What are all the possible rational roots of f(0) = 2x^4+ x^3+ 4?
Answers
Answer: the answer is 4, just 4
Related Questions
Simplify the expression x^4-x^3-3x-2 dived by (x-2), using synthetic division.
Please show work.
Answers
1. Write the coefficients of the polynomial in descending order, leaving a placeholder for any missing terms. In this case, we have:
1 | 1 -1 -3 0 -2
where the first term, 1, represents the coefficient of x^4, the second term, -1, represents the coefficient of x^3, and so on.
2. Write the constant term of the divisor (x-2) outside the division bracket and draw a line underneath it. In this case, the constant term is -2, so we have:
-2 | 1 -1 -3 0 -2
|
3. Bring down the first coefficient, which is 1, and write it underneath the line. This represents the value of the polynomial when x = 0.
-2 | 1 -1 -3 0 -2
| 1
4. Multiply the constant term outside the bracket by the first term inside the bracket and write the result underneath the second coefficient of the dividend. In this case, we have:
-2 | 1 -1 -3 0 -2
| 1 6
_________
1 0 3 0 -2
5. Repeat the process by bringing down the next coefficient, which is 0, and placing it underneath the line. Then, multiply the constant term by the second term of the dividend and write the result underneath the third coefficient. Continue this process until all the coefficients have been brought down and multiplied.
-2 | 1 -1 -3 0 -2
| 1 6 -6
_________
1 0 3 6 4
6. The final row of numbers represents the coefficients of the simplified polynomial, read from left to right. Therefore, x^3 + 3x^2 + 6x + 4 is the simplified form of x^4-x^3-3x-2 divided by (x-2).
So, the answer is:
x^4-x^3-3x-2 = (x-2)(x^3 + 3x^2 + 6x + 4)
Sarah is planning to take
aerobics classes at a gym.
Non-members pay $8 per
class, while members pay $4
per class and a $20
membership fee. If Sarah
plans to take 6 aerobics
classes, should she become a
member of the gym? Explain
why or why not?
Answers
Answer:
Yes
Step-by-step explanation:
Non members - 8*6 = $48
Members - 20+(4*6) = $46
She should become a member of the gym because she will pay $2 less overall.
Answer:
Sarah should become a member. She would be paying a lot less money and be able to take more classes for cheaper
Step-by-step explanation:
Non member amount for 6 classes- $8*6= $48
Member amount for 6 classes- $4*6= 24 ($20 fee) = $44
As you can see above, the cost for 6 classes with a membership is cheaper than without a membership
lukes house is located at the point shown on the coordinate grid. kyles house is located 4 units left and 2 units up from lukes house plot a point on the coordinate grid to represent the location of kyles house.
Answers
The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.
The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.
If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).
Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.
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36 divided by m over x times 9
Answers
Answer:
Step-by-step explanation:
4/mx
Paula's Pies is famous
for their apple pie. At
Thanksgiving, they receive
orders for 296 pies. If
Paula can prepare 8 pies
in 3 hours, then how many
hours will it take her
prepare the order?
(PLEASE MAKE THE WORK A RATIO TABLE!)
Answers
Sets of 8pies
296/8=37No if time for 8pies=3h
No of time for 37 sets of 8pies:-
3(37)=111h1. Which one of the following is NOT true about polynomial functions f(x) and g(x) if deg (f) = man * d deg * (g) =n?
A. deg (f + g) = max(m, n)
B. deg (f_{g}) <= m + n
C. If g is a factor of f then deg( f )<= m
D. The deg (f ^ 3) = 3m
Answers
The option that is not true about polynomial functions is:
Option D. The deg (f ^ 3) = 3m
How to Interpret the degree of Polynomial functions?For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:
Option A: deg(f + g) = max(m, n)
This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.
Option B: deg(f * g) <= m + n
This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.
Option C: If g is a factor of f, then deg(f) <= m
This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.
D. The deg(f ^ 3) = 3m
This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.
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To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.
Answers
The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.
Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:
1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.
2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.
3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.
4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.
5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.
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Ullany TVd How much 20k stamps can #2.00 buy
Answers
Answer: 4000
Step-by-step explanation:
In the Republic of Yemen, real per capita gross domestic product (GDP) in 2004 was $709.97. By 2005, it had increased to $832.84. At what rate did Yemen's economy grow in that time?
Answers
Answer:
$122.87 or 17.31% per year.
Step-by-step explanation:
Rate of growth
It's a measure of how a magnitude increases in a determined time. If the magnitude changes from x1 to x2 in a time t, then the rate of growth is:
\(\displaystyle r=\frac{x2-x1}{t}\)
The GDP of Yemen went from $709.97 to $832.84 in one year. Thus:
\(\displaystyle r=\frac{832.84-709.97}{1}\)
r=$122.87 per year
It can also be expressed as a percentage with respect to the initial value:
\(\displaystyle r=\frac{122.87}{709.97}*100\%\)
r=17.31% yearly
Answer:
$122.87 or 17.31% per year.
Step-by-step explanation:
Rate of growth
It's a measure of how a magnitude increases in a determined time. If the magnitude changes from x1 to x2 in a time t, then the rate of growth is:
The GDP of Yemen went from $709.97 to $832.84 in one year. Thus:
r=$122.87 per year
It can also be expressed as a percentage with respect to the initial value:
r=17.31% yearly
In a triathlon, an athlete swims 750 m in 15 minutes, cycles at an average speed
of 40 km/h for 30 minutes and runs 5 km at an average speed of 3 m/s. Find his
average speed for the entire competition, giving your answer in km/h
Answers
HOPE IT HELPS (◕‿◕✿)
Answer:
In triathlon an athlete swims 750meter in 15minutes cycles at an average speed of 40km/h for 30minutes and runs 5km at an average speed of 3meter/second find his average speed for the entire competition giving your answer in km/h
The average speed for the entire triathlon = 21.229 km/hr
Step-by-step explanation:
Calculate the distance covered and time taken in the first part of the Triathlon in Kilometers and hours respectively - Swimming
Distance 750 meters ⇒ 750/100= 0.75Km
Time = 15 minutes ⇒ 15/60 = 0.25 hours
Calculate the distance and time in Km and hours in the second phase:
Time is 30 minutes = 30/60 = 0.5 hours
Speed = 40km/hr
Distance = speed × time = 40km/hr × 0.5 = 20km
Calculate the distance covered and time taken in the last phase of the triathlon: Running
Runs 5 Km - this is the distance
5km = 5000m
Speed = 3 meters/sec
Time = Distance / speed
= 5000 m / 3m/s
= 1666.66666667 s
Convert to hours
1666.66666667 /3600 = 0.46 hours
Final step is to calculate the average speed:
Average speed = total distance travelled / total time taken
Total distance in Km = 0.75 km + 20 km + 5 km = 25.75 km
Total time taken = 0.25 hours + 0.5 hours + 0.46 hours = 1.21296296296 hours
Average speed of the athlete = 25.75 km / 1.21296296296 hours
= 21.229 Km/hr
The average speed for the entire triathlon = 21.229 km/hr
From the top of a lighthouse 82 m tall, a guard sees two ships at sea.
The angle of depression to the closer ship is 53° and to the further ship is 39°.
How far are the ships apart from each other to the nearest metre?
Answers
The distance between the two ship based on the angle of depression is 42 meters.
The distance of each ship can be calculated thus:
TanX = opposite / Adjacent
The first ship:
Tan53 = distance/ 82
distance= 108.82 meters
The second ship:
Tan39 = distance/ 82
distance= 66.40 meters
The Difference between the ships are :
108.82 - 66.40 = 42.42 metersTherefore, the distance between the two ships is 42 meters.
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Answers
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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question is attached thank you so much
Answers
Ratio remains same
\(\\ \sf\longmapsto \dfrac{18}{27}=\dfrac{x}{45}\)
\(\\ \sf\longmapsto 2/3=x/45\)
\(\\ \sf\longmapsto 3x=90\)
\(\\ \sf\longmapsto x=30\)
Three quarters of a number is 27. What is two ninths of the number?
Answers
Answer:
8
Step-by-step explanation:
let x be the number , then
\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )
3x = 108 ( divide both sides by 3 )
x = 36
the number is 36, so
\(\frac{2}{9}\) × 36 = 2 × 4 = 8
The two ninths of the number is 8
We know that Three quarters of a number is \(\frac{3}{4}\) times of a number
Hence we will assume the number x ,
\(\frac{3}{4} of x = 27\)
\(x = 27 X \frac{4}{3}\)
\(x = 36\)
Now as we know the number is 36
Therefore , the two ninths of the number assumed as y
We will multiply the number 36 by 2 and then divide by 9
Hence,
\(y = 36 X \frac{2}{9}\)
\(y = 8\)
Thus, the two ninths of the number 36 is 8
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Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new walls need to be 1 built . The total length of the two new walls must be 12 m.
Martin wants the length of the closet to be twice as long as the width, as shown in the diagram.
b) Let the function f(l) be the sum of the length and the width. Find the equation for f(1).
c) Graph y = f(l).
d) Find the desired length and width. ile riding a
Answers
The relationship between the length & the width of the closet and the length of the wall is an illustration of a linear equation.
The equation for f(l) is: \(f(l) = 1.5l\).The desired length and width are 8m and 4mGiven that:
\(l = 2w\)
Divide both sides by 2
\(w = 0.5l\)
Equation of f(l)
The sum of the length and the width is represented as: f(l).
So, we have:
\(f(l) = l + w\)
Substitute \(w = 0.5l\)
\(f(l) = l + 0.5l\)
\(f(l) = 1.5l\)
See attachment for the graph of f(l)
The desired dimension
From the question, we understand that the total length is 12m.
This means that:
\(f(l) = 12\)
So, we have:
\(1.5l = 12\)
Divide both sides by 1.5
\(l = 8\)
Recall that:
\(w = 0.5l\)
\(w = 0.5 \times 8\)
\(w = 4\)
Hence, the desired length and width are 8m and 4m, respectively.
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A drone flying over a field of corn identifies a dry area. The coordinates of the vertices of the area are shown. To what coordinates should the portable irrigation system be sent to water the dry area? Explain your reasoning.
Answers
The coordinates to which the portable irrigation system should be sent to water the area are:
(495.75, 672).
Where to send the portable irrigation system?The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.
Hence the coordinates are given as follows:
x-coordinate: Mean of the x-coordinates of x = 56, x = 144, x = 888, x = 895.y-coordinate: Mean of the y-coordinates of y = 289, y = 332, y = 1012, y = 1055.Hence the x-coordinate of the point to which the system should be sent is:
x = (56 + 144 + 888 + 895)/4 = 495.75.
(the mean is given by the sum of the observations divided by the number of observations).
The y-coordinate of the point to which the system should be sent is:
y = (289 + 332 + 1012 + 1055)/4 = 672.
Missing InformationThe area is given by the image at the end of the answer.
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The opposite sides of a parallelogram are called
Answers
Answer:
The opposite side and opposite of angles of parallelogram are equal. An these opposite sides an opposite angles make up for a congruent triangles, with the two diagonal being the sides of these two congruent triangle. Hence the diagonals of the parallelogram are equal.
Hope it will help you.
What is the answer to this question?
Answers
Answer:
27 cubic feet
Step-by-step explanation:
Answer:
27ft
Step-by-step explanation:
Multiply Height, Width, and Length
Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown.
Two circles are drawn by having another circle in the center. The center circle has points A, M, N, B, P, Q, and C. At C the two circles intersect, and at P the center circle and the top circle intersect.
To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C.
Which figures could Brian be constructing?
equilateral triangle MNQ inscribed in circle C
equilateral triangle ANP inscribed in circle C
regular hexagon AMNBPQ inscribed in circle C
square MNPQ inscribed in circle C
square ANBQ inscribed in circle C
Answers
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
Brian is constructing figures inscribed in circle C.
Equilateral triangle MNQ inscribed in circle C:
This option is possible since the points M, N, and Q are labeled and they lie on circle C.
Equilateral triangle ANP inscribed in circle C:
This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.
Regular hexagon AMNBPQ inscribed in circle C:
This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.
Square MNPQ inscribed in circle C:
This option is not possible based on the given information. The label points do not form a square.
Square ANBQ inscribed in circle C:
This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
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please answer see the image below
Answers
Answer:
64.8Step-by-step explanation:
total area = rectangle + semi circle
= (11 x 5) + (1/2 * π * 2.5²)
= 55 + 9.8
= 64.8 sq. units
Answer:
64.8² units. Hope it's help you.
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
–12 – 20x ≤ –6x + 9
–12 – 20x ≥ –6x + 9
–12 + 20x ≤ –6x + 9
–12 + 20x ≥ –6x + 9
Answers
Answer:
-12 + 20x ≥ -6x + 9
Fourth choice
Step-by-step explanation:
Inequalities
We are given the inequality:
-4(3 - 5x) ≥ -6x + 9
Solving the inequality implies having x isolated on one of the sides.
We must start by removing the parentheses. It will be done by multiplying -4 by (3 - 5x). Since this operation doesn't imply multiplying all the inequality by a negative number, the sign won't be flipped:
-4*3 - (-4)5x ≥ -6x + 9
Multiplying:
-12 + 20x ≥ -6x + 9
Fourth choice
In ADEF, f= 33 inches, ZF=140° and ZD=5°. Find the length of e, to the nearest 10th
of an inch.
Answers
The length of e is 29.53 inches.
what is Sine Law?In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".
Given:
f= 33 inches
<F= 140, <D = 5
Now,
<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35
Using Sine law
sin F / f = sin E/ e
sin 140 / 33 = sin 35 / e
0.642/ 33 = 0.573 / e
0.0194 e= 0.573
e= 29.53 inches
Hence, the length of e is 29.53 inches.
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Find the measure of the third interior angle of a triangle, given the measure of two angles.
62 and 24 and ______
Answers
We know that the sum of the internal angles is equal to 180°, then we write and solve a linear equation to see that the missing angle is 94°.
How to find the measure of the third angle?Remember that for any triangle, we know that the sum of the interior angles is equal to 180°.
In this case we know that two of the angles have a measure of 62° and 24°, and if the third angle is x, then we can write the linear equation:
62° + 24° + x = 180°
To solve this we need to isolate x, we will get:
x = 180° - 24° - 62°
x = 94°
So the measure of the third interior angle is 94 degrees.
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Please help and answer ASAP please will mark Brainlest
What is the value for x?
Enter your answer in the box.
x =
Answers
Answer:
x=45
Step-by-step explanation:
i hope its right good luck :)
i think im wrong
You have two upcoming work trips. For the first trip, you will cover 846 miles in 3.5 days. For the second trip, you will cover 322.5 miles in 6 days.
How many miles will you travel on average during each trip?
Answers
Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
In 3.5 days, distance covered = 846 miles,
To find distance covered in 1 day, use ratio property,
3.5 days = 846 miles
1 day = 846/3.5
1 day = 246.86 miles
Also given that,
In 6 days, distance covered = 322.5 miles,
To find distance covered in 1 day, use ratio property,
6 days = 322.5 miles
1 day = 322.5/6
1 day = 53.75 miles
The average trip = (246.86+53.75)/2
= 150.305
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A tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a survey ten years ago, a sample of 14 property tax bills is given below. Assume the property tax bill is approximately normally distributed. Use a TI-83, TI-83 plus, or TI-84 calculator to construct a 90% confidence interval for the population mean property tax bill. Round your answers to one decimal place and use increasing order.
Property Tax Bill
1715.35
1157.82
651.10
1093.36
1609.22
1391.47
1398.89
402.99
1028.76
1571.23
529.42
1579.48
699.56
2222.16
838.60
866.41
1066.60
1498.64
1784.28
2016.99
2465.65
1098.81
1346.65
1574.00
1447.78
2018.33
2156.75
1710.81
Answers
Answer:
The answer is below
Step-by-step explanation:
From the table, the mean (μ) = 1390.75 and the standard deviation (σ) = 518.75
The confidence level (C) = 90% = 0.9
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1 / 2 = 0.05
The z score of α/2 (0.05) is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.
The margin of error (E) is given as:
\(E=Z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{518.75}{\sqrt{14} } =228.07\)
The confidence interval = μ ± E = 1390.75 ± 228.07 = (1162.68, 1618.82)
The confidence interval is between 1162.68 and 1618.82.
Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is to have $20,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal assuming they compound daily? (Hint: solve the compound interest formula for the interest rate. Also, assume there are 365 days in a year)
Answers
The minimum annual interest rate for Kyoko to reach her goal, using daily compounding, is 9.903%.
How is the interest rate determined?The interest rate is computed using an online finance calculator that sets the following parameters.
The compounding period involved is 2,555 days for 7 years, based on the assumption that there are 365 days in a year.
N (# of periods) = 2555 days (7 years x 365 days)
PV (Present Value) = $10,000
PMT (Periodic Payment) = $-0
FV (Future Value) = $-20000
Results:
I/Y = 9.903% if interest compound 365 times per year (APR)
I/Y = 10.409% if interest compound once per year (APY)
I/period = 0.027% interest per period
Total Interest = $10,000.00
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In 1976, a certain model of car cost $5,000. What would be the cost of that car in 2012 dollars? Express your answer rounded to the nearest cent
Answers
Answer:
9100.09
Step-by-step explanation:
i did the math so this is it
Write the word sentence as an inequality.
One plus a number y is no more than -13.
Answers
Answer:
1+y \(\leq\) -13
Step-by-step explanation:
The problem states that one plus y is No greater than -13.
This means that is less than or equal to -13.
It also gives you one plus y, or 1+y
Put everything together to get 1+y \(\leq\) -13
Answer:
1+y=
Step-by-step explanation:
Throwing a ball describes what kind of graph.
Answers
Answer:
parabola
Step-by-step explanation:
The path followed by a ball can be modeled by a graph.
Throwing a ball is a parabola or quadratic graph.
When a ball is thrown, the path it follows can be represented by:
\(\mathbf{f(x) = ax^2 + bx + c}\)
or
\(\mathbf{f(x) = a(x - h)^2 + k}\)
The above equations are functions of a parabola or quadratic graph.
Hence, throwing a ball is a parabola or quadratic graph.
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