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].
For more details about Potential roots refer to the link given below.
https://brainly.com/question/25873992
Answer: ALL OF THEM
Step-by-step explanation:
Related Questions
how to turn 18/48 into the power of 10 please tell the answer as soon as possible, it's for my semester
Answers
2. You can write down a power or in text you use a carrot or a ^ and write 18/48^10
someone help pls pls
Answers
Answer:
3.636 hour. dividing 200miles /55m/h =3.636h
Answer:
3 hours 38 minutes is what calculators online say
Step-by-step explanation:
You should put both answers that were given to you. The answer on top seemed to do it the mathematical way youre suppose to. Maybe the teacher will take both answers i don’t know
Find the inverse function. f(x) = (x + 1
Answers
Answer:
( x + 1 ) ^ 3
Step-by-step explanation:
f(x) = 3√x - 1
replace x with y
x = 3√y - 1
solve for y,
x = 3√y - 1
x^3 + 3x^2 + 3x + 1 = (x+1)^3
HOPE THIS HELPS :)
Mr. Rao's gas tank holds up to 1718 gallons of gas. It took 12.65 gallons of gas to fill his tank.
How many gallons of gas did Mr. Rao have in his tank before he filled it?
Enter your answer as a decimal or as a mixed number in simplest form in the box.
gal
Answers
4.475 or 4 19/40 gallons
How?
12.65=253/20
253/20= 12 13/20
////////
I need a similar denominator of 12 13/20 and 17 1/8.
12 13/20×2/1= 12 26/40
17 1/8×5= 17 5/40
17 5/40-12 26/40= 4 19/40
Therefore,
the answer is 4 18/40 gals
Answer:
4 19/20
Step-by-step explanation:
17 1/8 - 12 13/20 = 4 19/20
R, P, Q act on the base AB, BC, CA triangles ABC in alphabetical order, respectively. Show that P sec A + Q sec B + R sec C = 0, if the fluid of this power system passes through the center of the triangle.
Answers
Answer:
(i) In △ABD and △ACD,
AB=AC ....(since △ABC is isosceles)
AD=AD ....(common side)
BD=DC ....(since △BDC is isosceles)
ΔABD≅ΔACD .....SSS test of congruence,
∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)
(ii) In △ABP and △ACP,
AB=AC ...(since △ABC is isosceles)
AP=AP ...(common side)
∠BAP=∠PAC ....from (i)
△ABP≅△ACP .... SAS test of congruence
∴BP=PC ...[c.s.c.t].....(ii)
∠APB=∠APC ....c.a.c.t.
(iii) Since △ABD≅△ACD
∠BAD=∠CAD ....from (i)
So, AD bisects ∠A
i.e. AP bisects∠A.....(iii)
In △BDP and △CDP,
DP=DP ...common side
BP=PC ...from (ii)
BD=CD ...(since △BDC is isosceles)
△BDP≅△CDP ....SSS test of congruence
∴∠BDP=∠CDP ....c.a.c.t.
∴ DP bisects∠D
So, AP bisects ∠D ....(iv)
From (iii) and (iv),
AP bisects ∠A as well as ∠D.
(iv) We know that
∠APB+∠APC=180
∘
....(angles in linear pair)
Also, ∠APB=∠APC ...from (ii)
∴∠APB=∠APC=
2
180
∘
=90
∘
BP=PC and ∠APB=∠APC=90
∘
Hence, AP is perpendicular bisector of
Step-by-step explanation:
HOPE ITS HELP YOU
scores on a test have a mean of 66 and Q3 is 80. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
A) 10.5
B) 20.9
C) 9.4
D) 18.7
Answers
I really need help!!
Answers
Answer:
Red: y=4
Green: x=-1
Yellow: x=6
Blue: x=-2
Step-by-step explanation:
The lines are all passing through the Axis, so there is no slope for each line.
What addition statement does this show?
A. 5.2 + 6.4 = –11.6
B. –5.2 + 6.4 = –11.6
C. 5.2 + (–6.4) = –11.6
D. –5.2 + (–6.4) = –11.6
Answers
Answer:
D. –5.2 + (–6.4) = –11.6
Step-by-step explanation:
First, you can eliminate A and C because 5.2 is positive. Since the red arrow is pointing left, it indicates that the number (-5.2) is negative.
Then, you look at the second arrow, the green one. It is pointing left, so it would be -6.4.
I hope this helps :)
NEED HELPPP ASAAPPPPPPP
Answers
Answer:
me too
Step-by-step explanation:
Rsound answer to two decimal places
80.75757575757575757575
Answers
Answer:
[tex]80. \bar{75}[/tex]
X
-9
-5
-1
3
Y
- 2
0
2
4
What is the slope of the line?
Answers
ok done. Thank to me :>
Help I give brainly
The acute angles of a right triangle measure (48 - x) and (3x – 10). What is the value of x?
Answers
Answer:
[tex]\huge\boxed{\sf x = 26}[/tex]
Step-by-step explanation:
The acute angles of a right-angled triangle other than the right angle always add up to 90 degrees.
So, we get:
(48 - x) + (3x - 10) = 90
48 - x + 3x - 10 = 90
-x + 3x - 10 + 48 = 90
2x + 38 = 90
2x = 90 - 38
2x = 52
Divide both sides by 2
x = 52 / 2
x = 26
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
Step-by-step explanation:
x=26
The acute angles of a right-angled triangle other than the right angle always add up to 90 degrees.
So, we get:
(48 - x) + (3x - 10) = 90
48 - x + 3x - 10 = 90
-x + 3x - 10 + 48 = 90
2x + 38 = 90
2x = 90 - 38
2x = 52
Divide both sides by 2
x = 52 / 2
x = 26
Hope this helped!
is this a function
Find the domain and range
Answers
Answer:
Yes
Domain: 1, -1, 0, -3, 3
Range: 1, -1, 6
Step-by-step explanation:
The domain is in the left oval, the range is in the right oval. To find if its a function you have to make sure the domain (left side) doesn't "cheat". One number in the domain cant have more than one number in the range (right side), BUT (for future reference) the range can cheat. As shown, the right side numbers 1 and 6 have two different arrow pointed at them. As long as the domain doesnt "cheat" it is a function
Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed
Answers
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
_____
Additional comment
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
i need answer please I got a them wrong
Answers
Answer:
See image
Step-by-step explanation:
I'm guessing a little bit, bc although you attached an image, it doesn't say what you are trying to prove, nor what you are given. Usually that is provided for a proof.
But we can see that the parallel segments are marked, so we'll call that the given information. Then there are actually two pairs of corresponding angles that are congruent by the Corresponding Angles postulate. But we only need one pair. Then Angle A is congruent to itself by Reflexive Property. Finally what we have proven is that the two triangles ABC and ART are similar by AA
WILL GIVE BRAINLIEST
y = 2x - 9
y = 1/2x + 3
These two lines are:
parallel
perpendicular
neither
Answers
Answer:
neither
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 9 ← is in slope- intercept form
with slope m = 2
y = [tex]\frac{1}{2}[/tex] x + 3 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
2 ≠ [tex]\frac{1}{2}[/tex] , then lines are not parallel
2 × [tex]\frac{1}{2}[/tex] = 1 ≠ - 1, then lines are not perpendicular
Which inequality is graphed below
Answers
Would someone help me out?
A)56.6
B)58.4
C)53.5
Answers
Answer:
it is c
Step-by-step explanation:
The function after synthetic division f(x) = 4x3 + 3x2 − 16x − 12
Answers
Answer:
[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]
»ANSWER«
(1) Write properties of function:
x intercept/zero:
[tex] x_{1} = \frac{3}{4} [/tex]
y intercept:
[tex]y = - 12[/tex]
domain:
[tex]( - \infty \: \infty )[/tex]
type of function: cubic fraction
standard form:
[tex]f(x) = 4 {x}^{3} - 3 {x}^{2} + 16x - 12[/tex]
factorize form:
[tex]f(x) = (4x - 3)( {x}^{2} + 4)[/tex]
even/odd/neither: neither
bounce/cross x axis:
[tex]x = \frac{3}{4} \: across[/tex]
increasing interval:
[tex]( - \infty \: \infty )[/tex]
decreasing interval: no
number of positive real zeros: 1
number of possible turning point: 2
order/degree: 3
leading term:
[tex]4x ^{3} [/tex]
leading coefficent: 4
constant term: -12
end behavior:
[tex]as \: x \: → \infty f(x) → \infty \: as \: x → - \infty f(x) → - \infty [/tex]
#CarryOnLearning
can someone tell me if i did this right lol
Answers
Answer:
Your calculation is correct, but I'd answer 33.0 in.
Step-by-step explanation:
You are correct. Good job.
Answer:
I'm 96% sure its right, and those are pretty good odds ^^
5x-15y=-20, 5x-4y=-9 systems of equations (elimination)
Answers
Answer:
(- 1, 1 )
Step-by-step explanation:
5x - 15y = - 20 → (1)
5x - 4y = - 9 → (2)
Multiplying (2) by - 1 and adding to (1) will eliminate the x- term
- 5x + 4y = 9 → (3)
Add (1) and (3) term by term to eliminate x
0 - 11y = - 11
- 11y = - 11 ( divide both sides by - 11 )
y = 1
Substitute y = 1 into either of the 2 equations and solve for x
Substituting into (1)
5x - 15(1) = - 20
5x - 15 = - 20 ( add 15 to both sides )
5x = - 5 ( divide both sides by 5 )
x = - 1
solution is (- 1, 1 )
A) by AA similarity
B) by sas similarity
C)Not enough information
D) by sss similarity
Please see the photo
Please don't answer randomly because if you answer randomly you are gonna lose points
Answers
Answer: b
Step-by-step explanation:
Answer: It's yes and (D) SSS because all the angles are side side side and all have the same angles but one's smaller while the other is bigger but that doesn't change anything. :)
Step-by-step explanation:
What is 2/3 – (-2/3)
Answers
Answer:
2/3 - (-2/3)
=0.66 - (-0.66)
=0.66+0.66
= 1.32
I tried to make sense of this and it doesn’t make sense. Can someone please help?
Answers
Answer:
85 because if you do the math
h(8) = -2(8)^2 + 4(8)- 7
Answers
Answer:
h = - 103/8
Step-by-step explanation:
1) Re-order terms so constants are on the left
8h = = -2(8)²+4(8)-7
2) Evaluate the exponent
8h = -2·64+4(8)-7
3) Multiply the numbers
8h = -128+4(8)-7
4) Multiply the numbers
8h = -128+32-7
5) Add the numbers
8h = -103
6) Divide both sides of the equation by the same term
8h/8 = -103/8
7) Simplify
- Cancel terms that are in both the numerator and denominator
h = -103/8
Carmen can make 9 bracelets each day. She needs to make at
least 120 bracelets to sell at a craft fair. She estimates she will need more
than 13 days to make enough bracelets. Is she correct? Explain.
Answers
Step-by-step explanation:
yes because If you divide 120 by 9 you get 13.333 so technically speaking she is correct
can anyone plz help me with this math problem
Answers
To make 8 dozen cookies, you must use 2 eggs. How many eggs are needed to make 40 dozen cookies? Use a proportion to solve.
Answers
Answer:
10 eggs for 40 dozens
Step-by-step explanation:
40÷8=5
5*2=10
Our created proportion is 8:2::40:x
=> 8x = 80=> x = 10Conclusion:Therefore, for 40 dozen cookies, 10 eggs are required.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
2.4x-9.1x+12.5= -39.44
Solve for x
Answers
Answer:
x= 2597/335
Step-by-step explanation:
collect like terms
2.4x-9.1x= -6.7x
-39.44-12.5 = -51.94
-6.7x=-51.94
divide both sides by -6.7
x= 2597/335
The table displays the amount of money Stephen has in his piggy bank.
Stephen’s Piggy Bank
Types of Coins Amount ($)
Quarters 7.50
Dimes 6.00
Nickels 5.50
Pennies 3.00
Which answer choices accurately approximate a comparison between the value of the dimes in the piggy bank and the total value of Stephen’s coins?
Select all the correct answers.
Answer choices:
6%
3/11
6/22
60%
27%
3/5
Answers
Answer:
The answer is 27%, 6/22, and 3/11.
Pls mark brainliest. :D