Someone help me solve all this + include working out.
Will mark as brainliest. Thanks
Answers
Answer:
We know that P(x) = 30*x^3 + k*x^2 + 1
a) If (3x - 1) is a factor, let's find the value of k.
Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.
Then:
30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)
30*x^3 + k*x^2 + 1 = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c
30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c
The terms with the same exponent should be equal, then:
30*x^3 = 3*a*x^3
30 = 3*a
30/3 = a = 10
k*x^2 = (3*b - a)*x^2
k = (3*b - 10)
0*x = (3*c - b)*x
0 = (3*c - b)
b = 3*c
and
1 = -c
then:
c = -1
Replacing this in the equation: b = 3*c
we get: b = -3
Replacing this in the equation for k, we get:
k = (3*b - 10) = (3*-3 - 10) = -19
k = -19
And we can write:
P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)
b) Now we want to write P(x) as a product of its linear factors.
Then we need to factorize the quadratic part:
We need to solve
10*x^2 - 3*x - 1 = 0
We can use the Bhaskara's equation to get the solutions:
[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]
Then the two zeros of that polynomial are
x = (3 + 7)/10 = 1
x = (3 - 7)/10 = - 4/10 = -2/5
So we can write the polynomial as:
10*(x - 1)*(x - (-2/5))
Replacing this in the equation of P(x) we get:
P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)
= 10* (3*x - 1)*(x -1)*(x + 2/5)
So P(x) is written as a product of lineal factors.
C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.
For the first factor, we have a zero at x = 1/3
for the second, we have a zero at x = 1
for the third one, we have a zero at x = -2/5
Related Questions
what is 1 x 5?
also what is 200 plus 200
Answers
Answer:
1 x 5 = 5
and
200 + 200 = 400
(Hope this helps! Btw, I answered first. Brainliest please! :D)
Please help me in this. ASAP!
Answers
Answer:
Thermal energy -- sand on beach feels warm to touch
Gravitational potential energy -- a piece of fruit hanging from a tree
Electric energy -- Lightning produced during a storm
Kinetic energy -- A box moving along a conveyer belt
Radiant energy -- Radio waves transmitted from a tower
Step-by-step explanation:
PLZ mark me as brainliest
A triangle has vertices at (-2, 1), (1, 1), and (1, -3). Find its area and round to the nearest whole number if necessary.do not include units in your answer
PLEASE HELP ME
Answers
Answer:
6Step-by-step explanation:
Plot the points and connect in pairs.
We got a right triangle.
The legs have the length:
1 - (-2) = 3 units and1 - (-3) = 4 unitsThe area of the triangle is:
A = 1/2bh A = 1/2*3*4 = 6 square unitThe seagull population on a small island in the Atlantic Ocean can be calculated using the formula
P(t) = 5.3/11/?, where P is the population in hundred thousands, and t is in years. What will the seagull
population on the island be after 5 years? (Round to the nearest tenth.)
a. about 41.6 hundred thousand
c. about 172.4 hundred thousand
about 3.7 x 10' hundred thousand d. about 66.5 hundred thousand
Answers
The correct relation for the sea gull population is: P(t) = 5.3t^(11/7)
Answer:
d. about 66.5 hundred thousand
Step-by-step explanation:
Given that :
P(t) = 5.3t^(11/7)
Population, P is in hujdred thousand ; t = number of years
Population after 5 years ;
t = 5
P(5) = 5.3 * 5^(11/7)
P(5) = 5.3 * 5^1.5714285
P(5) = 5.3 * 12.542422
P(5) = 66.474840
P(5) = 66.5 (approximately)
Hence, population after 5 years will be about 66.5 hundred thousand.
if someone did a summary of a horror movie then i will give brainliest and 1818 pionts pls brainlies
Answers
Answer:
My summary is on Happy Death Day
Basically there is this girl, she got murdered in the night but before being murdered she spent the entire day being mean and making choices she would later on regret, but when she dies she wakes up again in her room and the same exact things that happened the day the died happened, it was exactly the same. This happened over and over again and she kept dying no matter what she did, it was like a time loop that restarted whenever she was murdered. She had to solve it by killing the one who murdered her or stopping it somehow, she tried everything to avoid being killed. She even got herself sent to jail but still died there, she made a list and tried figuring out who the murderer was. She spent one day being nice to everyone, thinking she had figured out how to stop the murderer because she wanted her day to be great because she thought she wouldnt be killed that night as she thought she knew how to survive. She ate the cupcake her roommate offered her and wasnt murdered that night (the other days she ignored her roommate) Before she went to sleep she said a quote when she was making her Birthday wish (she died on her birthday, hence the name happy death day) "What do you wish for?" "Tomorrow."
"Just...Tomorrow?" "Yeah." She then woke up again in the time loop, and the day repeated. She was confused to why this happened when at the end of the day her roommate offered her the cupcake. She realized the cupcake had poison in it and killed her roommate. But she died again, still in the time loop. She was so confused, all she knew was that her killer wore a mask. Then, after research she figured out it was a mentally ill patient who was killing her. Her best friend (boy friend/guy friend) then sacrificed himself for her taking the hit so she could live, she finally was able to escape the killer. But she realized, if she broke out of the time loop, it would continue so that her guy friend/boy friend was dead. The one who sacrificed himself for her, so she (I don't want this answer to get taken down for describing what she did, but let's say she died on purpose) And woke up again in the time loop. This time she rushed to kill the patient who had been killing her every night in the time loop, and the time loop was broken. That's the summary.
Answer:
will a summary of sinister do?
Summary of "Sinister'
so basically it all starts out with a family downsizing their house because of the dad's job. So they move into the house and they find a weird box in the attic, with a few old tapes and a projector, so the dad starts watching the tapes. (on the tapes their are murders of like 5 other families but he doesnt know that.) so then creepy stuff starts happening like first the attic where they found the creepy box keeps opening by itself. then the little girl starts drawing pictures of murders and her with mr.boogie, and the boy keeps waking up with bruises and injuries, and at the end the girl kills the whole family.
What is the Mode? 21,28.27.26.27.27.33.28.26.31
Answers
Answer:
The mode is 27.
Step-by-step explanation:
To find the mode we must first put them in order from least to greatest.
21, 26, 26, 27, 27, 27, 28, 28, 31, 33
The mode means the most common number out of the data. Therefore since 27 is the most common number, it is the mode.
Hey there!
The mode is basically the number you see MORE THAN ONCE.
So, the numbers in your data plot is/are
“21, 28, 27, 26, 27, 27, 33, 28, 26, 31”
(I’m assuming)
21 is shown ONE TIME
28 is shown TWO TIMES
27 is shown THREE TIMES
26 is shown TWO TIMES
33 is shown ONE TIME
31 is shown ONE TIME
THE BIGGEST ONE THAT’S SHOWN IS: 27 because it was shown in your data plot three times
Answer: 27
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
suppose I have a 30, 60, 90 right triangle. The hypotenuse is 10 units long. How long are the other sides?
a) short leg = 5; long leg = 5 √2
b) short and long leg = 5 √2
c) short leg = 5; long leg = 5 √3
d) short leg = 5; long leg =8
Answers
Answer:
option c
Step-by-step explanation:
The angles are 30° , 60° , 90° . So its a right angled triangle . We can use trigo.
⇒ sin 30 = p/h
⇒ 1/2 = p/10
⇒ p = 10/2
⇒ p = 5
Using Cosine now ,
⇒ cos 30° = b/h
⇒ √3/2 = b/10
⇒ b = √3/2 × 10
⇒ b = 5√3
Short leg = 5Long leg = 5√3 Hence option C is correct.Answer:
c) short leg = 5; long leg = 5 √3
Step-by-step explanation:
How long are the other sides?
short leg = 5; long leg = 5 √3
How do you leave an answer in terms of pi?
Answers
In terms of pi means to include pi in your answer. In other words, don't use 3.14 or 22/7 for pi.
3/10 divied by 2/7 pls help
Answers
Answer:
21/20
Step-by-step explanation:
Answer:
1.05 or 21/20 or 105% or
Step-by-step explanation:
a car travels the first 15 km of the journey at an average speed 60km/h and the remaining 40 km at an average speed of 30 km/h find the average speed of the whole journey
Answers
Answer:
the average speed of the whole journey is 45 km/h
Step-by-step explanation:
The computation of the average speed of the whole journey is shown below:
Average speed is
= (Speed 1 + speed 2) ÷ 2
= (60 km/h + 30 km/h) ÷ 2
= 90 km/h ÷ 2
= 45 km/h
Hence, the average speed of the whole journey is 45 km/h
We simply ignored the distance as it is not relevant for the given situation
The same would be considered
HELP!!! ANYONE!! ASAP!!!
Answers
Answer:
A
Step-by-step explanation:
I'm not going to give an explanation but for next time, the stem is the tens place and the leaf is the ones place.
Find the missing side lengths. Can someone help me please
Answers
Guys help don't have enough time left. This can really effect everything if this is correct so try your best.
Answers
Answer: 180
Step-by-step explanation:
Answer: 180ft^3
Step-by-step explanation:
1 - (-3) 2+ (-3) - 5
Answers
Answer:
1 - (-3) X 2 + (-3) - 5 = ?
To find your answer, first group the same number if there are any. In this situation, there are two -3.
You can take your calculator if you have one and input your information.
In the end, you should get -1 as your final answer.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
What is the mean? If the answer is a decimal, round it to the nearest tenth.
-4 ,4 ,6 ,-7 ,7, 10, 7,9
Answers
Answer:
The mean is 4 if im correct.
Answer:
4
Step-by-step explanation:
-4+4+6+-7+7+10+7+9=32
32/8=4
URGENT!!!! BRAINLIEST FOR CORRECT ANSWER!
At the Little Rock Zoo, the cost for one children's ticket is $10 and the cost for one adult's ticket is $13. On Saturday, the zoo had a total of 1,465 people visit the zoo and took in a total of $16,603. How many CHILDREN visited the zoo? (Number Only)
Answers
Answer:
1663
Step-by-step explanation:
Brad swims 4 laps every 6min how long does it take him to swim 14 laps?
Answers
Answer:
21 minutes
Step-by-step explanation:
4 goes into 14 three times which is 18 minutes. We need 2 more laps four for 6 can be 2 for 3.
Solve for the number problem 11
Answers
Answer:
1,000
Step-by-step explanation:
10x10x10 = 1,000
this lock has 1,000 possible combinations
A grocery store sells an 8 ounce bottle of juice for $1.76 what is the cost of the juice per ounce? Show your work
Answers
Answer:
22 cents
Step-by-step explanation:
8 ounces coat $1.76
So,
1 ounce costs $1.76 divided by 8 = $ 0.22 = 22cents
Hope this helps
If a grocery store sells an 8 ounce bottle of juice for $1.76. The cost of the juice per ounce is: $0.22.
Cost of juice per ounceUsing this formula
Cost of juice per ounce=Cost of juice/Ounce bottle of juice
Where:
Cost of juice=$1.76
Ounce bottle of juice=8 ounce
Let plug in the formula
Cost of juice per ounce=$1.76/8
Cost of juice per ounce=$0.22 per ounce
Inconclusion the cost of the juice per ounce is: $0.22.
Learn more about Cost of juice per ounce here:https://brainly.com/question/1564020
6(x+4)+1= What is the answer to this great math problem
Answers
Answer:
6x+25
Step-by-step explanation:
Answer:
The simplified equation is 6x+25
Step-by-step explanation:
First, you open parentheses or in other words, use distributive property: 6*x+6*4+1. If you simplify that, you get 6x+24+1 which is basically 6x+25. So 6x+25 is your final answer.
What are the coordinates of the point (-1, 5) when it is reflected across the y-axis? *
Answers
Answer:
1,5
Step-by-step explanation:
when reflecting across y-axis it'll be in the same order, but using whatever form that quarter of the coordinate plane is in (e.g. 5,7 ----> -5,7)
Lisa tossed two fair coins at the same time. She repeated this trial 180 times. How many trials should Lisa expect to result in both coins showing tails?
Answers
Answer:
47
Step-by-step explanation:
4-3=7 7x3= 54 54-13= 47
What is the factored form of the expression x^2 - 16?
Answers
Answer:
(x + 4)(x - 4)
Step-by-step explanation:
Answer:
( − 4 ) ( + 4 )
Step-by-step explanation:
x^2 - 16
x^2 + 4x - 4x = 16
x^2 + 4x - 4x - 16
( + 4 ) − 4 ( + 4 )
( − 4 ) ( + 4 )
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
Find the scale factor that was used
Answers
30/15 = 2
20/10 = 2
15/10=1.5
30/20=1.5
Marina picked X apples in Orchard she and her friends 86 then leaving 36 Apples The number of apples can be represented by the equation X -6 equals 36 plot a point on the number line to represent X
Answers
Answer:
[tex]x = 42[/tex]
See attachment for number line (see that the dot is on 42)
Step-by-step explanation:
Given
[tex]x - 6 = 36[/tex]
Required
Plot x on a number line
First, we solve for x
[tex]x - 6 = 36[/tex]
Add 6 to both sides
[tex]x - 6 +6= 36+6[/tex]
[tex]x = 42[/tex]
See attachment for number line
Distributive property and Combine like terms
Answers
Answer:
k = 55
Step-by-step explanation:
First clear the fraction by multiplying all three terms by 5. We get:
k - 10 = 45
Adding 10 to both sides results in
k = 55 (after having combined like terms)
Write 10^-7 as a fraction
Answers
Answer:
-10000000/1 or 10^-7/1
Step-by-step explanation:
You can divide anything by 1 to make a fraction.
Have a nice day!
At sunrise the temperature was -12 C. By sunset the temperature had increased 5 degrees. What is the temperature at sunset? *At sunset the temperature was 19 C. By sunrise the temperature had decreased 4 degrees. What is the temperature at sunrise?
Answers
Answer:
-17°C at sunset
15°C at sunrise
work out 4/11 + 2/5, Give your answer in its simplest form
Answers
Answer:
42/55
Step-by-step explanation:
4/11+2/5 LCD=55
20/55+22/55
42/55
The graph represents the length and
I height of a wheelchair ramp. Find the
slope of the ramp.
Answers
Answer: 1/4
Step-by-step explanation: Take point (1,1) put the rise (2) over the run (8) and then simplify.