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
Jake is building a fence around his property. He wants the perimeter to be no more than 100 feet. He also wants the length to be at
least 10 feet longer than the width. If he builds his fence according to these limits, which would be the maximum possible width of
the fence?
Answers
Answer:
C
Step-by-step explanation:
Let the length be l and width be w.
The perimeter will be 2 lengths + 2 widths = 2l+2w
2l+2w cannot be more than 100ft
[tex]21+2w \leq 100[/tex]
Also, the length has to be at least 10ft longer than the width.
[tex]l\geq w+10[/tex]
If we substitute w=20, l=30. 2l+2w can be equal to 100 but not over it.
If w=20 and l=30, 2w+2l = 40+60 = 100.
Hence the maximum length of the width of the fence is 20 ft. C
what is the slope of the graph??? (hint: it’s either 4 or 0) or if u get another answer pls tell me.
Answers
Answer:
The slope is 4
Step-by-step explanation:
rise is 4, run is 1
4/1=4
An ice machine uses 3 gallons of water every 9 hours How many gallons of water does it use each hour? How many hours does it
take to use one gallon?
A)gallon per hour, 1 hour
B)gallon per hour; 3 hours
C)3 gallons per hour, 1/9 hour
D) 1/3 gallon per hour
1/3 hour
Answers
Answer:
1/3 gallon per hour, and it takes 3 hours to use one gallon
Step-by-step explanation:
Simplify the ratio
3-9
Which simplifies to
1-3
———————————————
SOMEBODY HELP PLSS I DONT GET IT
Answers
23+25+27+29+31
PLSSS HELP (What are the square roots of 121?)
Answers
Answer:
11
Step-by-step explanation:
Answer: The square root of 121 is 11!
Step-by-step explanation:
11x11= 121
Another example:
9x9=81
So, 9 is the square root of 81
Another example:
8x8=64
so, 8 is the square root of 64!
what is 34 divided by 5
Answers
Answer:
6.8
Step-by-step explanation:
The solution is : 6.8 is the decimal when 34 divided by 5.
Here, we have,
given that,
34 divided by 5
Given the following mathematical expression;
34 / 5
We would apply the law of division for fractions.
34 / 5
= 34 ÷ 5
= 6.8
the decimal form.
Hence, The solution is : 6.8 is the decimal when 34 divided by 5.
To learn more on division click:
brainly.com/question/21416852
#SPJ6
You ask learners to select their course section number for your survey. For example, (1) 101, (2) 102, (3) 103. What type of variable is course section in this example?
Answers
Answer:
The variable is a nominal categorical variable
Step-by-step explanation:
As the 3 options are available and the survey taker is required to select from these options, this indicates that the variable is of categorical nature, where only a fixed number of options are available. As the order is not important thus the variable is a nominal categorical variable.
What is the perimeter of this
Answers
26ft+17ft+25ft
=68ft
The perimeter is 68 ft
Answer:sorry I don’t know
Step-by-step explanation:
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answers
hhh
Step-by-step explanation:
Find the area of the composite figure
Answers
Answer:
The answer is 180ft
Step-by-step explanation:
The reason the answer is 180ft is because your using area which means your are multiplying all your answers.
Hi!pls can u help me factorise this
Answers
50d^2 - 98e^2
Factor out 2.
2(25d^2 - 49e^2)
We now factor the difference of two perfect squares within the parentheses.
2(5d - 7e)(5d + 7e)
This is as far as we can factor.
Done!
The factor of the expression into an equivalent form 50d²- 98e² would be; 2(5d - 7e)(5d + 7e)
What is factorization?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
We are given that expression is given that 50d²- 98e².
We have to Factorise .
Factor out 2.
2(25d² - 49e²)
We have to factor the difference of two perfect squares within the parentheses.
2(5d - 7e)(5d + 7e)
Learn more about factorization here:
https://brainly.com/question/10454590
#SPJ2
what is the answer to this?
Answers
Answer:
5 inches
Step-by-step explanation:
Since the length irl is 60 yards you should divide 60 by 3.
60/3=20
Then convert 1/4 to a decimal.
1/4=0.25
Finally multiply 20 and 0.25 to get the length of the park on the map.
20x0.25=5
your answer is Option F 5 inches
A right triangle is displayed.
The area of the right triangle is
A. 24 in ^2
B. 48 in ^2
C. 432 in ^2
D. 864 in ^2
Answers
Answer:
You have to use the Pythagorean Theorem to find the other side, which will be your base in the Area formula (A=1/2bh). So the Pythagorean theorem would be 36^2 + b^2 = 60^2. This gives you 48 in for your base/missing side length. Then, you plug it into the area formula. So, A=1/2(48) (36). This gives you 864 in^2 for the area of your triangle.
Monica goes to a stationery shop to buy pens and pencils. She has $35 in pocket change, and she's looking to buy pens for $7 each and pencils for $2 each.
Write an inequality to describe the possible number of pens and pencils that Monica can buy. If Monica buys 3 pens, what is the maximum number of pencils she
can buy?
Answers
Answer:
7 pencils
Step-by-step explanation:
Let x equal the number of pencils Monica buys and y equal the number of pens.
The expression would then be 2x + 7y ≤ 35. Plugging in 3 for y:
2x + 7(3) ≤35
2x +21 ≤ 35
2x ≤ 14
x≤ 7
I Need help fast please answer
Answers
Answer:
Top choice, A.
Step-by-step explanation:
Count the dots
Answer:
its choice A
Step-by-step explanation:
please help giving brainliest!
Answers
Answer:
0.20
Step-by-step explanation:
total of marbles
= 6 + 4 + 3 + 2
= 15
the probability of blue
= 3/15 × 100%
= 20%
= 0.20
What is the mean of the data set?
{21, 23, 25, 25, 26, 28, 28, 28, 31, 33}
A.26.8
B.27
C.27.8
D.28
Answers
Answer:
A. 26.8
Step-by-step explanation:
268/10
Solve for angle x please help fast
Answers
Answer:
X=18
Step-by-step explanation:
you can find what the missing angle is by subtracting 92 from 180 since its a straight line. After putting in the missing angle you can easily solve for 2X which is 36 and then divide by 2 and get 18.
Answer:
x = 23
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
92° is an exterior angle of the triangle, then
2x + 46 = 92 ( subtract 46 from both sides )
2x = 46 ( divide both sides by 2 )
x = 23
Which representation shows a translation three units to the left and one unit up?
(x + 3, y + 1)
B.
(x - 3, y + 1)
C.
(x + 3, y - 1)
D.
(x - 3, y - 1)
Answers
Answer:
B. (x-3,y+1)
Step-by-step explanation:
because they are integars
brainlyyest pls
Write a unit rate that compares 48 kids to 6 teams.
(Answer in the form of a:b)
Answers
a : b = 8 : 1
Answer:
kids : teams
a : b
48 : 6
( 48 : 6 ) ÷6
8 : 1
Write the equation of the line in slope- intercept form
Answers
Answer:
y=8x+1
Step-by-step explanation:
y=mx+b
m=rise/run=(8)/(1)=8
y=8x+b
b is the y-intercept
y=8x+1
please answer fast however answer i will make brainilest
Answers
y=x+1
aka
B
explanation:
ok
use distributive property to rewrite 8(x+3)
Answers
Answer:
8x + 24
Step-by-step explanation:
1. 8(x + 3) - Distribute
2. 8x + 24 - Answer
What is the area of the figure below? Please help me urgent 30 points!!!
Answers
Answer:
75
Step-by-step explanation:
[tex]5 \times 10 = 50[/tex]
[tex]5 \times 10 \div 2 = 25[/tex]
[tex]50 + 25 = 75[/tex]
A diagonal of a square is 20cm long. How long is each side
Answers
Answer:
Diagonal of square = 20 cm. = 200 cm². Side = 10√2 cm
Step-by-step explanation:
Answer:3
Step-by-step explanation:divide
How much sales tax would you pay for a $55 pair of roller blades if the tax rate is 6.625%?
Answers
55 x 0.06625 = 3.64
Answer:
≈ 3.64 sales tax
Step-by-step explanation:
55 × 0.06625 = 3.64375
Please help me. I will marks as Brainly if correct
Answers
an angle inscribed in the same os equal arc are equal?
Answers
Answer:
yes
Step-by-step explanation:
Find the surface area of the cone. Round your answer to the nearest tenth..
Answers
Answer:
S.A. = 15.7
Step-by-step explanation:
S. A. = [tex]\pi r^{2} + \pi rl[/tex]
1 x 1 x 3.14 = 3.14
3.14 x 1 x 4 = 12.56
12.56 + 3.14 = 15.7
A scientist keeps track of bacteria cells. She starts with 1 cell. After one hour, there are 2 cells. The number of cells continues to double in each of the following hours
Answers
Answer:
the number of cells increases by a factor of 2.
Explanation:
the number of cells doubles with each hour, which means that they are multiplied by 2. thus, the number of cells increases by a factor of 2.
i hope this helps! :D
Answer: The number of cells increases by a factor of 2.
After four hours, the number 2 is used as a factor 4 times.
Step-by-step explanation: The cells multiply by 2, and make double the amount of cells.
The number 2 is used 4 times after 4 hours to make 16 cells.