Given:
The function is
[tex]f(x)=3x^3+2x^2+x+4[/tex]
To find:
The value from the given options that is NOT a possible root of the function.
Solution:
According to rational root theorem, all possible roots are in the form of
[tex]x=\dfrac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}[/tex]
We have,
[tex]f(x)=3x^3+2x^2+x+4[/tex]
Here,
Leading coefficient = 3.
Constant term = 4
Factors of 3 are ±1, ±3.
Factors of 4 are ±1, ±2, ±4.
Using rational root theorem, all possible roots of given functions are
[tex]\pm 1,\pm 2,\pm 4,\pm \dfrac{1}{3}, \pm \dfrac{2}{3},\pm \dfrac{4}{3}[/tex]
Clearly, [tex]\dfrac{4}{3},1,2[/tex] are possible roots but [tex]\dfrac{3}{4}[/tex] is not the possible root.
Therefore, the correct option is C.
can you please answer the following
Answer:
5. 4
6. ?
7. c- 8
8. b-13
9. ?
10. d. 12
Step-by-step explanation:
i hope this helps, sorry for the question marks :)
A commuter train travels 31 kilometers in 27 minutes. What is its speed in per hour?
The speed of the train in kilometer per hour is 68.9km/hr.
What is speed?The rate of change of position of an object in any direction.
Formula for speed[tex]speed = \frac{distance}{time}[/tex]
According to the given question
Distance travelled by commuter train = 21km
Time taken by a train to travel 31 km = 27 minutes = [tex]\frac{27}{60} =0.45hour[/tex]
Therefore, the speed of the train in kilometer per hour is given by
[tex]speed = \frac{31}{0.45}[/tex]
⇒[tex]speed = 68.9km/hr[/tex]
Hence, the speed of the train in kilometer per hour is 68.9km/hr.
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Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
5
3.5
=
12
x
3.5x = 60
x = $17.14
Answer:
Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.
Step-by-step explanation:
Can I get brainliest?
Let R be a relation on a collection of sets defined as follows,
R={(A,B)|A⊆B}
Then pick out the correct statement(s).
1) R is reflexive and transitive
2) R is symmetric
3) R is antisymmetric.
4) R is reflexive but not transitive
Answer:
Options 1) and 3) are correct.
Step-by-step explanation:
R={(A,B)|A⊆B}
Reflexive:
As A⊆A, [tex](A,A)[/tex]∈ R.
So, R is reflexive
Symmetric:
Let [tex](A,B)[/tex]∈ R. So, A⊆B
Take [tex]A=\{1,2\}\,,\,B=\{1,2,3,4\}[/tex]
Here, A⊆B but B⊄A
So, [tex](B,A)[/tex]∉ R
R is not symmetric
Transitive:
Let [tex](A,B)[/tex]∈ R and [tex](B,C)[/tex]∈ R
So, A⊆B and B⊆C.
Therefore, A⊆C
So,
[tex](A,C)[/tex]∈ R
Hence, R is transitive.
Option 1) is correct.
Antisymmetric:
Let (A,B)∈R and (B,A)∈R
So, A⊆B and B⊆A
Hence, A = B
So, R is antisymmetric
Option 3) is also correct.
What does it mean to be a medium of exchange
Answer:
The medium is the middle of something. More like math thought. So what even the numbers are it will be the middle.
Step-by-step explanation:
Answer: Any item that can be traded for another item.
Step-by-step explanation: took the quiz
A number is doubled and then the product is increased by 6. This sum is then multiplied by -3, and the result is 54 greater than three times the opposite of the number. What is the number? *
Answer:
-24Step-by-step explanation:
Let the number be x
Then we have the equation
(2x + 6)*(-3) = -3x + 54 -6x - 18 = -3x + 546x - 3x = -18 - 543x = -72x = -72/3x = - 24let the number be "x" .
now according to the given question ;
(2x+6)×(-3)=-3x +54 -6x -18 = -3x + 54 6x - 3x = -18-543x = -72x = -72/3x = -24 The required answer is -24 .Can -0.05 be a probability?
Answer:
Yes
Step-by-step explanation:
Answer:
The probability of an event can only be between 0 and 1 and can also be written as a percentage. ... If P ( A ) > P ( B ) P(A) > P(B) P(A)>P(B)P, left parenthesis, A, right parenthesis, is greater than, P, left parenthesis, B, right parenthesis, then event A has a higher chance of occurring than event B.
so that means yes
How do you these two questions?
Answer:
a) A = 3π/16
b) A = ∑₂°° (π/n⁴) = π⁵/90 − π
Step-by-step explanation:
(a) The area between the curve and the x-axis is:
A = ∫ₐᵇ y (dx/dt) dt
x = ½ (1 − cos t) cos t
dx/dt = ½ (1 − cos t) (-sin t) + ½ sin t cos t
dx/dt = -½ sin t + ½ cos t sin t + ½ sin t cos t
dx/dt = -½ sin t + sin t cos t
dx/dt = -½ sin t (1 − 2 cos t)
y dx/dt = -½ sin t (1 − 2 cos t) × ½ (1 − cos t) sin t
y dx/dt = -¼ sin²t (1 − 3 cos t + 2 cos²t)
y dx/dt = -¼ sin²t + ¾ sin²t cos t − ½ sin²t cos²t
y dx/dt = ⅛ (-2 sin²t) + ¾ sin²t cos t − ½ (sin t cos t)²
y dx/dt = ⅛ (-1 + 1 − 2 sin²t) + ¾ sin²t cos t − ½ (½ sin(2t))²
y dx/dt = ⅛ (-1 + cos(2t)) + ¾ sin²t cos t − ⅛ sin²(2t)
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + 1 − 2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + cos(4t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t − ¹/₁₆ + ¹/₁₆ cos(4t)
y dx/dt = -³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)
A = ∫₀ᵖⁱ [-³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)] dt
A = -³/₁₆ t + ¹/₁₆ sin(2t) + ¼ sin³t + ¹/₆₄ sin(4t) |₀ᵖⁱ
A = [-³/₁₆ π + ¹/₁₆ sin(2π) + ¼ sin³π + ¹/₆₄ sin(4π)] − [0 + ¹/₁₆ sin(0) + ¼ sin³0 + ¹/₆₄ sin(0)]
A = -³/₁₆ π
We got a negative answer because the graph traces to the left (x decreases as t increases). So the area is simply ³/₁₆ π.
b) Each circle has radius 1/n², so the area is π (1/n)² = π/n⁴.
The sum of the areas from n=2 to n=∞ is:
A = ∑₂°° (π/n⁴)
A = ∑₁°° (π/n⁴) − π
A = π ∑₁°° (1/n⁴) − π
A = π (π⁴/90) − π
A = π⁵/90 − π
on Monday it rained 1 3/4 of an inch and on Tuesday it rained 2 2/3 of an inch. how many inches did it rain altogether?
Answer:
4 5/12
Step-by-step explanation:
Convert to mixed fraction 7/4 + 8/3
Find common denominator, 12
21/12 + 32/12
add numerators (21+32)/12 = 53/12
reduce fraction 4 5/12
Which number line can be used to find the distance between (4, -1) and (8,-1)?
Answer:
the first one
The number line which can be used to find the distance between (4, -1) and (8,-1) is 1
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
Given the points;
(x1, y1) = (4, -1)
(x2, y2) = (8, -1)
Here, we have the same values of y for both points.
This means that the line that contains both points is a horizontal line.
To find the distance, apply the formula:
[tex]d= \sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
Since they have the same y values, the number line to represent the distance between both points must have the points 4 and 8;
Hence, we have;
[tex]d= \sqrt{(8-4)^{2}+(-1+1)^{2} }[/tex]
[tex]d= \sqrt{4^{2} + 0^{2} }[/tex]
d= 4
The distance between both points is 4;
Therefore, the number line that can be used to find the distance between both points is the number line in option A.
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A box of cereal states that there are 87 calories in a 3/4 -cup serving. What is the unit rate for calories per cup? How many calories are there in 4 of the cereal?
Answer: The unit rate is
116 calorie(s) per cup
and
There are 464 calories in 4 cups of the cereal
Question Progress
"HOT PIZZA” is offering a 20% discount on all its pizzas.
Tim orders a pizza for the reduced price of £7.20
What was the original price of the pizza?
Answer:
the answer is £1.44
Step-by-step explanation:
hope this helps
Find the inverse of the function f(x) = 2x - 4.
g(x) = 1/2x - 1/4
g(x) = 1/4x - 1/2
g(x) = 4x + 2
g(x) = 3x+2
Answer:
None of the options are correct, but I got g(x)=1/2x+2.
Step-by-step explanation:
You start with the equation. You first need to change f(x) to y, and switch the x and y values. After this, your equation would be x=2y-4. Then, you need to icolate the y value, and to do that you first cancel out the four by adding it to both sides, and now your equation should be x+4=2y. The second step in icolating the y value is dividing everything in the equation by two. Now that the y is icolated, you equation should be y=1/2x+2. You then change the y to be g(x), and that's how I got my answer, g(x)=1/2x+2. You should ask your teacher about this, becuase from my calculations, none of the given responses would be correct. Sorry if that doesn't help you at all but yeah
Answer:
D, g(x) = 1/2 x + 2
Step-by-step explanation:
The second answer IS ONE TO ONE
Yasmin had 3 bananas she shared them equally among the 4 people in her family write an expression that shows how much banana each person got
Answer:
3/4 of a banana
Step-by-step explanation:
3 divided by 4 = 3/4
What is the remainder when 18,049 is divided by 14? (Input numeric values only)
Answer:
18049/14= 1289 with a remainder of 3
Answer:
3
Step-by-step explanation:
determine whether the ordered pair is a solution of the linear equation. thanks in advance!!
What is an equation for the line that passes through the coordinates (- 1, 2) and (7, 6) ?
Answer:
y = 1/2x + 2.5
Step-by-step explanation:
First we want to plug it into the [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. This gets us 6-2/7-(-1) which solves to 4/8 which simplifies to 1/2. This gives us the slope. Now, when using slope intercept form y = mx + b, we can plug our newly found slope in for m and get y = 1/2x + b. To find b plug in any point on the line into the equation, I chose (7,6) because we are given that, and both numbers are positive. Now plug those in for x and y. 6 = 1/2(7). Solve, and get 2.5. are final equation is
y = 1/2x + 2.5
4. Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6. a. What are you ultimately interested in here (the value of the roll or the money you win)? b. In words, define the Random Variable X. c. List the values that X may take on. d. Construct a PDF. e. Over the long run of playing this game, what are your expected average winnings per game? f. Based on numerical values, should you take the deal? Explain your decision in complete sentences.
Answer:
Explained below.
Step-by-step explanation:
The rules of the deal are as follows:
If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6.(a)
The correct option is: "the money you win".
(b)
The random variable X denotes the amount won or lost.
(c)
The value of X are as follows:
X = {-$6, $5 and $10}
(d)
The probability function of X is as follows:
P (X = 10) = 1/6
P (X = 5) = 1/3
P (X = -6) = 1/2
(e)
Compute the expected value as follows:
[tex]E(X)=\sum x\times P(X=x)\\[/tex]
[tex]=(10\times\frac{1}{6})+(5\times\frac{1}{3})+(-6\times\frac{1}{2})\\\\=0.333333\\\\\approx $0.33[/tex]
Thus, the average winnings per game is $0.33.
(f)
Since the expected value of the game is a positive amount, the deal will not lead to me paying up.
Thus, you take the deal.
(1) alex has a collection of coins, consisting of nickels and dimes that total to $3.90. if the number of dimes is 4 more then 3 times the number of nickels. find the number
of each of coin. "please show the work"
(2)a satellite television company charges a one time installation fee and a monthly service charge.(A)use your equation from above to find out how many months(m)of television were used if the charges totaled $650.(B)write an equation for the total charges.(C)if they charge $75.per month(m) and a one time installation fee is $50.
The answer is 8months "i need help showing the work so please show the work."
Answer:
1. 10 nickels and 34 dimes
Step-by-step explanation:
Standard of living is the level at which
Answer:
hope it helped you
Step-by-step explanation:
Standard of living refers to the level of wealth, comfort, material goods, and necessities available to a certain socioeconomic class or geographic area. Quality of life, on the other hand, is a subjective term that can measure happiness.
Answer:
D( consumer enjoy desired goods
Step-by-step explanation:
just did the quiz
so, my teacher barley taught us this yesterday and i'm still having trouble with some questions, could anyone please help? ( this is 7th grade math )
5.) x>20
11.)x≤−15
13.)x≥−21
2.)x≤−7
6.)x≤−45
10.)x≤10
12.)x≥−12
16.)x≤−4
Answer:
2. x ≤ -7
5. x > 36
6. x ≤ -40
10. x ≤ 10
11. x ≤ -15
12. x ≥ -12
13. x ≥ -21
16. x ≤ -4
Step-by-step explanation:
2. x ≤ -7 (You want to add 8 to both sides like any equation, but don't forget it is an inequality, not an equation!)
5. x > 36 (You need to multiply by 2, to get rid of the division. So multiply both sides by 2, that gets rid of the 2 on the one side, and you get 36 on the other side when you multiply 18 by 2).
6. x ≤ -40 (You need to multiply by -5. REMEMBER: When you multiply or divide by a negative, you switch the sign. So if it is a < then it would be a > and same with if you had ≤ then it would be ≥ instead).
10. x ≤ 10 (You need to divide by -2. And once again you switch the signs).
11. x ≤ -15 (Add 8, like you did in number 2).
12. x ≥ -12 (Multiply by 6. REMEMBER: Do NOT switch the signs if you the number you are dividing by is in the numerator, or if you multiply and the negative number is first, UNLESS you have 2 negatives.
13. x ≥ -21 (Multiply by 7).
16. x ≤ -4 (Divide by 10).
A driver averaged 51 miles per hour and took 14 hours to travel between two cities. What is the distance between the two cities?
Answer:
714 miles
Step-by-step explanation:
if he drove 14 hours and in each hour he drove 51 miles then multiply
14*51=714
880,005 rounded to the nearest hundred thousand is
Answer:
900,000
Step-by-step explanation:
What is the domain of the relation graphed below?
Answer:
you need to show us the graph
Each time a machine is repaired, it remains up for an exponentially distributed time with mean 5 hours. When it fails, its failure will be a type 1 failure with probability 0.7 and a type 2 failure with probability 0.3. Type 1 failures take an exponential amount of time with mean 1 hour to repair. Type 2 failures take an exponential amount of time with mean 1.25 hours. The status of the machine can be monitored as a continuous-time Markov chain with states 0 (= working), 1 (= repairing a type 1 failure), 2 (= repairing a type 2 failure). The parameters for the continuous-time Markov chain are:______
There is was an article in a travel magazine that posed the question..."Why are flights so much cheaper in Europe than in the United States?" The article reported that transatlantic round-trip flights originating in the United States can be more expensive than the same flights originating in Europe. The data on several flights was gathered for 3 airline companies. What is the Average Price of a ticket originating in Chicago using United Airlines? Round your answer to two decimal places. NOTE: This data corresponds with worksheet tab, Q33, in the Exam 2 Excel file in Canvas. You will use this for questions Q33-39. United Air France British Chicago 1063 1314 1442 1299 1493 1413 995 1443 1063 1299 1577 1442 1406 1314 1575 London 1015 1374 1603 856 977 1531 802 1043 1079 850 1070 807 935 1428 870
Answer:
The average price of a ticket originating in Chicago using United Airlines is $1212.40.
Step-by-step explanation:
The data provided is as follows:
United Air France British
Chicago 1063 1314 1442
1299 1493 1413
995 1443 1063
1299 1577 1442
1406 1314 1575
London 1015 1374 1603
856 977 1531
802 1043 1079
850 1070 807
935 1428 870
The data for the price of a ticket originating in Chicago using United Airlines is:
Chicago = {1063, 1299, 995, 1299, 1406}
Compute the average price as follows:
[tex]\bar X=\frac{1}{n}\sum X[/tex]
[tex]=\frac{1}{5}\times [1063+1299+995+1299+1406]\\\\=\frac{6062}{5}\\\\=1212.40[/tex]
Thus, the average price of a ticket originating in Chicago using United Airlines is $1212.40.
Which equation is an identity? O 3(x - 1) = x + 2(x + 1) + 1 O x-4(x + 1) = -3(x + 1) +1 O 2x + 3 = 1 = 1 (4x + 2) + 2 01 1 (6x – 3) = 3(x + 1) - x-2
HURRY!!!!
Answer:
Step-by-step explanation: C. 2x+3=1/2(4x+2)+2 hopes this helps:)
The equations that are identities are option B x – 4(x + 1) = –3(x + 1) + 1 and option C 2x + 3 = 1/2(4x + 2) + 2.
To check which equation is an identity, we need to simplify each equation and see if it is true for all values of x.
A. 3(x – 1) = x + 2(x + 1) + 1
Expanding the right side:
3(x – 1) = x + 2x + 2 + 1
3x – 3 = 3x + 3-3 = 3
This is a contradiction and cannot be true for any value of x. Therefore, option A is not an identity.
B. x – 4(x + 1) = –3(x + 1) + 1
Expanding both sides:
x – 4x – 4 = –3x – 3 + 1
-3x – 3 = -3x – 3
This equation simplifies to -3x - 3 = -3x - 3, which is true for all values of x. Therefore, option B is an identity.
Similarly,
Option C is an identity.
Option D is not an identity.
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The graph shows a function that models the value V (in millions of dollars) of a stock portfolio as a function of time t (in months) over a 18-month period.
Answer:
Option (A)
Step-by-step explanation:
Graph attached shows a function that models the value V of a stock portfolio as a function of time.
y-values on the graph shows the value of V and x-values represent the time.
Lowest point of the curve shows the minimum value of V and highest point of the curve shows the maximum value.
Maximum value of the function → 6.93 at t = 4
Minimum value of the function → 1.05 at t = 15
Therefore, Option (A) will be the answer.
v/3=1 Please help what is V
Answer:
3
Step-by-step explanation:
v=1*3
Answer:
3
Step-by-step explanation:
Multiply each side by 3 and you get 3
v=1*3=3
v=3
If a standard die is rolled twice, what is the probability that it lands on a
number greater than 4 both times?