangle acute, right, or obtuse. Explain.

12. A person can see the top of a building at an angle of 42˚. The person is standing 30 ft away from the building and has an eye level of 6 ft. How tall is the building to the nearest tenth of a foot?

Answers

2: They do not because the hypotenuse is larger and a^2 + b^2
3. The tiangle is acute because it has all angles smaller than 90*
12: The buillding is approximately 100 ft tall give or take. I am sorry If i am wrong on the last one

how many numbers are between 1 and 3 ?

Answers

If we are talking about whole numbers, the only number in between 1 and 3 is 2 but if we are talking about numbers in general, there are an infinite amount of numbers (for example, 1.1, 1.12, 1.004, and 1.80543285 are all in between 1 and 3).

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 90 people in the 18-21 age bracket and finds that 76 of them respond and 14 refuse to respond. when 297 people in the 22-29 age bracket are contacted, 262 respond and 35 refuse to respond. assume that 1 of the 387 people is randomly selected. find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond. report the answer as a percent rounded to one decimal place accuracy. you need not enter the "%" symbol. prob = 23.3 incorrect%

Answers

Answer: 91.0%

To find this, create a two way table.
On the top row, put the 18-21 group with the 76 responding then 14 not responding.
On the second row, put the 22-29 group with 262 responding then 35 not responding.

We are looking for people in the 18-21 group, those are the numbers 76 and 14. However, we must also include those in the older group that responded, 262.

So our fraction becomes (76 + 14 + 262 ) / 387 or 91.0%

Interest rates of 5%,6%,8%, earned on investments of $13,000,$12,000,$4,000. Calculate total amount of interest earned

Answers

[tex]13,000*0.05+12,000*0.06+4,000*0.08=1,690.00[/tex]

Please Help
A motorcycle cost $12,000 when it was purchased. The value of a motorcycle decreases by 6% each year. Find the rate of decay each month and select the correct answer below.

−0.005143%
−0.5143%
−0.005%
−0.5%

Answers

If the rate of decay is 6% per year, that means the motorcycle retains 93% of its value every year. Because there are 12 months in a year, you can use the following equation:
x^12 = 0.94,
where x = the rate of decay each month, 12 = the number of months, and 0.94 = the retained value each year. Next, set a logarithmic function on each side as such:
LOG(x^12) = LOG(0.94)
When applying log functions, exponentials (like the 12 in the equation) are moved outside of the function like so:
LOG(x^12) = 12(LOG(x))
Therefore,
12(LOG(x)) = LOG(0.94) = -0.0268721464
When you divide both sides by 12, the equation becomes
LOG(x) = -0.00223934553
Finally, remove the LOG from the left side by applying both sides of the each by 10^() as such:
10^(LOG(X)) = 10^(-0.00223934553)
X = 0.994856987
Therefore, the motorcycle retains that 0.994856987 of its value every year.
1 - 0.994856987 = 0.005143
Expressed as a percentage, this value is 0.5143013%

The rate of decay each month is given by 0.5143% and this can be determined by forming the expression from the given data.

Given :

A motorcycle cost $12,000 when it was purchased.The value of a motorcycle decreases by 6% each year.

There are 12 months in a year then the value motorcycle retains every year is:

[tex]x^{12}=0.94[/tex]

Now, take the log on both sides in the above equation.

[tex]\rm logx^{12}=log(0.94)[/tex]

12 log x = log(0.94)

Now, divide log(0.94) by 12 in the above expression.

[tex]\rm log x = \dfrac{log(0.94)}{12}[/tex]

log x = -0.00223934553

[tex]x = 10^{-0.00223934553}[/tex]

x = 0.994856987

Now, to determine the rate of decay:

= (1 - x)100

= (1 - 0.994856987)100

= (0.005143)100

= 0.5143%

Therefore, the correct option is B).

For more information, refer to the link given below:

https://brainly.com/question/9695463

how many 1020 flats can fit on (2) 8'x4' tables?

Answers

32 flats will fit on 2 8' by 4' tables.

The dimensions of each 1020 flat is 11" by 22". We will convert the measurements of the table to inches. 8(12) = 96". 4(12) = 48". If we lay the longest edge of the flat side along the long edge of the table, 4 flats will fit along it with 8 inches left over. This would put the smaller edge of the flat along the smaller edge of the table, which would allow for 4 rows of 4, or 16 flats on each table. 16*2=32 flats between both tables.

This works out the same if we turn the flats around. Let the smaller edge of the flat, 11", be along the longer edge of the table, 96". This would allow for 8 flats. This puts the longer edge of the flat, 22", along the shorter edge of the table, 48"; this puts 2 rows of 8, which would be 16 flats on each table, for a total of 32 flats.

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