The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.
Explanation:In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:
Step 1: Set the equation to zero: x^3-3x^2+2 = 0.Step 2: Try to factor the polynomial or use a solving method such as the quadratic formula if it was a second-order polynomial. But in this case, the polynomial is of third order, and in such cases you typically apply synthetic division or the Rational Root Theorem to find the roots.Note: This explanation suggests general approaches. The actual solution would require longer calculations.
Learn more about Roots of polynomial function here:https://brainly.com/question/12158280
#SPJ12
The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.
Explanation:Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.
A. First, let's consider 2+i as a possible root.
We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.
Upon evaluation, it turns out that F(2+i) does indeed equal 0.
B. Now let's see if -2+i is a root.
We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.
C. Then, we check if 1 is a root by computing
F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root
D. Finally, let's check if 2 is a root.
We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.
In conclusion, the only given number that is a root of the function is 2 + i.
https://brainly.com/question/31214281
#SPJ6
Question:Which of the following are roots of the polynomial function below?
F(x)=x³-3x²+x+5
A. 2+i
B. -2+i
C. 1
D. 2
Janice bought juice packed for the 15 players on the soccer team the juice packets come in boxes of 6 how many boxes did Janice buy
Answer:
It would be 90 because if there are 15 soccer people on the team and there are 6 in the packets then each would get 1 and if you multiply 15 times 6 you will get 90.
So the answer would be 90
Answer:
90
Step-by-step explanation:
just do 15x6
Sammy bought a new car. The depreciation equation is given by f(x) = 30,000(.85)x, where x represents the number of years since the purchase of the car, and f(x) represents the value of the car. By what percent does Sammy's car depreciate each year?
In a depreciation equation, you multiply the value of the car by the percent of depreciation minus 1.
In the given equation you are multiplying the value of the car by (.85)
This means the percent of depreciation would be 1 - 0.85 =0.15 which is 15%
The car depreciates by 15% every year.
Answer:
The car depreciates by 15% every year.
Step-by-step explanation:
Can someone help me please
Add 1,1.5,1.25,2.5, and 3 to get D, or 9 and 1/4.
Answer:
9 and 1/4 hope this helps!!!!!
23/50 of Zanders friends prefer to stay home on Friday night what percent of Xander's friends prefer to stay home on Friday nights
Answer:
46% of Xander's friends prefer to stay home on Friday nights.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]
i.e
Zanders friends prefer to stay home on Friday night = 23
Total numbers of Zanders friends are 50.
Part value = 23
Total value = 50
Put in the formula
[tex]Percentage = \frac{23\times 100}{50}[/tex]
[tex]Percentage = \frac{2300}{50}[/tex]
Percentage = 46%
Therefore 46% of Xander's friends prefer to stay home on Friday nights.
Answer:
wasdd ada
Step-by-step explanation:
please help? i honestly don't know
a population of bacteria doubles every 15 hours, initially the population of bacterica is 40. what is the population of the bacteria after 40 houra?
Answer:
the bacteria's population is 120
Step-by-step explanation:
Answer:
After 40 hrs it is 213.333 bacterias
Approximately 213 bacterias
Step-by-step explanation:
Initial population of bacteria is 40
And it doubles every 15 hrs
If 15 hrs is double
1 hrs is 0.13333
Then 10 hrs is 1.3333
So the first 15 hrs
It multiplies to 40*2= 80
The second 15 hrs it multiplies by 80*2=160
The next 10 hrs it multiplies by
160*1.33333= 213.333
Could I get some help on this question?
Answer:
The triangles are similar, because the angles are congruent and the sides are proportional.
Step-by-step explanation:
The first step to see if the triangles are similar is to see if the angles are the same.
The third angle in the large triangle is
30 + 65+ unknown = 180
95 + unknown = 180
Subtract 95 from each side
unknown = 180-95
unknown = 85
So the angles are the same.
Lets check the ratio of the the sides
14 10
------ = ----------
7 5
Both simplify to 2/1 so the ratio's are the same.
The triangles are similar because the angles are congruent and the sides are proportional.
A total of 60 60 children signed up for hockey. There were 3 3 boys for every 1 1 girl who signed up. How many of the children who signed up for hockey were girls?
Answer: 15
Step-by-step explanation:
Boys : Girls
3x + 1x = 60
4x = 60
x = 15
Girls (1x) = 1(15) = 15
Answer:
The answer is 15
PLEASE PLEASE HELP PLEASE
Answer:
arc ≈ 25.13 feet
Step-by-step explanation:
arc length = circumference × fraction of circle
= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π
= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet
Help me with this please
4.42×10^34 molecules/min
Step-by-step explanation:Multiply the various factors, along with the unit conversion (60 s/min).
... (3.35×10^25 molecules/L) × (2.2×10^7 L/s) × (60 s/min)
... = (3.35×2.2×60)×10^(25+7) molecules/min
... = 442.2×10^32 molecules/min
... ≈ 4.42×10^34 molecules/min
_____
Comment on scientific notation problems
Your scientific or graphing calculator will allow you to enter and display numbers in scientific notation.
A mayoral candidate would like to know her residents’ views on a public open space before the mayoral debates. She asks only the people in her office. Her co-workers are an example of a ______.
census
population
convenience sample
simple random sample
Answer:
convenience sample
Step-by-step explanation:
Answer: Convenience Sample
Step-by-step explanation: Biased sample–Parts of the population are favored over others. She only asked people in her office
35 POINT QUESTION, WILL MARK BRAINLIEST. Which of the following options is a 3rd degree polynomial with exactly 1 real root?
Answer:
A. F(x) = x^3+9x^2+27x+27
Step-by-step explanation:
I am not 100% sure but I think this is right.
I found the root for this equation: x=-3
Hope this helps!
Answer:
The correct option is D.
Step-by-step explanation:
In option A,
The given function is
[tex]F(x)=x^3+9x^2+27x+27[/tex]
[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]
[tex]F(x)=(x+3)^3[/tex] [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]
The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.
In option B,
The given function is
[tex]F(x)=x^3+3x^2-9x-27[/tex]
[tex]F(x)=x^2(x+3)-9(x-3)[/tex]
[tex]F(x)=(x^2-9)(x+3)[/tex]
[tex]F(x)=(x+3)(x-3)(x+3)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]
Therefore, this function has 3 real roots.
In option C,
The given function is
[tex]F(x)=x^3-9x^2+27x-27[/tex]
[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]
[tex]F(x)=(x-3)^3[/tex] [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]
Equate the function equal to zero, to find the roots.
[tex](x-3)(x-3)(x-3)=0\Rigtharrow x=3[/tex]
The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.
In option D,
[tex]F(x)=x^3+3x^2+9x+27[/tex]
[tex]F(x)=x^2(x+3)+9(x+3)[/tex]
[tex]F(x)=(x+3)(x^2+9)[/tex]
Equate the function equal to zero, to find the roots.
[tex](x+3)(x^2+9)=0[/tex]
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]
The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.
Use substitution to find the solution to the system of equations. 5x+7y=-29 y=x+1
Answer:
(x, y) = (- 3, - 2)
Step-by-step explanation:
given the 2 equations
5x + 7y = - 29 → (1)
y = x + 1 → (2)
substitute y = x + 1 into (1)
5x + 7(x + 1) = - 29 ( distribute and simplify left side )
5x + 7x + 7 = - 29
12x + 7 = - 29 ( subtract 7 from both sides )
12x = - 36 ( divide both sides by 12 )
x = - 3
substitute x = - 3 into (2)
y = - 3 + 1 = - 2
solution is (- 3, - 2 )
Answer:
(-3,-2)
Step-by-step explanation:
hey please help me with this
Answer:
Two real solutions
Step-by-step explanation:
z=-1.45
z=0.45
Answer:
ANSWER: Two real solutions
Step-by-step explanation:
its z=-1.45
its z=0.45
At the beginning of the week Fayez writes drown the mileage of his limousine - 2529 At the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during the week. The handbook states that the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limousine used 1 gallon of petrol for every 20 miles this week 1 gallon = 4.54 litres Did his limo use 1 gallon of petrol for every 20 miles that week? Explain answer in full Please help!!
Select the statement that is true for the graphs of all functions g(x). A. The graph of g(x + 1) is the graph of g(x) shifted right 1 unit. B. The graph of g(x + 1) is the graph of g(x) shifted up 1 unit. C. The graph of g(x + 1) is the graph of g(x) shifted left 1 unit. D. The graph of g(x + 1) is the graph of g(x) shifted down 1 unit.
Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
As per the given information option (A) is correct because it will shift to the right side by one unit when the function of [tex]g(x)[/tex] is [tex]g(x+1)[/tex].
For example:-
[tex]x=2[/tex]
So,
[tex]g(2)\\g(2+1)[/tex]
Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.
To know more about the functions
https://brainly.com/question/29633660
#SPJ6
Final answer:
The true statement for the graphs of all functions g(x) is that the graph of g(x + 1) is the graph of g(x) shifted left by 1 unit.
Explanation:
When considering the transformation of the graph of a function g(x) to g(x + 1), we are applying a horizontal shift to the graph. According to the principles of graph transformation, when we add a positive constant to the input of a function, every point on the graph shifts left by that amount. Therefore, the graph of g(x + 1) is the same as the graph of g(x), shifted to the left by 1 unit. This corresponds to the option C, which states that adding 1 to the input of the function shifts the graph to the left by 1 unit.
Simplify f+g / f-g when f(x)= x-6 / x+7 and g(x)= x-7 / x+6
Answer:
C. 2x^2 - 85 / 13
The sales tax in your city is 8.8\%8.8%, and an item costs \$63$63 before tax. How much tax would you pay on that item? Round to the nearest hundredth or cent.
Kyle has 125 marbles. Fifty of these marbles are red and the reat are other colors. What is the ratio of the nunber of red marbles to the total of marbles expressed in simplest terms?
Answer:
The required simplest form is: [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
We have been given Kyle has 125 marbles.
And 50 out of total 125 are red and rest of them are other colours
that means other colour marble are 125-50=75
we need to find ratio of the number of red marbles to the total of marbles
The rat io is: [tex]\frac{50}{125}=\frac{2}{5}[/tex]
The required simplest form is: [tex]\frac{2}{5}[/tex]
Answer:
Step-by-step explanation:
2/5
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 152. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
Answer:
Number of restaurant-purchased meals eaten in a restaurant = 70
Number of restaurant-purchased meals eaten in a car = 22
Number of restaurant-purchased meals eaten in a home = 60
Step-by-step explanation:
Let the number of people that will eat in a restaurant be R.
Let the number of people that will eat in a car be C.
Let the number of people that will eat in a home be H.
From the information given in the problem we have,
R+C+H = 152 ____equation (1)
C+H-R = 12 ____equation (2)
R = H+10 ____equation (3)
1) Plugging in R=H+10 from equation 3 into the equation 2, we get
C+H-R=12
=> C+H-(H+10)=12
=> C+H-H-10=12
2) Cancelling out +H and -H, we get
C-10=12
3) Add 10 to both sides
C-10+10=12+10
4) Cancelling out -10 and +10, we get
C=22
5) Plugin C=22 in equation 1, we have
R+C+H = 152
=> R+22+H=152
Subtract 22 from both sides,
R+22+H-22=152-22
Cancelling out +22 and -22 from the left side, we get
R+H=130 ____let it be equation (4)
6) Plugin C=22 in equation 2, we have
C+H-R = 12
22+H-R = 12
Subtracting 22 from both the sides, we get
22+H-R-22 = 12-22
Cancelling out +22 and -22 from the left side,
H-R = -10 ____let it be equation (5)
7) Adding equation 4 and equation 5, we get
(R+H)+(H-R) = 130 + (-10)
=> R+H+H-R = 130-10
8) Cancelling out R and -R from the left side, we get
2H = 120
9) Dividing both sides by 2, we get
[tex]\frac{2H}{2} = \frac{120}{2}[/tex]
10) Cancelling out the 2's from the left side, we have
H=60
11) Plugging in C=22 and H=60 in the equation 1, we have
R+C+H = 152
=> R+22+60=152
=> R + 82 = 152
12) Subtracting 82 from both the sides, we get
R + 82 -82 = 152 -82
13) Cancelling out +82 and -82 from the left side, we get
R = 70
So, C=22, H=60, R=70
Antonio earns $5 an hour for raking leaves. He also has $35 in savings. Which equation shows the amount of money, m, Antonio will have after raking leaves for a number of hours, h?
Answer:
35 + 5h = m
Step-by-step explanation:
Ms. Kincaid keeps a supply of dimes and quarters in her car to pay for highway tolls. A week’s supply of toll coins contains 5 more dimes than quarters and totals $4.00. How many quarters does Ms. Kincaid spend on highway tolls in one week
A. 10
B.15
C.16
D.40
Answer: (A) 10
Step-by-step explanation:
Value Quantity = TOTAL Value
dimes: .10 Q + 5 = .10(Q = 5)
quarters: .25 Q = .25Q
Dimes + Quarters = $4.00
.10(Q + 5) + .25Q = 4.00
.10Q + .50 + .25Q = 4.00
.50 + .35Q = 4.00
.35Q = 3.50
Q = 10
Quarters = 10
Dimes = Q + 5
= 10 + 5
= 15
Answer: Option A, she has 10 quarters.
Step-by-step explanation:
We have quarters of $0.25 and dimes of $0.10
We have 5 more dimes than quarters and a total of $4.00
How many quarters Ms. Kincaid has?
Q is the number of quarters and D the number of dimes.
We have the system of equations:
D = Q + 5
Q*$0.25 + D*$0.10 = $4.00
First, we can replace the first equation into the second and solve it for Q.
Q*$0.25 + (5 + Q)*$0.10 = $4.00
Q*($0.25 + $0.10) + $0.50 = Q*($0.35) + $0.50 = $4.00
Q = (4.00 - 0.50)/0.35 = 3.50/0.35 = 10
So she has 10 quarters.
The correct option is A.
Kimberly got 3 problems wrong on a test of 25 questions. What percent of the questions did she get correct
Answer:
88%
Step-by-step explanation:
if she got 3 problems wrong, so she got (25-3)=22problems correct,
22/25=x/100,x=88
The percent of the questions did she get correct will be 88%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Kimberly got 3 problems wrong on a test of 25 questions.
Then the number of the correct question will be
⇒ 25 – 3
⇒ 22
Then the percent of the questions did she get correct will be
⇒ (22 / 25) x 100
⇒ 0.88 x 100
⇒ 88%
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
If $a$, $b$, $c$, and $d$ are replaced by four different digits from $1$ to $9$, inclusive, then what's the largest possible value for $a.Bc + 0.D$ ?
The largest possible value for (a.bc + 0.d) is (10.56).
The largest possible value for (a.bc + 0.d) when (a), (b), (c), and (d) are replaced by four different digits from 1 to 9, inclusive, can be found by selecting the largest digits for (a), (b), and (c), and the smallest digit for (d).
This results in the number (9.86 + 0.7), which equals (10.56).
Therefore, the largest possible value for (a.bc + 0.d) is (10.56).
Complete question:
If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?
Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.
1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.
Answer:
1) [tex]2s+s\leq18[/tex]
2) 6 years old
Step-by-step explanation:
Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]
Hannah is 2 times her sister’s age:It means [tex]h=2s[/tex]
The sum of their ages is no more than 18 years:It means the sum is LESS THAN or EQUAL TO 18. So we can write:
[tex]h+s\leq18[/tex]
1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,
[tex]h+s\leq18\\2s+s\leq18[/tex]
2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,
[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]
Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.
Martha estimated there were 89 marbles in a jar for a contest. The actual number of marbles in the jar was 111. What was the percent error of Martha's estimation?
Answer:
18.91 percent
Step-by-step explanation:
Percent error equation: Difference or Difference/Actual
Actual
The difference is the greater amount minus the smaller.
111 - 89 = 22
The actual is 111.
Now divide 22/111.
22/111 = 0.189 repeating
0.189 repeating = about 18.91 percent
Find tan θ if sec θ = √26/5 and sin θ < 0.
Answer:
Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0 = tan θ = -1/5
Step-by-step explanation:
cos θ = 5/√26
opposite side = s
s^2 = 26-25 = 1
s = -1
tan θ = -1/5
PLEASE HELP ASAP WILL MARK BRAINLIST
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.
Which function equation represents the population of the city after t years?
f(t)=451,400(0.968)t
f(t)=451,400(0.032)t
f(t)=451,400(1.032)t
f(t)=451,400(3.2)t
2.The ordered pairs model an exponential function, where j is the function name and e is the input variable.
{(1, 10), (2, 50), (3, 250), (4, 1250)}
What is the function equation in sequence notation?
Enter your answer in the box.
Answer:
f(t) = 451,400(0.968)^t
Step-by-step explanation:
Exponential Decay Function:
y = b (1-r) ^t
where
b is the initial amountr is the rate of changet is timef(t)= 451,400 ( 1 - 0.032) ^t
f(t) = 451,400 (0.968) ^t
Answer:
This was the correct answer, I even provided proof from my own test. Hope this helps!
Step-by-step explanation:
Which of the following ordered pairs represents the solution to the system given below?
x − 4y = 7
5x + 9y = 6
Answer:
The solution to the system would be (3, -1)
Step-by-step explanation:
You can find the solution to this system by using the elimination method. To do that, start by multiplying the top equation by -5 and then adding it through.
-5x + 20y = -35
5x + 9y = 6
-----------------
29y = -29
y = -1
Now that we have the value of y, we can plug it into either equation and find the x value.
x - 4y = 7
x - 4(-1) = 7
x + 4 = 7
x = 3
Final answer:
The solution to the given system of equations is the ordered pair (3, -1).
Explanation:
To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
1. Solve the first equation for x:
x = 7 + 4y
2. Substitute this value of x into the second equation:
5(7 + 4y) + 9y = 6
3. Simplify and solve for y:
35 + 20y + 9y = 6
29y = -29
y = -1
4. Substitute the value of y back into the first equation to find x:
x = 7 + 4(-1)
x = 3
Therefore, the solution to the system is the ordered pair (3, -1).
Melanie's trip was 500 miles long. She drove the same number of miles each day for 3 days. How many miles did she drive each day? Write the answer as a mixed number
Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.
Explanation:The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.
This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.
Learn more about Division here:
https://brainly.com/question/2273245
#SPJ3
The perimeter of a rectangle is 26 meters. The difference between the length and the width is 5 meters. Find the width
l - lenght
w - width
l - w = 5 → l = 5 + w
26 m - perimeter
l + l + w + w = 2l + 2w - perimeter
substitute l = 5 + w:
2(5 + w) + 2w = (2)(5) + (2)(w) + 2w = 10 + 2w + 2w = 10 + 4w
The equation:
10 + 4w = 26 subtract 10 from both sides
4w = 16 divide both sides by 4
w = 6
Answer: The width = 6 m.