Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
A lottery has a grand prize of 25and 1/2 million dollars. There are 5 people who have winning tickets and they share this prize equally. How many millions of dollars does each person get? Express the answer as a mixed number.
Answer:
5 1/10 million dollars
Step-by-step explanation:
25and 1/2 million dollars = 25 1/2 million dollars
= (25*2) + 1 / 2
= 50+1/2
= 51/2
Total prize = 51/2 million dollars
Number of people with winning ticket = 5
How many millions of dollars does each person get?
Amount of prize each person get = Total prize / Number of people with winning ticket
= 51 / 2 ÷ 5
= 51/2 × 1/5
= (51 * 1) / (2 * 5)
= 51/10
= 5 1/10 million dollars
Amount of prize each person get = 5 1/10 million dollars
How do you fix a uneven face in a month?
Tips
Answer:
I know this may not help but
Step-by-step explanation:
Fillers. Inserting a “soft filler” into your face by way of an injection may correct the appearance of facial asymmetry. ...
Facial implants
Rhinoplasty
these are the top ideas I have searcehd online although it may not look good in a month if your going with Rhinoplasty
all perfect numbers from 20 to 30
Answer:
There is only one perfect number between 20 to 30 which is 28.
Explanation:The number 28 is a perfect number because its factors are 1, 2, 4, 7, 14 and 28.
In how many ways can alice give 12 apples to 3 children if each child must get at least 1 apple
There are 91 ways in which Alice can give 12 apples to 3 children, with each child receiving at least 1 apple using a combination formula.
The question can be solved using a method called "stars and bars".
Now, we need to find the number of ways to arrange 12 stars and 3 bars. The number of ways to arrange 12 stars and 3 bars in the given formula:
Number of ways = (n + k - 1) choose (k - 1)
Where n is the total number of objects = 12
k is the number of groups = 3
Number of ways = (12 + 3 - 1) choose (3 - 1)
Number of ways = 14 choose 2
The combination formula can be used as:
Number of ways = {14!}{(2! [tex]\times[/tex] (14 - 2)!)}
Number of ways = 14! / (2! * 12!)
Number of ways = (14 * 13) / 2
Number of ways = 91
So, there are 91 ways in which Alice can give 12 apples to 3 children, with each child receiving at least 1 apple.
Learn more about combinations here:
https://brainly.com/question/20211959
#SPJ4
John leaves his house at Sam. It
takes 35 minutes to walk to
school. He then has 2 hours and 2
minutes of lessons. Break time is
15 minutes long, What time does
break finish?
Answer:
7:52am
Step-by-step explanation:
John leaves by 5:00am
He gets to school after 35 minutes
The time now is 5:00 + 0:35 = 5:35am
After 2 hours and 2 mins of lectures, the time is 5:35 + 2:02 = 7:37am
After 15 minutes, the time is 7:37 + 0:15 = 7:52am
Therefore the answer is 7:52am.
Find the volume of this square based pyramid. 5 cm 5 cm 5 cm. Round to the nearest tenth.
V=?cm3
Answer:
41.666 cm³ or 41.7 cm³ rounded to the nearest tenth.
Step-by-step explanation:
Volume of a square pyramid = base length² × height ÷ 3
25 × 5/3 = 41. 666
Have a great day:)
Answer:
41.7
Step-by-step explanation:
It says to ROUND which will get you 41.7
A triangle has asides of 7cm, 24cm, and 25cm. how can you tell whether it is the right triangle?.
( If you can answer this I will take you on my brain list)
Answer:
because it has 7 cm a helper of right angle triangle and me can also use phythogorreas triplet formula
Can someone help me with these 2 answers
Answer:
2. Side length =9
Step-by-step explanation:
A square has all sides equal. and it has 4 sides, so 36 divided by 4 =9.
3.x squared =6
answer is x=3
square root both sides.
Find the length of side x in simplest radical form with a rational denominator.
45
4
45
x
Answer: =
Submit Answer
✓
attempt 1 out of 2
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Could I get some help with this
Answer:
x=2*sqrt(2)
Step-by-step explanation:
cos(theta)=Base/Hypotenuse
cos(45)=x/4
x=2*sqrt(2)
What is the factored form of
Answer:
C
Step-by-step explanation:
You can distribute the values or even plug in x=2 and see which one matches.
Which expression is a sum of cubes
Answer: what is the rest of the question?
Step-by-step explanation:
The following figures are parallelogram. find X and y
==============================================================
Explanation:
For any parallelogram, the diagonals always cut each other in half.
This means the pieces that are y+5 and 18 cm long are equal
y+5 = 18
y = 18-5
y = 13
And so are the pieces that are x+y and 16 cm long
x+y = 16
x+13 = 16
x = 16-13
x = 3
Side note: the term "bisecting" is often used when saying "cutting in half".
Kylee manages a small theme park and she has been analyzing the attendance data. Kylee finds that the number of visitors exponentially as the tempature increases, and this situation is represented by the function f(x) = 4 ^ x Kylee also finds a linear equation that no deals the number of people who leave the park early depending on the change in temperature , and it is represented by f(x) = - x + 5. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
Answer:
(1 , 4)
Step-by-step explanation:
f(x) = 4^x ,where x is the temperature, and y or f(x) is the number of visitors that come to the park
f(x) = -x +5 , where x is the temperature and, y or f(x) is the number of visitors that leave early
the solution of the system of equations is the point of intersection of the 2 graphs and is (1,4)
when the temperature is 1 will have 4 visitors who will come at the park and also leave early
4 over 5 in standard form
Answer:0.8
Step-by-step explanation:
it is basically 10 times 8 to the power of -1
need help solving the equation, trying to figure whether I multiply or divide.
Answer:
m∠B = 43°
b = 26.1
c = 38.3
Step-by-step explanation:
By applying triangle sum in the given triangle,
47° + 90° + m∠B = 180°
137° + m∠B = 180°
m∠B = 43°
By applying sine ratio to the angle measuring 47°.
sin(47°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{28}{c}[/tex]
c = [tex]\frac{28}{\text{sin}(47^{\circ})}[/tex]
c = 38.28
c ≈ 38.3
By applying cosine rule,
cos(47°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{b}{c}[/tex]
= [tex]\frac{b}{38.3}[/tex]
b = 38.3[cos(47°)]
b = 26.1
Find AC , given that line AD is the perpendicular bisector of BC
Answer:
AC = 29
Step-by-step explanation:
We'll begin by calculating AD. This can be obtained as follow:
AB = 29
BD = 17
AD =?
AB² = BD² + AD²
29² = 17² + AD²
841 = 289 + AD²
Collect like terms
841 – 289 = AD²
552 = AD²
Take the square root of both side
AD = √552
Finally, we shall determine AC. This can be obtained as follow:
DC = BD = 17
AD = √552
AC =.?
AC² = DC² + AD²
AC² = 17² + (√552)²
AC² = 289 + 552
AC² = 841
Take the square root of both side
AC = √841
AC = 29
Read the poem "The Snake" by Emily Dickinson.
A narrow fellow in the grass
Occasionally rides;
You may have met him, — did you not,
His notice sudden is.
The grass divides as with a comb,
A spotted shaft is seen;
And then it closes at your feet
And opens further on.
He likes a boggy acre,
A floor too cool for corn.
Yet when a child, and barefoot,
I more than once, at morn,
Have passed, I thought, a whip-lash
Unbraiding in the sun, —
When, stooping to secure it,
It wrinkled, and was gone.
Several of nature's people
I know, and they know me;
I feel for them a transport
Of cordiality;
But never met this fellow,
Attended or alone,
Without a tighter breathing,
And zero at the bone.
Which statement best describes Dickinson’s use of figurative language in the final stanza?
She uses comparisons to show the speaker’s connection to the snake .
She uses a simile to show that snakes are harmless creatures .
She uses a metaphor to describe the movement of the snake.
She uses exaggeration to emphasize the speaker’s fear of snakes.
Answer:
I think it is the last answer: She uses exaggeration to emphasize the speakers fear of snake.
Have a Wonderful Day ;) ;D
Answer:
The answer is D! I took the topic test review!
Step-by-step explanation:
D- She uses exaggeration to emphasize the speaker’s fear of snakes.
The radius of the circle below intersects the unit circle at (3/5 • 4/5)What is the approximate value of e?
Answer:
do you have a pic of it but i think its 15.75
Step-by-step explanation:
What are the restrictions on the domain of the following function?
f(x)=x-3/(x-3)(x-4)(x-5)
Answer:
Step-by-step explanation:
C
Question 2 Multiple Choice Worth 1 points)
(02.05 MC)
Graph g(x), where f(x) = 4x - 2 and g(x) = f(x + 1).
Answer:
Solution: means we replace 'x' with 'x+1' and we get g (x). Let us put x = 0 and then y = 0 to find two points on coordinate axis to easily plot the graph of g (x). Now, let us put y = 0 and find out x. So, second point is . Now, let us plot A and B then extend the line joining AB.
Identify the segments that are parallel, if any, if ∠DCB and ∠CDA are supplementary.
Answer:
C
Step-by-step explanation:
We are given that
[tex]\angle[/tex]DCB and [tex]\angle[/tex]CDA are supplementary.
We have to identify the parallel segments if [tex]\angle[/tex]DCB and [tex]\angle[/tex]CDA are supplementary.
Supplementary angles: If the angles are supplementary then the sum of two angles is 180 degrees.
Therefore,
[tex]\angle DCB+\angle CDA=180^{\circ}[/tex]
Therefore, angle DCB and angle CDA are interior angles .
Because CA is a transversal line and sum of interior angles is 180 degrees.
When the sum of interior angles formed between two lines and on same side of transversal line is 180 degrees. Then the lines are parallel.
Therefore, angle DCB and angle CDA are formed between line AD and BC.
Hence, AD is parallel to BC.
Option C is correct.
Answer:
c
Step-by-step explanation:
i had the same question
Mr Rai sale a watch for Rs 2035 a profit of 10% how much money has he paid to buy the also find his profit amount
Answer:
He paid Rs 1,850 to buy the watch
Profit = Rs 185
Step-by-step explanation:
Cost price = x
Profit = 10% of x
Selling price = Rs 2035
Profit = Selling price - cost price
10% of x = 2035 - x
0.1x = 2035 - x
0.1x + x = 2035
1.1x = 2035
x = 2035 / 1.1
x = 1,850
Cost price = x = Rs 1,850
Profit = 10% of x
= 10% of 1,850
= 0.1 × 1850
= 185
Profit = Rs 185
Which value is equivalent to x +4/4+x?
–4
–1
1
4
For the function f(x) = -4^-x + 5, if x→∞, then y → ____.
y approaches 5.
As x approaches infinity, -4^(-x) approaches 0.
0 + 5 = 5
Hi! Please help me im really confused >.< tysm
g² - 4g = -3
Answer:
g = 1, 3
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
g² - 4g = -3
Step 2: Solve for g
[Addition Property of Equality] Add 3 on both sides: g² - 4g + 3 = 0Factor: (g - 1)(g - 3) = 0Solve: g = 1, 3How do I do this question
Answer:
Graph:
Solution: (1, 1)
Check:
y = -3x +4
1 = -3 +4
1 = 1
y = 3x -2
1 = 3 -2
1 = 1
Maria's luggage travels 36 m in 3 minutes. What is the speed of the conveyer belt in kilometers per hour?
Answer:
0.72 km per hour
Step-by-step explanation:
First, find the speed in meters per hour. Create a proportion where x is this speed:
[tex]\frac{36}{3}[/tex] = [tex]\frac{x}{60}[/tex]
3x = 2160
x = 720
So, the speed is 720 meters per hour. Convert this to kilometers per hour by dividing 720 by 1000, since there are 1000 meters in a kilometer:
720/1000
= 0.72
So, the speed of the conveyer belt is 0.72 km per hour
What is the truth value for the following conditional statement?
p: true
q: true
~q —> ~p
Find the image of -2 under the function f(x) =2x-1
Answer:
- 5
Step-by-step explanation:
Substitute x = - 2 into f(x)
f(- 2) = 2(- 2) - 1 = - 4 - 1 = - 5
Whoever gives answer gets brainliest asap
Answer:
m=y2-y1/x2-x1 ⇒ m=-48+64/-15+21
m=16/6=8/3
y-y1/x-x1= m⇒ 8/3=y+64/x+21
8x+168=3y+192
3y=8x-24
x-intercept
3(0)=8x-24
x=24/8 →x=3
x-intercept: (3,0)
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