Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
Answers
The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
And the accurate root is 3 it can be determined by using rules of the rational root equation.
Given that,Function; [tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
We have to determine,Which of the values shown are potential roots of the given equation?
According to the question,Potential roots of the polynomial are all possible roots of f(x).
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
[tex]\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}[/tex]
[tex]\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}[/tex]
The factor of the term 45 are,
[tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45[/tex]
And The factor of 3 are,
[tex]\pm1, \ \pm3[/tex]
All the possible roots are,
[tex]\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
Now check for all the rational roots which are possible for the given function,
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0[/tex]
Therefore, x = 3 is the potential root of the given function.
Hence, The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex].
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Answer: ALL OF THEM
Step-by-step explanation:
Related Questions
Solve for x the equation 6cos^2 x+4sin^2 x=5.Forex 2 question 6 cos square x + 4 sin square x is equal to 5
Answers
Step-by-step explanation:
[tex]6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5[/tex]
[tex]6 - 2 \sin { }^{2} (x) = 5[/tex]
[tex] - 2 \sin {}^{2} (x) = - 1[/tex]
[tex] \sin {}^{2} (x) = \frac{1}{2} [/tex]
[tex] \sin(x) = \frac{1}{ \sqrt{2} } [/tex]
Take the arc Sine of the function
[tex]arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} [/tex]
Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)
Use the identity
[tex] \sin(x) = \sin(x + \pi) [/tex]
We know that
[tex] \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } [/tex]
so using the identity
[tex] \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) [/tex]
So we have two answers.
[tex]( \frac{\pi}{4} )[/tex]
[tex]( \frac{5\pi}{4} )[/tex]
1,7,19,37,61,91,127,169…
Answers
Answer:
Sequence sum? but it has no right sequence
(BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE THREE QUESTIONS)
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable.
2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote.
Answers
Answer:
Cheryl's posts + 7 posts =Kevin Posts
K-C=7 or C+7+K I use them because C is Cheryl and K is Kevin
Operation=subtraction or addition because it could be K-C=7 or C+7+K
Cheryl wrote K-7=C posts
Answer:
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable. (2 points)
The expression will be P for "of posts Kevin writes."
2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice. (2 points)
The operation I will use is subtraction so P-7.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote. (3 points)
Subtraction would be the operation and my expression would be ( P-7 ) which would also be ( 21 - 7 )
In a solid cube made up of smaller black and white cubes. The black and white cubes are at alternate places of the larger cube. How many black cubes are there in the above arrangement?
Answers
There are 168 black cubes in the arranagement.
A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.
To get the number of black cubes in the arrangement, we will use the equation below;
Number of black cubes = Total number of black cubes on a face * number of small cubes along the edgeNumber of black cubes = 24 * 7Number of black cubes = 168Hence there are 168 black cubes in the arrangement.
Learn more about cubes at https://brainly.com/question/1972490
Martin spent six dollars on four avocados how much money does he spend for two avocados
Answers
Answer:
$3
Step-by-step explanation:
cut the price in half because the amount of items was reduced by half
Answer:
three dollars
Step-by-step explanation:
$6 for 4
$x for 2
6=4
x=2
cross multiply
2×6=4×x
12=4x
Divide through by 4
x= 3
A car travels 470.7 kilometers on 52.3 liters of gas. How much gas will it need to go 345.6 kilometers?
Answers
Answer:
38.4[litres].
Step-by-step explanation:
[tex]1. \ the \ rule \ \frac{470.7[km]}{52.3[l]} =\frac{345.6[km]}{x};[/tex]
[tex]2. \ x=\frac{345.6*52.3}{470.7}=38.4[l].[/tex]
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
Answers
y = -2x + 5
hope this helps!
How i can answer this question
Answers
So, because 4q and 2q are like terms that would become 6q
Because 3 and 1 are like terms it would be 3-1 which is 2
Therefore your answer is 6q+2
Hope this helps :)
Answer:
3(2q+1)
Step-by-step explanation:
6q+2
3(2q+1)
how many integers between 100 and 999 (inclusive) have distinct digits
Answers
Answer:
648
Step-by-step explanation:
Running this in Python, with the code as follows,
import math
cur_numbers = [0] * 3
num = 0
for i in range(100, 1000):
cur_numbers[2] = i % 10
i = math.floor(i/10)
cur_numbers[1] = i % 10
i = math.floor(i/10)
cur_numbers[0] = i % 10
if(len(set(cur_numbers)) == 3):
num += 1
print(cur_numbers)
print(num), we get 648 as our answer.
Another way to solve this is as follows:
There are 9 possibilities for the hundreds digit (1-9). Then, there are 10 possibilities for the tens digit, but we subtract 1 because it can't be the 1 same digit as the hundreds digit. For the ones digit, there are 10 possibilities, but we subtract 1 because it can't be the same as the hundreds digit and another 1 because it can't be the same as the tens digit. Multiplying these out, we have
9 possibilities for the hundreds digit x 9 possibilities for the tens digit x 8 possibilities for the ones digit = 648
Please help me solve for n
Answers
To solve for N, you have to work backwards
1. Take off the absolute sigh
the absolute sign only means that the answer must be positive. So that means N could equal to positive and Negative
2. What is 1x6?
This process is called inverse operation. Where you have division, you have multiplications. The answer is 6.
3. The answer is 6 or negative 6, in the fact that -6 would equal to six in the absolute sign.
I hope this helped! If it's wrong blame me!
I will report you if you send a link ;-; help correctly.
Answers
Answer:
the correct is 39
Step-by-step explanation:
there is nine number there so the fifth is it and it was in order that helped alot
Please help if it’s correct I will give brainliest :)
(–4v–5)–(v–1)
Answers
Answer:
(-4v-5)-(v-1)= -5v-4
Step-by-step explanation:
hope it helps :D
Answer:
ok you want to come then come here
Estimate the product. Round each factor to the nearest whole number, and then multiply.
0.9 × 1.084
Answers
0.10 x 2.000 = 0.2
0.9 = 0.10
1.084=2.000
Do now: Balance the following equation.
1.
C₂H₂ + O₂--
+
--->
- CO2 + H2O
Answers
Answer:
C2H2 + 3O2 ---> 2CO2 + 2H2O
Step-by-step explanation:
calculate the volume of a cone with r=6.2 and h=10.9 and Pi=3.14
Answers
Answer: The volume(v) is 438.77.
Explanation: The formula for a right circular cone is in the image.
97 term of-5,-23,-41
Answers
Answer:
-1147
Step-by-step explanation:
Answer:
-1733
Step-by-step explanation:
-5-96*18 = -1733
The price of 50 litres of petrol is £36, find the price of each litre of petrol.
Answers
Tyra, Elle, Tran, and Ann share equally in the rental of a car. If the total cost of the rental is C dollars, which expression represents Tyra's share of the cost?
Answers
Answer:
c/4
Step-by-step explanation:
Since it's equally shared, and the total cost is C, then the answer is c/4
Please help with the steps to get the answer. Thank you.
15^(4x-8 )= 1
Answers
[tex]15^{4x-8} =1\\\\\implies 15^{4x-8} = 15^0\\\\\implies 4x -8 = 0\\\\\implies 4x = 8\\\\\implies x = \dfrac 84\\\\\implies x =2[/tex]
Luke has a piece of rope that is 3.6 meters long. He cuts the rope into two pieces. One is 1.93 meters long. How long is the other piece of rope?
Answers
What proportion of US women have a height between 62 and 67 inches?
Answers
Answer:
short ppl
Step-by-step explanation:
if u 62 inches u short as hell
Please help me with this question.
Answers
Answer:
aww i help u.....
Step-by-step explanation:
my answer is letter ~~B CAUSE STUDEN BIS CONDYCTION LIKR FREE AT THE SCORED
Kiara bought fabric to make a dress and a sewing machine. The total cost of her purchase, $80.50, included both the cost of her sewing machine
Write an equation to determine the cost of fabric per foot
find the cost of fabric per foot
Answers
If m∠2=4x+7 and m∠7=5x-13, find x.
Answers
Answer:
x =20
Step-by-step explanation:
m∠2 ≅ m∠6 because they are corresponding angles
m∠6 ≅ m∠7 because they are vertical angles
∴ m∠2 ≅ m∠7 by substitution
4x+7 = 5x-13
7 = x-13
20 = x
The value of x is 20.
What are vertically opposite angles?Vertical angles are angles opposite each other where two lines cross.
What are corresponding angles?Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are corresponding angles.
According to the given question.
We have
m ∠2 = 4x + 7
and m ∠7 = 5x - 13
From the given figure we can say that
m ∠7 = m ∠6...(i) (because they are vertically opposite angles)
and m ∠6 = m ∠2...(ii) ( corresponding angles)
From (i) and (ii)
m ∠7 = m ∠2
⇒ [tex]5x - 13 = 4x + 7[/tex]
⇒ [tex]5x - 4x = 7 +1 3[/tex]
⇒ [tex]x = 20[/tex]
Hence, the value of x is 20.
Find out more information about vertically opposite angles and corresponding angle here:
https://brainly.com/question/18296786
#SPJ3
help me please i cant math
Answers
Answer:
(b) 3 +x = 12
Step-by-step explanation:
To solve these for x, you would ...
a) divide by 3
b) subtract 3
c) add 3
d) multiply by 3
The subtraction property of equality says you can subtract the same value from both sides of an equation without affecting the value of the variable(s). It is applicable when you need to subtract a quantity in order to get the variable by itself.
Solving 3 +x = 12 would make use of the Subtraction Property.
Anna is making soft toys she can sell at the fair. She can make 3 soft toys
in 5 hours. How many soft toys can she make in 20 hours?
OA) 10
OB) 12
OC) 16
OD 20
Answers
Answer:B
Step-by-step explanation:
20/5 = 4
4 x 3 =12
Answer:
C
Step-by-step explanation:
Show and explain how you found the answer to this problem. Marion read 616 pages in 14 days. If she read the same number of pages each day, how many pages did she read each day?
Answers
Based on the number of pages read and the time it was read in, the number of pages read per day was 44 pages.
Marion read 616 pages and did this in 14 days.
She read the same number of pages each day so the number of pages read per day was:
= Number of pages read in total / Number of days
= 616 / 14
= 44 pages
In conclusion, she read 44 pages per day.
Find out more about divisional problems at https://brainly.com/question/13417862.
Which theorem would be used to prove the triangles below as congruent?
A: HL
B: SSS
C: ASA
D: AAA
Answers
Answer:
A: HL
Step-by-step explanation:
The hypotenuses of these right triangles are marked congruent.
One leg of these right triangles is marked congruent.
The HL theorem applies.
Answer:
A
Step-by-step explanation:
The hypotenuses of these right triangles are marked congruent.
One leg of these right triangles is marked congruent.
The HL theorem applies.
How many minutes make a hour
Answers
Answer:
60 minutes make an hour
Step-by-step explanation:
Because 1 hour = 60 minutes
Simplify this question
Answers
[tex]3 + \sqrt{ - 12} \\ = 3 + \sqrt{ 2 \times 2 \times - 3} \\ = 3 + 2 \sqrt{ - 3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\\ \sf\longmapsto 3+√-12[/tex]
[tex]\\ \sf\longmapsto 3+√12i[/tex]
[tex]\\ \sf\longmapsto 3+√2(2)(3)i[/tex]
[tex]\\ \sf\longmapsto 3+2√3i[/tex]