Required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]
Solution:Need to determine a polynomial of degree 4 and the zeros are -2, 4 , 4 and 8
Let the required polynomial be represented by f(x)
The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial.
If the polynomial p(x) is divided by cx−d and the remainder, given by p(d/c), is equal to zero, then cx−d is a factor of p(x).
-2 is zero of a polynomial means when x = -2, f(-2) = 0, so from factor theorem we can say that
=> x = -2 that is x + 2 = 0 is factor of polynomial f(x)
4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that
=> x = 4 that is x -4 = 0 is factor of polynomial f(x)
4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that
=> x = 4 that is x -4 = 0 is factor of polynomial f(x)
8 is zero of a polynomial means when x = 8, f(8) = 0 , so from factor theorem we can say that
=> x = 8 that is x -8 = 0 is factor of polynomial f(x)
So now we have four factors of polynomial f(x) that are (x + 2), (x -4) , (x -4) and (x – 8)
And as given that degree of polynomial f(x) is 4
Now f(x) is equal to product of factors
[tex]\begin{array}{l}{\Rightarrow f(x)=(x+2)(x-4)^{2}(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{2}-8 x+16\right)(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{3}-8 x^{2}+16 x-8 x^{2}+64 x-128\right)} \\\\ {=>f(x)=(x+2)\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x\left(x^{3}-16 x^{2}+80 x-128\right)+2\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x^{4}-16 x^{3}+80 x^{2}-128 x+2 x^{3}-32 x^{2}+160 x-256} \\\\ {=>f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256}\end{array}[/tex]
Hence required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]
Decimal Operati
1. Find the sum of the expression.
0.975 + 3.8
Answer:
4.775
Step-by-step explanation:
Answer:
4.775
Step-by-step explanation:
Add
0.975
3.800 =
4.775
i need help with my math
Answer:
12 hours
Step-by-step explanation:
Let the cruise ship travel x hours before the container ship caught up and the container ship starts y hour after the cruise ship starts.
So, the distance traveled by the cruise ship in x hours = distance traveled by the container ship in (x - y) hours.
So, x - y = 10 ........ (1) (Given)
And 5x = 6(x - y)
⇒ x = 6y .......... (2)
Now, solving equations (1) and (2, we get 5y = 10, ⇒ y = 2 hours.
And x = 6y = 12 hours.
So, the cruise ship travels for 12 hours before the container ship caught up. (Answer)
Katelynn earned $1240 in two weeks at the recreation
center during a trap shooting tournament. She earned
$480 the first week and the rest the second week.
Write an algebraic equation to model the situation.
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Step-by-step explanation:
Given,
Total amount earned = D = $1240
Amount earned in first week = y = $480
Let,
x be the amount earned in second week.
Therefore,
Total amount earned = Amount earned in 1st week + 2nd week amount
D = x + y
1240 = x + y
Solving for x;
[tex]x= 1240- y [/tex]
x = 1240-y can be used to model the situation where x is the amount earned in second week.
Keywords: linear equation, subtraction
Learn more about linear equations at:
brainly.com/question/10364988brainly.com/question/10435816#LearnwithBrainly
y = 3x - 1
12x – 4y = 12
Answer:
8 and 23
Step-by-step explanation:
let the 1st equation be i and 2nd be ii
now putting the value of x in eqn ii, we get
12x -4×(3x-1) = 12
12x-12x+4=12
x=12-4
x=8
again,
y=3×8-1
y=23
Jack ran 150 miles a week.Joanna ran 39 mote times than Jack.How many miles did Joanna run?
Answer:
5850 miles
Step-by-step explanation:
150 X 39 = 5850
We multiple because it says Joanna ran 39 more TIMES than Jack.
Joanna ran 5850 miles.
For every 8 tokens you have your friend has 3.
After you give half of your tokens to your friend Your friend now has 18 more tokens than you.
How many tokens did you start with.
Initially I had 48 tokens initially
Solution:Given that , For every 8 tokens you have your friend has 3
Then, let us assume that, we have 8n tokens. Then our friend will have 3n tokens
After you give half of your tokens to your friend Your friend now has 18 more tokens than you.
We have to find how many tokens did you start with
Now, after giving away half of tokens we will have 8n/2 = 4n tokens
And our friend will have 4n + 3n = 7n tokens.
And according to given information
Friends tokens – my tokens = 18 tokens
7n – 4n = 18
3n = 18
n = 6
Then, I will have initially 8n = 8 x 6 = 48 tokens.
Hence, I had 48 tokens initially
When a 49 pound weight is attached to a spring, the spring stretches 7 inches. Assume that the length of the spring y varies directly
with the weight attached x. Write and solve a direct variation equation to
find the length of the spring when a 63 pound weight is attached.
Write each percent as a fraction in lowest terms.
1. 15% Too 2. 36% tos
3. 44% 10
4. 45%
5. 8% 18o
- 6. 60%
Answer:
Step-by-step explanation:
1) 15%=15/100=3/20
2) 36%=36/100=9/25
3) 44%=44/100=11/25
4) 45%=45/100=9/20
5) 8%=8/100=2/25
6) 60%=60/100=6/10=3/5
In one year , Melinda’s parents spend 2,440.90 on cable and internet service . If they spend the same amount each month , estimate with the monthly fee is for cable and internet .
Answer:
The monthly fee for cable and internet is 200.
Step-by-step explanation:
Given:
Amount spend on one year for cable and internet service is 2440.90.
Now, to get the monthly fee for same amount spend on a year, by dividing the amount spend on a year with 12. As in one year there are 12 months.
So, [tex]2440.90\div 12[/tex]
=[tex]203.41[/tex]
By estimating the amount we get 200. As estimating means to round off the number to the nearest of whole number.
Therefore, the monthly fee for cable and internet is 200.
What is the answer to this?
Answer:
6
Step-by-step explanation:
Split the numerator/ denominator into like factors, that is
= [tex]\frac{72}{12}[/tex] × [tex]\frac{x^2}{x^2}[/tex] ← cancel to give 1
= 6 × 1
= 6
What’s the LCM of 6 and 9
Answer:
Step-by-step explanation:
The answer is 18
Answer: The LCM of 6 and 9 is 18.
Step-by-step explanation: Using your basic multiplication facts, you know that 6 and 9 are both multiples of 18. Check to make sure 18 is the LCM.
Plz tell me the domain
Answer:
Step-by-step explanation:
this is an solution
Kaitlin's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Kaitlin $5.50 per pound, and type B coffee costs $4.25 per
pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $448.00. How many pounds of type A coffee were used?
Answer:
The quantity of Type A coffee were used is 32 pounds .
Step-by-step explanation:
Given as :
The cost of type A coffee = $ 5.50 per pound
The cost of type b coffee = $ 4.25 per pound
The total cost of coffee = $ 448.00
The quantity of coffee of type B is twice than type A
Let The quantity of type A coffee = x pound
So, The quantity of type B coffee = 2 × x pound
Now, According to question
x × $ 5.50 + 2 x × $ 4.25 = $ 448
Or, x × $ 5.50 + x × $ 8.5 = $ 448
Or, 14 x = 448
∴ x = [tex]\frac{448}{14}[/tex]
I.e x = 32
∴ The quantity of type A coffee = 32 pound
And, The quantity of type B coffee = 2 × 32 = 64 pound
Hence The quantity of Type A coffee were used is 32 pounds . Answer
Final answer:
By setting up an equation based on the costs per pound and the relationship between quantities of coffee types A and B, we find that Kaitlin used 32 pounds of type A coffee for her blend.
Explanation:
We need to determine how many pounds of type A coffee were used in the blend, given that twice as many pounds of type B were used and that the total cost was $448.00. Let x be the pounds of type A coffee. Then, 2x will represent the pounds of type B coffee since twice as much type B is used compared to type A.
The cost equation can be represented as:
5.50x + 4.25(2x) = 448
Solving for x:
5.50x + 8.50x = 448
14x = 448
x = 448 / 14
x = 32
Therefore, Kaitlin used 32 pounds of type A coffee for her blend.
Help Please !!!
Will mark the brainliest.
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Answer:
The mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
Explanation:
The figure attached represents the situation.
The triangle on the left and the triangle on the right are similar triangles because they are right triangles and the marked angles are congruent.
The distance between the mirror and the basketball goal is represented by the unknown x.
By similarity:
[tex]10/6=x/4[/tex]Solving:
[tex]x=40\times 10/6=40/6=20/3[/tex]Thus, the mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.
Raffle tickets are sold and 6 prizes are available for the lucky draw. A total of 1,356 raffle tickets are sold for 4/5 dollars each and the 6 prizes cost 8 3/10 each. How much money was raise from the raffle tickets?
Answer:
US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of raffle tickets sold = 1,356
Cost of each raffle ticket = US$ 4/5
Number of prizes = 6
Cost of each prize = US$ 8 3/10
2. How much money was raised from the raffle tickets?
For easier calculation, let's convert the fraction numbers to decimal numbers:
Cost of each raffle ticket = US$ 4/5 = US$ 0.80
Cost of each prize = US$ 8 3/10 = US$ 8 + 0.30 = US$ 8.30
Now, we use this formula to calculate how much money was raised and the profits:
Profits = (Number of tickets sold * Cost of each ticket) - (Number of prizes * Cost of each prize)
Replacing with the real values, we have:
Profits = 1,356 * 0.80 - 6 * 8.30
Profits = 1,084.80 - 49.80
Profits = 1,035
US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.
Final answer:
The total amount of money raised from the sale of 1,356 raffle tickets, priced at 4/5 dollars each, is $1,084.8.
Explanation:
To determine how much money was raised from the raffle tickets, we first need to calculate the total cost of each ticket and then multiply it by the total number of tickets sold. The question states that each raffle ticket is sold for 4/5 dollars. Since a total of 1,356 raffle tickets were sold, the total amount raised can be calculated as follows:
Total amount raised = Price per ticket × Total number of tickets
= (4/5) × 1,356
= 1,084.8 dollars
Therefore, the total amount of money raised from the raffle tickets is $1,084.8.
I am a two-digit even number. I am
a multiple of 5. My tens digit is 8
more than my units digit.
Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solution. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous
Answer:
1; solution is not extraneous
Step-by-step explanation:
the value 3=3 is true, meaning its not extraneous and also I got it correct on the test
The value of x is 1, and the solution is not extraneous.
Given that,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
We have to determine,
The value of x and identify if it is an extraneous solution.
According to the question,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
To find the value of the x following all the steps given below.
Squaring both the sides to solve the equation,
[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, The solution is not extraneous.
Hence, The value of x is 1, and the solution is not extraneous.
To know more about Function click the link given below.
https://brainly.com/question/12431044
Nancy is taking inventory in the pharmacy to make sure there is enough eye medication in the pharmacy. She counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in stock. Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes. Calculate how many boxes of each Nancy needs to order.
Answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.
Step-by-step explanation:
Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.
So, there is a need to order (15 - 10) = 5 boxes of travoprost.
Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.
So, there is a need to order (12 - 3) = 9 boxes of latanoprost.
Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)
Final answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.
Explanation:
Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:
15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.
For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:
12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.
A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 feet,and the larger shipping container has side lengths of 10 feet. How many crates will fit in the largest shipping container?Explain your reasoning
Answer:
64 crates
Step-by-step explanation:
Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet
Larger Container (Cube) Side Length = 10 feet
We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.
Volume of Cube = x^3
Where x is the side length of the cube
Now,
Small Crate Volume = (2.5)^3 = 15.625 cubic feet
Large Container Volume = 10^3 = 1000 cubic feet
Number of crates that would fit = 1000/15.625 = 64
So, 64 crates will fit in the largest shipping container
64 crates will fit into the largest shipping container.
1. Calculate the volume of each crate:
Volume [tex]\( V_{\text{crate}} \)[/tex] of a cube with side length s:
[tex]\[ V_{\text{crate}} = s^3 = (2.5)^3 \] \[ V_{\text{crate}} = 2.5 \times 2.5 \times 2.5 \] \[ V_{\text{crate}} = 15.625 \text{ cubic feet} \][/tex]
2. Calculate the volume of the larger container:
Volume [tex]\( V_{\text{container}} \)[/tex] of the larger cube-shaped container:
[tex]\[ V_{\text{container}} = (10)^3 = 1000 \text{ cubic feet} \][/tex]
3. Determine the maximum number of crates that can fit:
To find out how many crates can fit into the container, divide the volume of the container by the volume of one crate:
[tex]\[ \text{Number of crates} = \frac{V_{\text{container}}}{V_{\text{crate}}} \] \[ \text{Number of crates} = \frac{1000}{15.625} \] \[ \text{Number of crates} \approx 64 \][/tex]
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? −5x2 − 9x + 12 = 0
A:a = −9, b = 12, c = 0
B: a = −5, b = −9, c = 12
C: a = 5, b = 9, c = 12
D:a = 9, b = 12, c = 0
Answer:
B
Step-by-step explanation
Answer:
Option B. a = −5, b = −9, c = 12
Step-by-step explanation:
The general form of the quadratic equation is as following
ax² + bx + c = 0
Where a, b and c are constants.
And the given equation is −5x2 − 9x + 12 = 0
Comparing the given equation to the general form
ax² + bx + c = 0
−5x2 − 9x + 12 = 0
So, a = -5 , b = -9 and c = 12
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
So, the answer is option B: a = −5, b = −9, c = 12
SINGLE AND DOUBLE REPLACEMENT
ASSIGNMENT 4
Balance the equations below:
1. Al +_HCI- H2 + AICI:
Answer:
gl hf
Step-by-step explanation:
Supposed charity received a donation of $23.9 million. If this represents 54% of the charity donated funds what is the total amount of its donated funds? round your answer to the nearest million dollars.
Total amount of funds is $44.26 million.
Step-by-step explanation:
Given,
Donation received = $23.9 million
As it represents 54% of charity.
Let,
Total amount = x
Therefore,
54% of x = 23.9 million
[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]
Dividing both sides by 0.54
[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]
Total amount of funds is $44.26 million.
Keywords: percentage, division
Learn more about percentages at:
brainly.com/question/3950386brainly.com/question/4021035#LearnwithBrainly
Help me find the value of the missing variable
Answer:
Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6
Moves to one side. 12=x
x=12
Step-by-step explanation:
x=12
Step-by-step explanation:
You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.
QUICK!!! WILL GIVE BRAINLIEST!!!!
The table represents a linear function.
A two column table with six rows. The first row, x, has the entries negative 4, negative 2, negative 1, 1, 2. The second column, y, has the entries, negative 2, negative 10, negative 14, negative 22, negative 26.
What is the slope of the function?
–8
–4
2
5
Answer:
-4
Step-by-step explanation:
You can tell because every time the slope decreases by 5.
Answer:
-4
Step-by-step explanation:
Take the first two sets of points (-4,-2) and (-2,-10)
Then use the formula Y2 - Y1 / X2 - X1 to find the slope
-10 + 2 / -2 + 4 = -8/2 which can be reduced to -4
-3x+12y=24 What is the Y intercept
Answer:
(0,2)
Step-by-step explanation:
y-intercept: when x = 0
-3(0) + 12y = 24
12y = 24
y = 2
Factor the expression into an equivalent form. ab^2 - b
Answer:
ab² - b = b(ab -1)
Step-by-step explanation:
The variable b is common to both terms here. Thus,
ab² - b = b(ab -1)
Sheldon needs to buy 8 gallons of coleslaw for a family reunions the table shows the prices for different size of two brands of coleslaw use the table for exercises 11 and 12
3) 8p + 7q= 43
2p-7=-q
I need to solve using substitution. thanks.
Answer:
p=1, q=5. (1, 5).
Step-by-step explanation:
8p+7q=43
2p-7=-q
------------------
q=-2p+7=7-2p
8p+7(7-2p)=43
8p+49-14p=43
8p-14p=43-49
-6p=-6
6p=6
p=6/6=1
2(1)-7=-q
2-7=-5=-q
q=5
Which of the following expressions could be used to represent "three less than half a number"?
A. 3 - 1/2n
B. 1/2n - 3
C. 3n - 1/2
D. 1/2 - 3n
Answer:
B. 1/2n - 3
Step-by-step explanation:
One way to get half a number is to multiply it by 1/2.
The phrase "a number less than an other number" often indicates subtraction.
[tex]\frac{1}{2}n-3[/tex]
Answer:1/2n-3
Step-by-step explanation:
because three less than half of a number means half minus three
F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]
So
[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]
Hence,
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Keywords: functions, Function composition
Learn more about functions at:
brainly.com/question/4279146brainly.com/question/4354581#LearnwithBrainly