Determine whether the rational root theorem provides a complete list of all roots for the following
polynomial functions.
f(x) = 4x^2 - 25
g(x) = 4x^2 + 25
h(x) = 3x^2 - 25
Answers
Answer:
1) Yes
2) No, this polynomial has complex roots
3) No, this polynomial has irrational roots
Step-by-step explanation:
a. Rational roots theorem provide a complete list of all roots of
f (x) = 4x² - 25
b. Rational roots theorem does not provide a complete list of all roots of
g (x) = 4x² + 25
c. Rational roots theorem does not provide a complete list of all roots of
h (x) = 3x² - 25
What is Function?
A relation between a set of inputs having one output each is called a function.
Functions are given as;
f (x) = 4x² - 25
g (x) = 4x² + 25
h (x) = 3x² - 25
Now,
a. f (x) = 4x² - 25
To find the roots we can set up 0,
f (x) = 4x² - 25 = 0
4x² - 25 = 0
4x² = 25
Divide by 4,
x² = 25/4
Take square root both side,
x = √25/4
x = ±5/2
Thus, The function has rational roots.
So, Rational roots theorem provide a complete list of all roots.
b) g (x) = 4x² + 25
To find the roots we can set up 0,
4x² + 25 = 0
4x² = - 25
Divide by 4,
x² = - 25/4
Taking square root,
x = √-25/4
x = ±5i/2
Thus, The function has complex roots.
So, Rational roots theorem does not provide a complete list of all roots.
c) h (x) = 3x² - 25
To find the roots we can set up 0,
3x² - 25 = 0
3x² = 25
Divide by 3,
x² = 25/3
x² = 8.333
Take square root both sides,
x = √8.333
x = ±2.89
Thus, The function has irrational roots.
So, Rational roots theorem does not provide a complete list of all roots.
Therefore,
a. Rational roots theorem provide a complete list of all roots of
f (x) = 4x² - 25
b. Rational roots theorem does not provide a complete list of all roots of
g (x) = 4x² + 25
c. Rational roots theorem does not provide a complete list of all roots of
h (x) = 3x² - 25
Learn more about the rational root theorem visit:
https://brainly.com/question/25216212
#SPJ5
Related Questions
What is the sample space of rolling a 6 sided number cube? SELECT ALL THAT APPLY
1
2
3
4
5
6
Answers
Answer:
Its all of them or just 6
Step-by-step explanation:
4x< 20; x = 20
can you show me the work?
Answers
Answer:
Step-by-step explanation:
Here you go mate
Step 1
4x<20 Equation/Question
Step 2
4x<20 Simplify
4x<20
Step 3
4x<20 Divide by 4
answer
x<5
A cash register contains $10 bills and $50 bills with a total value of $1080. If there are 28 bills total, then how many of each does the register contain?
Answers
Answer:
20 $50 bills
8 $10 bills
Step-by-step explanation:
Find how many $10 and $50 bills are in the cash register.
Make a systems of equations:
t = Amount of $10 bills
f = Amount of $50 bills
10t + 50f = 1080
t + f = 28
Lets solve for $50 bills first:
10t + 50f = 1080
-10(t + f = 28) = -10t - 10f = -280
----------------------
Solve for f:
10t + 50f = 1080
-10t - 10f = -280
40f = 800
Divide both sides by 40.
f = 20
There are 20 $50 bills.
Now we need to find how many $10 bills are in the register.
Plug in 20 to "f" in one of the equations and solve for "t".
Solve:
t + 20 = 28
Subtract 20 from both sides.
t = 8
There are 8 $10 bills.
Your answer should be:
20 $50 bills
8 $10 bills
r(x)=2square root of x S(x)= square root of x (rs)(4)=
Answers
Answer:
[tex](rs)(4) = 8[/tex]
Step-by-step explanation:
Given
[tex]r(x) = 2\sqrt{x[/tex]
[tex]s(x) = \sqrt x[/tex]
Required
Determine [tex](rs)(4)[/tex]
In functions:
[tex](fg)(x) = f(x) * g(x)[/tex]
This implies that:
[tex](rs)(x) = r(x) * s(x)[/tex]
Substitute values for r(x) and s(x)
[tex](rs)(x) = 2\sqrt{x} * \sqrt{x}[/tex]
[tex](rs)(x) = 2(\sqrt{x})^2[/tex]
[tex](rs)(x) = 2x[/tex]
Substitute 4 for x
[tex](rs)(4) = 2 * 4[/tex]
[tex](rs)(4) = 8[/tex]
Please I really need help on this one
Answers
Answer:
r=
[tex]r = \frac{d}{2} \\ r = \frac{5}{2} \\ r = 2.5cm[/tex]
28) Solve the inequality: 12x−10>170
A. x>15
B. x<−90
C. x<−58
D. x<15
Answers
Answer:
p=5x+3y
solve for x, number of cupcakes. isolate x
5x=p-3y
divide by 5
x=(p-3y)/5
Step-by-step explanation:
D. x<15
help ....................................................
Answers
Answer:
i think it's the subtraction one
Step-by-step explanation:
because if you find out what b is maybe you will get 2 1/2
2x + 8=12 what is the value of 4x + 2
Answers
Answer:
2x + 8 = 12
x = 2
4x = 2 = 10
Step-by-step explanation:
Triangle ABC is shown below. Which point is the coordinate of the image of
Answers
Step-by-step explanation:
there is no image how am I supposed to solve it
Answer:
The answer is C.
Step-by-step explanation:
Hope this helps :)
Allen traveled 6 kilometers in 2 hours How many hours does it take Alan to travel 1 kilometer?
Answers
Answer:
1/3
Step-by-step explanation:
6x=2
x= 1/3
Answer:
1 kilo takes 20 minutes
Step-by-step explanation:
6kilo in 2hrs
3kilo in 1 hr
1hr = 60min
3kilo/3 = 1 kilo
60min/ 3 = 20 min
1 kilo * 6 = 6kilo
20min * 6 = 120min ( 2 hours )
How do the values compare? Order the values from least to greatest. 1/2 , 2 , 2 1/2 , -1/2 , 1 1/2 , 2 1/2
Answers
Answer:
First always the positive is greater than the negative
Then 1/2, 2, 21/2, 2, 11/2 are greater than - 1/2
1/2=0.5
21/2=10.5
11/2=5.5
Then from lowest to greatest
-1/2,1/2,2,11/2,21/2
I hope you understand
Angles in a triangle
Answers
Answer
1=62
2=45
3=24
Angle 1
1 plus 118 equals 180 degrees (because both of the angles combined creates a straight angle).
1+118=180
180-118=1
1=62
Angle 2
The angles in a triangle add up to 180 degrees.
You know that angle 1 is 62 degrees.
And the other angle is 73 degrees.
You can now find angle 2.
62+73+2=180
2=180-62-73
2=45
Angle 3
Angle three is in a different triangle.
You already know that the angles in a triangle added up are 180 degrees.
The other missing angle in the triangle can be found by subtracting 73 from 180.
180-73=107
Now you know that two of the angles in the triangle are 107 and 49.
You can now find angle 3.
107+49+3=180
3=180-107-49
3=24
Look in the document
Answers
an industry representative claim that 60% of all satellite owners subscribers movie channel. suppose that representative’s claim is true and also suppose that 20 dish owners are randomly selected. find the probability that: (i) none of the dish owners subscribes movie channel (ii) exactly 3 dish owners subscribe movie channel (iii) more than 17 dish owners subscribe movie channel.
Answers
Answer:
1.099 * 10^-8 ; 4.23 * 10^-5 ; 0.0036
Step-by-step explanation:
Given :
p = 0.6
Sample size, n = 20
P(x = 0)
Using binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
1 - p = 1 - 0.6 = 0.4
P(x = 0) = 20C0 * 0.6^0 * 0.4^20
P(x = 0) = 1 * 1 * 1.099511627776E−8
P(x = 0) = 1.099 * 10^-8
2) Exactly 3;
P(x = 3) = 20C3 * 0.6^3 * 0.4^17
P(x = 3) = 1140 * 0.216 * 0.00000017179869184
P(x = 3) = 0.0000423037098786816
P(x = 3) = 4.23 * 10^-5
3.) More than 17
P(x > 17) = P(x = 18) + P(x = 19) + P(x = 20)
Using calculator :
P(x > 17) = 0.0036
I think this is the last question
Answers
Answer:
○ [tex]\displaystyle One\:relative\:maximum\:(-1, 8)\:and\:one\:relative\:minimum\:(2, -4)[/tex]
Step-by-step explanation:
The minimum is the lowest possible point a certain graph touches, while the maximum is the highest possible point a certain graph touches.
I am joyous to assist you at any time.
Write the correct name for each of the following polygons.
Answers
Answer:
a. Pentagon (The figure has 5 sides.)
b. Triangle (The figure has 3 sides.)
c. Hexagon (The figure has 6 sides.)
d. Hexagon (The figure has 6 sides.)
Step-by-step explanation:
PH
I want to double-check my answer. I think it may be wrong. I need this ASAP. Have a great day.
Answers
This is not the correct answer.
1. 2.30 is not even close to the point given in the number line.
2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.
A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?
a. For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.05.
b. For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.07.
c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
d. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.07.
e. The probability that the mean of the sampling distribution of sample proportions is greater than 0.07 is 0.05.
Answers
Answer: c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
Step-by-step explanation:
Mean of the sampling distribution of the sample proportion = p (Population proportion.)
Here, the population proportion of those who make a donation when contacted by phone is known to be p=0.05.
Then, Mean = p = 0.05
Hence, the correct option is
c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
This question is based on the concept of statistics. Hence, the correct option is (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
Given:
A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion p=0.05. For samples of size 100.
According to the question,
Mean of sampling distribution of the sample proportion = p (Population proportion.)
It is given that, the population proportion of those who make donation when contacted by phone is known to be p=0.05.
Thus, Mean = p = 0.05
Hence, the correct option is (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
For more details, prefer this link:
https://brainly.com/question/10211620
Do this very simple equation for monE
Answers
Answer:
Were my money?
Step-by-step explanation:
May I have brainliest please I'm trying to level up!
</3 PureBeauty
jason went to the store to buy a trampoline with his dad the trampoline was 60% off and they paid $90 how much did it cost without the discount
Answers
Answer:
It costed $150 dollars
Step-by-step explanation:
You divide 90 by 60 to get 1.5 then you multiply that by 100 to get 150
24 apples and 36 oranges in a basket. What percentage of the fruit is oranges
Answers
Answer:
24 %
Step-by-step explanation:
thats easy
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.
a) They select a random sample of 500 applications, and find that 46 of those students attend private schools. Check the conditions required for inference. (3 marks)
b) Create the 90% confidence interval. (6 marks)
c) Interpret the confidence interval in the context of the problem. (3 marks)
d) Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%? Explain. (2 marks)
Answers
Answer:
a) p*n = 46 and q*n = 454 data is enough for inference
b) CI = ( 0,099 ; 0,141)
c) CI we will find with 90% of confidence the value of p in that interval
d) No, we accept H₀ we don´t have evidence to claim that the percentage in the State University is smaller than that of the Department of Education
Step-by-step explanation:
Information from A state´s Department of Education is:
p₀ = 12 % p₀ = 0,12
The State University sample:
Sample size n = 500
Sample proportion 46 out of 500
p = 46/500 p = 0,092 then q = 1- p q = 1 - 0,092 q = 0,908
Both p*n = 46 and q*n = 454
a) Are big enough to approximate the binomial distribution to normal distribution
b) CI = 90% CI = 0,9 significance level α = 0,10 for an CI we need
α/2 = 0,10/2 α/2 = 0,05
z(c) = - 1,64 ( from z-table)
MOE = z(c)*√(p*q)/n
MOE = 1,64 * √ ( 0,092*0,908)/500
MOE = 1,64 *√0,08353/500
MOE = 1,64 * 0,0129
MOE = 0,021
Then CI = 90 % is:
CI = ( 0,12 - 0,021 < P < 0,12 + 0,021 )
CI = ( 0,099 ; 0,141)
We have with 90 % of confidence for finding the value of p in the interval
Test Hypothesis
Null Hypothesis H₀ p = p₀
Alternative Hypothesis Hₐ p < p₀
we have for α = 0,1 z(c) = - 2,32 from z table
And z(s) = ( p - p₀ ) / √ (p*q)/n
z(s) = ( 0,092 - 0,12 ) / √(0,092*0,908)/500
z(s) = - 0,028 / 0,0129
z(s) = - 2,17
Comparing z(s) and z(c) we see that
|z(s)| < |z(c)|
So z(s) is in the acceptance region. We can support the claim that the percentage in the State University is the same than that of the Departament of Education
6 cans of soup cost $12. Fill in the correct number over or under each hash mark. How much does one can of soup cost ?
Answers
Answer:
12 / 6 = $2
Step-by-step explanation:
Answer:
they each cost 2 dollors
Step-by-step explanation:
3. Two linear functions are shown below. Which function has the greater rate of change? Justify your response LOOK AT PIC! plz help
Answers
Answer:
Function B has the greater rate of change
Step-by-step explanation:
Function A has a slope of 1/3
Function B has a slope of 1/2
When comparing slopes, the higher value has the greater rate of change
1/2 > 1/3
solve for (0)
12
15
Round to the nearest hundredth
Answers
Answer:
.014
Just trust me, you know I have your back
who knows this answer ?!!
Answers
Answer:
D is the answer
Step-by-step explanation:
twice as many children is 24 because 12x2 is 24
Jake’s rental car service uses the equation y = 0.45x + 39.50 to calculate the total cost, y, where x is the number of miles driven. Angie’s rental car service uses this table to calculate the cost of a car rental.
Answers
Answer:
Step-by-step explanation:
what is the point of this
Answers
Answer:
B and I are both coplanar
Step-by-step explanation:
III
4.09 Unit Test: Lines - Part 1
What is an equation in point-slope form for the line that passes through the points (4, -1) and (-3,4)?
A.y+4= -(0+3)
B.y-3= -(x+4)
C.y+4= (x+3)
D.y-4= -(x+3)
Quick please
Answers
Answer:
D.y-4=-5/7(X=3)
Hope this helps!!!
///////////////////////////////////////////////////////////////////////////////////////////////////////////////
write the standard number 723,600 in scientifict notation
Answers
Answer:
723,600 = 7.236 × [tex]10^{5}[/tex]
Step-by-step explanation:
Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations.