Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24
We want to find a polynomial
f(x) = a x³ + b x² + c x + d
such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.
The factor theorem for polynomials tells us that we can factorize f(x) as
a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)
Expand the right side:
(x + 3) (x + 1) (x - 4) = x³ - 13x - 12
So we have
a x³ + b x² + c x + d = a x³ - 13a x - 12a
In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means
a = a (of course)
b = 0 (there is no x² term on the right)
c = -13a
d = -12a
We also have that f (-2) = -24, which means
f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)
-24 = 6a
a = -4
which in turn tells us that c = 52 and d = 48.
So we found
f(x) = -4x³ + 52x + 48
Solve the system using multiplication for the linear combination method
6x-3y=3
-2x+6y=14
Answer:
Step-by-step explanation:
(2,3)
If the original quantity is 10 and the new quantity is 15, what is the percent increase?
Given the value of the original quantity and the value of the new quantity, the percentage increase is 50%.
What is percent increase?Percent increase is aimply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.
It is expressed as;
C = ((x₂ - x₁) / x₁)100%
Where x₁ is initial value and x₂ is new value
Given the data in the question;
Initial value x₁ = 10New value x₂ = 15Percentage increase C = ?We substitute the given values into the expression above.
C = ((x₂ - x₁) / x₁)100%
C = ((15 - 10) / 10)100%
C = (5/10)100%
C = 0.5 × 100%
C = 50%
Therefore, given the value of the original quantity and the value of the new quantity, the percentage increase is 50%.
Learn more about Percentages here: brainly.com/question/24159063
#SPJ2
A company that makes hair-care products had 6,000 people try a new shampoo. Of the 6,000 people, 48 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
I would say 2880 sorry if am wrong
Step-by-step explanation:
6000*48=288,000 then divide by 100 because percent means 100. 288,000/100= 2,880. hope this helps can I get brainlist and add effort before you come to look for anwer.
Charles always spend the same amount of money each morning.Sunday he bought a newspaper for $2.50 and also purchased a coffee.Monday he purchased a newspaper for $1.50 and purchased two coffees. Determine the price of one coffee.
Answer:
a coffee is one dollar
Step-by-step explanation:
if he spends the same amount of momey each day, lets say a coffee is a dollar. the first day he spends 2.50 on a newspaper plus 1 dollar on a coffee equaling 3.50 dollars. if he purchased a 1.50 dollar newspaper and two coffees, two coffees would equal two dollars plus 1.50 equaling 3.50 dollars. that answer equals the same amount that he spent on monday.
What is 20% as a fraction in its lowest terms?
Please help me this is due at 11:59 I need help. Please show work
Answer:
See below :D
Step-by-step explanation:
Well, 20% is simply 20/100. By reducing it would go down to 2/10... try to reduce 2/10 in its lowest terms! You can do it, I believe in you :D
Another way is converting it to a decimal:
0.20
Which is another way of saying 0.2
0.2 = 2/10
2/10 is not reduced in its lowest terms, but I'm sure you can figure out the rest. Good luck and ask if you need more details in the works or if you can't figure it out! I'll be here.
It takes a book editor 28 minutes to edit 6 pages. Find how long it takes her to edit 45 pages
Answer:
Around 9.57 minutes to edit
Step-by-step explanation:
Do 28 divided by 6 to get around 4.7. Then do 45 divided by 4.7 to get the answer.
Please Help me this is due soon and I really need help!!!
Answer:
Hey, I got 20 and I asked my friend to work it and he got 20 too.
Step-by-step explanation:
what's is the difference of -1/2 and 2/5
Answer:
-9/10
Step-by-step explanation:
Answer:
Step-by-step explanation:
I think -9/10
the table below shows different possibilites for the number of games a team would need to win to maintain a certain percentage of wins
Answer:
here hope this helps please mark brainly
Step-by-step explanation:
2 1/3 Sam's car uses gallons of gasoline whenever Sam drives to work and then home againHow many complete trips to work and back home can Sam make in his car on gallons of gasoline ? 9 2/3
Answer:
Step-by-step explanation:
4, because multiplying 2 1/3 by 4 would get you up to 9 1/3 just 1/3 below how much he had
7. Plx is greater than 7, x> 7)
Answer:
I think 7 is the answer
hope it helps
HELP ME PLEASEEEEEEEEEEEE
A auto manufacturer claims that one of its car brands has mean MPG (miles per gallon) rating of 40 on the highway. Identify Type I error for this claim.
a. Fail to reject the claim that mean is 40 MPG when it is actually 40 MPG.
b. Fail to reject the claim that mean is 40 MPG when it is actually not 40 MPG.
c. Reject the claim that mean is 40 MPG when it is actually not 40 MPG.
d. Reject the claim that mean is 40 MPG when it is actually 40 MPG.
Answer:
d. Reject the claim that mean is 40 MPG when it is actually 40 MPG.
Step-by-step explanation:
The type 1 error could be said to have been made if the null hypothesis is erroneously rejected.
In the scenario above :
The null hypothesis (H0) : mean = 40
Hence, if the Null hypothesis defined above is rejected when in fact the hypothesis that the mean miles per gallon is actually 40.
On the other hand, the type 2 error occurs when a null which is false is not rejected.
Hence, when a true null is rejected, a type 1 error is committed. Similarly, when a false null isn't rejected, then a type 2 error has been committed.
hope this photo helps.enjoy
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page
Answer:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Answer:
26
Step-by-step explanation:
13 in 1/2 hour
13:1/2
26:1
I need help with this.
Answer: f(2)=15, f(-2)=18, all real #s
Step-by-step explanation:
1. f(2)=4(2)^2-2+1=16-1=15
2. f(-2)=4(-2)^2-(-2)+1=16+3=18
A new cell phone has a purchase price of $225. With the extended warranty, the total cost comes to $289. What
percent of the purchase price is the price of the warranty?
a. 28%
b. 22%
C. 25%
d. 20%
Answer:
The answer would be Letter A which is 28%
Step-by-step explanation:
Took the practice on edge 2020 and got it correct.
Solve the equation 5(2x -3) = 15
Answer:
x=3
Step-by-step explanation:
5(2x-3)=15
10x-15=15
10x=30
x=3
Answer:
x=3
Step-by-step explanation:
5(2x -3) = 15
10x-15=15
10x-15+15=15+15
10x=30
To find the x divide 10 to 30 so that is why 30÷10=3.
A brand of popcorn instructs users to microwave for 90–120 seconds on high. A student wonders what the ideal microwave time for popcorn might be and designs an experiment to find out. Bags of popcorn are placed in the microwave for different lengths of time: 90 seconds, 100 seconds, 110 seconds, and 120 seconds. Also, 2 types of microwaves with different power capacity will be used: 900 watts and 1,000 watts. At the end of the experiment, the number of unpopped kernels will be counted.
Using 3 lengths of time and 2 types of microwaves describes which part of the experiment?
the levels
the treatments
the response variable
the experimental units
Answer:
A.) the levels
Step-by-step explanation:
edge 2020
Answer:
A
Step-by-step explanation:
edge2o2o
Evaluate 24 + |-27-y| (-7)-x
Answer:
kr3kf,,xdk,xe3,ke,kex,ks,l,sl,r4kf
Step-by-step explanation:
nyjogtqGTKJMIYTRFEWDGTYU87R4EW2ERT5YUIO0IUJHYGFREDRGHJKL.BBRTBTRN
which equation is equivalent?
Answer:
C
Step-by-step explanation:
Peter has just returned from the Philippines and wants to exchange his remaining
Philippine pesos for U.S. dollars. If the exchange rate that day is 43.35 pesos per
U.S. dollar, how many U.S. dollars would he get for his remaining 1,500
Philippine pesos? Round your answer to the nearest dollar.
Answer:
$35
Step-by-step explanation:
1,500/43.35
Solve 1x = 7(x + 6).
Answer: answer is -7
Step-by-step explanation:
Step-by-step explanation:
Original Equation;
1x=7(x+6)
Multiply the 7 by the x and 6
1x=7x+42
Group like terms
1x-7x=42
-6x=42(Divide both sides by -6)
x= -7 (We have -7 because 42 can be divided by 6 7 times)
What value of a, b, and c make this equation true?
Answer:
I think you need to know the value of X to get this answer.
Step-by-step explanation:
Please who ever gets right gets brainliest to
Answer:
The Trench or The Mariana Trench is the deepest part of the ocean.
Answer:
B) trench
Step-by-step explanation:
The deepest part of the ocean is called the Challenger Deep and is located beneath the western Pacific Ocean in the southern end of the Mariana Trench
I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)
If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0? –18 –12 12 18
Answer:
Option 3: 12 is the correct answer.
Step-by-step explanation:
Given functions are:
[tex]f(x) = 16x-30\\g(x) = 14x-6[/tex]
In order to find the value of x on which (f-g)(x) will be zero, first of all we have to find (f-g)(x) and then equate it equal to zero to find the value of that will make (f-g)(x)
So,
[tex](f-g)(x) = f(x) - g(x)\\= (16x-30)-(14x-6)\\=16x-30-14x+6\\= 2x-24[/tex]
Now to find the value of x on which (f-g)(x) will be zero, putting (f-g)(x) = 0
[tex](f-g)(x) = 0\\2x-24 = 0[/tex]
Adding 24 on both sides
[tex]2x-24+24 = 0+24\\2x = 24[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2} = \frac{24}{2}\\x = 12[/tex]
For x=12, (f-g)(x) will be zero.
Hence,
Option 3: 12 is the correct answer.
Answer:
C got it right on edge 2022
Step-by-step explanation:
Use the factor theorem to determine whether or not the first polynomial is a factor of the second
Answer/Step-by-step explanation:
Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.
Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.
1. x - 1; x² + 2x + 5
By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.
f(1) = 1² + 2(1) + 5
= 1 + 2 + 5
= 8
Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.
2. x + 1; x³ - x - 2
By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.
f(1) = -1³ - (-1) - 2
= -1 + 1 - 2
= -2
Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.
3. x - 4; 2x³ - 9x² + 9x - 20
By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.
f(4) = 2(4)³ - 9(4)² + 9(4) - 20
= 128 - 144 + 36 - 20
= 0
Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.
4. a - 1; a³ - 2a² + a - 2
By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.
f(1) = 1³ - 2(1)² + 1 - 2
= 1 - 2 + 1 - 2
= -2
Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.
5. y + 3; 2y³ + y² - 13y + 6
By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.
f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6
= -54 + 9 + 39 + 6
= 0
Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.
______has gate cells
Answer:
gating
Step-by-step explanation:
This is your answer
if you answer correctly ill give brainliest
The Umbrella Corporation has found that in any given month, they sell fewer umbrella when the cost of the umbrella is higher. When the price of the umbrella is $10, they sell on average 18,000 umbrellas. When the price of the umbrellas is $16, they sell on average 9,000 umbrellas.
(a) Write a linear function U(p) that predicts the number of umbrellas sold based on the price p.
(b) How many umbrellas do they expect to sell if they raise the price to $20?
Answer:
The answer is below
Step-by-step explanation:
a) A linear function shows the relationship between variables. A linear equation is in the form: y = mx + b, where m is the rate of change, b is the value of y when x = 0, y is the dependent variable and x is an independent variable.
Let U represent the number of umbrellas and p the price of the umbrella. At $10 the number of umbrella sold is 18000, it can be represented as (10, 18000) i.e. (p, U)
At $16 the number of umbrella sold is 9000, it can be represented as (16, 9000).
The linear function is determined using:
[tex]U-U_1=\frac{U_2-U_1}{p_2-p_1}(p-p_1)[/tex]
Given (10, 18000) and (16, 9000):
[tex]U-U_1=\frac{U_2-U_1}{p_2-p_1}(p-p_1)\\\\U-18000=\frac{9000-18000}{16-10}(p-10)\\\\U-18000=-1500(p-10)\\\\U-18000=-1500p+15000\\\\U=-1500p+15000+18000\\\\U=-1500p+33000\\\\U(p)=-1500p+33000[/tex]
b) At p = $20, The number of umbrella is:
U(20) = -1500(20)+33000
U(20) = 3000 umbrella
