how can you divide polynomials
Answers
Polynomials can be divided using long division method and
synthetic division method.
What is a polynomial?
Algebraic expressions which are made up of coefficients and variables are called polynomials.
For example x + 3, 3y² -10, r³, t³ + 4t³ - 80, etc.
Polynomials can be classified as monomials, binomials and trinomials based upon the number of terms present.
According to the given question:
There are two methods that can be employed while dividing two given polynomials:
1. Long Division Method
The long division method is the most frequent and general method for dividing polynomials by binomials or any other form of polynomials.
Steps:
Step 1: Divide the dividend’s first term by the divisor’s first term, and use it as the quotient’s first term.
Step 2: Multiply the divisor, then place the product beneath the dividend
Step 3: To make a new polynomial, subtract.
Step 4: Use the new polynomial obtained after subtraction to repeat the operation.
2. Synthetic Division Method
It is a technique for dividing a polynomial by a linear binomial using only the coefficient values. We write the polynomials in standard form from the greatest degree term to the lowest degree term in this manner.
Steps:
Step 1: Ensure that the divisor is in the form of x − k.
Step 2: Write the dividend coefficients on the right and k on the left to set up the division.
Step 3: Now, reduce the coefficient of the dividend’s highest degree term to zero.
Step 4: Multiply k by that leading coefficient and write the product below the second coefficient on the dividend’s left side.
Step 5: Multiply the numbers in the second column.
Step 6: Multiply k by the number obtained in step 5 and write the result in the next column to the right.
Step 7: Finally, we’ll write the final solution, which will be one degree below the dividend.
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Related Questions
Of the 50 U.S. states, 4 have names that start with the letter \text{W}Wstart text, W, end text.
What percentage of U.S. states have names that start with the letter \text{W}Wstart text, W, end text?
Answers
Answer:
8%
Step-by-step explanation:
4 is what percentage of 50 ?
4/50 X 100% = 8%
I need help please please please
Answers
Answer:
$28
Step-by-step explanation:
5.5% is $1.54 of what number? (%/100= is/of)
5.5/100 = 1.54/X
X = (1.54 * 100) / 5.5 = $28
Answer:
sus
Step-by-step explanation:
O_O
A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 230 feet by 180 feet
Answers
Answer:
14 bags
Step-by-step explanation:
Dimension of lawn : 230 feet by 180 feet
area of rectangle is given by length * width
Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet
Given that one bag of fertilizer covers 3000 square feet of lawn.
Thus , to find no. of bags required to cover whole lawn will be
total area of lawn/area which one bag of fertilizer covers
no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet
= 13.8 bags.
As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.
Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing time to failure (in hours) at 90% breaking strength.
0.52 1.80 1.52 2.05 1.03 1.18 0.80 1.33 1.29 1.12
3.34 1.54 0.08 0.12 0.60 0.72 0.92 1.05 1.43 3.05
1.81 2.17 0.63 0.56 0.03 0.09 0.18 0.34 1.51 1.45
1.52 0.19 1.55 0.02 0.07 0.65 0.40 0.24 1.51 1.45
1.60 1.80 4.69 0.08 7.89 1.58 1.64 0.03 0.23 0.72
(a) Find the range.
(b) Use a calculator to calculate ?x and ?x2.
(c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure.
(d) Use the results of part (c) to compute the coefficient of variation.
What does this number say about time to failure?
1) The standard deviation of the time to failure is just slightly smaller than the average time.
2) The coefficient of variation says nothing about time to failure.
3) The standard deviation of the time to failure is just slightly larger than the average time.
4) The standard deviation is equal to the average.
Why does a small CV indicate more consistent data, whereas a larger CV indicates less consistent data? Explain.
1) A small CV indicates more consistent data because the value of s in the numerator is smaller.
2) A small CV indicates more consistent data because the value of s in the numerator is larger.
Answers
Answer:
range = 7.87
X = 62.12, X²= 164.3516
mean = 1.2424
variance = 1.779
standard deviation = 1.33379
coefficient of variation = 107.3559%
Step-by-step explanation:
a.) The range =
highest number - lowest number
= 7.89 - 0.02
= 7.87
b.) from the attachment I solved for X and X²
∑X = 62.12
∑X² = 164.3516
c.)
the mean = ∑x/n
n = 50
= 62.12/50
= 1.2424
variance =
σ² = [∑x²-(∑x)²/n] / n-1
= [164.3516 - (62.12)²/50] / 50-1
= 164.3516 - 77.17788/49
= 87.173712/49
= 1.779
standard deviation = √σ
= √1.779
= 1.33379
d. coefficient of variation
= σ/mean * 100
= 1.33379/1.2424 * 100
= 107.3559
This number tells us that the the standard deviation of the time to failure is larger than the average time. option 3 is the correc4 answer here
A) The range of the given values is; 7.87
B) The values of ∑X and ∑X² are respectively; 62.12 and 164.3516
C) The values of the sample mean, variance and standard deviation are respectively; 1.24, 1.78 and 1.334
D) The coefficient of variation is; 107.356
Mean, Range, variance, standard deviationA) Formula for range is;
Range = Highest term - Lowest term
Range = 7.89 - 0.02
Range = 7.87
B) Sum of all the given 50 epoxy samples is gotten to be;
∑X = 62.12
From online statistics calculator, we have; ∑X² = 164.3516
C) Formula for sample mean here is;
x' = ∑x/n
x' = 62.12/50
x' = 1.24
Formula for variance is;
σ² = [∑x² - [(∑x)²/n]]/(n - 1)
σ² = (164.3516 - (62.12²/50))/(50 - 1)
σ² = 1.78
Formula for the standard deviation is;
σ = √variance = √1.78
σ = 1.334
D) Formula for coefficient of variation is;
CV = (σ/x') * 100
CV = (1.33379/1.2424) * 100
CV = 107.356
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An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$5000 with a standard deviation of o-$250
distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses.
If we create a sampling distribution with a sample of 64 homeowners, what is the z-score that corresponds to a sample average of $5100?
Round to four decimals
Type your answer.
1 point
Answers
Answer:
To find the z-score, we use the formula:
z = (x - mu) / (sigma / sqrt(n))
where:
x = sample mean = $5100
mu = population mean = $5000
sigma = population standard deviation = $250
n = sample size = 64
Substituting the values, we get:
z = (5100 - 5000) / (250 / sqrt(64))
z = 2.56
Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).
Step-by-step explanation:
I clicked on the black picture. thought is was the box to enter the answer.
Which expression uses the associative property to make it easier to evaluate
(16- })?
OA. (16 )2
OB. ( 16)
Oc. 16(3)
OD. ( 16)
Answers
Answer:
Option B: (½•16)⅓
Step-by-step explanation:
The associative property states that we can add or multiply numbers in a group regardless of how those numbers are grouped. And that we will get the same answer.
For example;
x(y•z) = (x•y)z = (x•z)y
Now in our question, we want o evaluate; ½(16•⅓)
Using the associative property, the best expression will be: (½•16)⅓
It's the best expression because the terms in the bracket are easy to multiply out without remainder.
Thus, option B is correct
A school spent $780,000 in one year to pay all of its teachers and administrators. The school has a total of twenty-four teachers and administrators combined. If teachers make $35,000 per year and administrators make $40,000 per year, how many teachers and how many administrators does the school have?
Answers
Answer: Impossible
Step-by-step explanation: Even if 24 people were on the teacher salary, 780,000 still couldn't cover them all.
4x + 8 + 6x – 5 = 33
Answers
Answer:
x = 3
Step-by-step explanation:
4x + 8 + 6x – 5 = 33
10x + 3 = 33
10x = 30
x = 3
Best of Luck!
This summer Andrea's family will
rent a cabin in the mountains for
two weeks. The total cost is $500.
About how much does the cabin
cost per day?
Answers
Answer:
$35
Step-by-step explanation:
500 divided by 14 which is how many days are in two weeks it solves to 35
I need your help! there’s a photo above ^^
Answers
Answer:
1. c 2. No, its not the original figure. Its 270 degree turn.
Step-by-step explanation:
Answer:
1.) C 2.) choice d flipped left to right.
of 100 athletes 31 like to run 65 like to walk ans 22 neither like to walk nor run .how many athletes like to both run or walk
Answers
There are 22 athletes who like both running and walking.
Let R be the set of athletes who like to run, and
let W be the set of athletes who like to walk.
Then we want to find the size of the intersection R ∩ W.
We know that there are 31 athletes who like to run,
65 athletes who like to walk, and
22 athletes who like neither.
Therefore, the total number of athletes who like to run or walk (or both) is:
31 + 65 - 22 = 74
This number includes athletes who like both running and walking, as well as athletes who like only running or only walking.
Now we can use the formula:
|A ∪ B| = |A| + |B| - |A ∩ B|
So |R ∪ W| = |R| + |W| - |R ∩ W|
Substituting the known values, we get:
74 = 31 + 65 - |R ∩ W|
Simplifying, we get:
|R ∩ W| = 22
Therefore, there are 22 athletes who like both running and walking.
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seb buys 1 gallon of paint that covers 400 square feet
Answers
The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.
How to find the amount of paint ?There would be two walls with 10 x 16 dimensions so the area is :
= 2 x 10 x 16
= 320 square feet
Two walls with 20 x 10 dimensions :
= 2 x 20 x 10
= 400 square feet
The total area is :
= 400 + 320
= 720 square feet
One gallon of paint can cover 400 square feet so the number of gallons needed is:
= 720 / 400
= 1. 8 gallons
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Full question is:
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.
use four rectangles to estimate the area between the graph of the function and the x-axis on the interval using the right endpoints of the subintervals as the sample points
Answers
we have the function
f(x)=6/(7x)
the interval [2,6]
Divide into fur rectangles
the width of each rectangle is equal to
(6-2)/4=1
the intervals are
(2,3) (3,4) (4,5) and (5,6)
using the right endpoints
the approximate area is equal to
A1=f(3)*(1)=[6/(7*3)]*(1)=6/21
A2=f(4)*(1)=[6/(7*4)]*(1)=6/28
A3=f(5)*(1)=[6/(7*5)]*(1)=6/35
A4=f(6)*(1)=[6/(7*6)]*(1)=6/42
therefore
the approximate area is
A=(6/21)+((6/28)+(6/35)+(6/42)
simplify
A=(6/7)*[(1/3)+(1/4)+(1/5)+(1/6)]
A=(6/7)*[(20+15+12+10)/60]
A=(6/7)*[57/60]
A=57/70 unit2 -----> exact answerlet C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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what is the answer pls Question 29 of 45
In the triangle below, what is the length of MN?
OA. 50
OB. 100
OC. 20
OD. 40
50
20
M
50
Answers
The calculated length of the segment MN in the triangle is 20
How to find the length of the segment MN in the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
The third angle in the triangle is calculated as
Third angle = 180 - 50 - 50
Evaluate
Third angle = 80
The length of the segment MN is then calculated as
MN/sin(50) = 20/sin(50)
This gives
MN = sin(50) * 20/sin(50)
Evaluate
MN = 20
Hence, the length of the segment MN in the triangle is 20
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The surface area of the United States is 3.797 million square miles. The state of Alaska, our largest state in terms of area, occupies 655,400 square miles. Using ratios, determine what percentage of the surface area of the United States is occupied by Alaska, rounded to the nearest whole number.
Answers
Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%
We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%
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HELP ME WITH THIS MATHS QUESTION
IMAGE IS ATTACHED
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Each point moves to the same distance on the other side of the mirror line. The slope of the mirror line is 1, so the points move along a line perpendicular to that, one with a slope of -1. You can make sure the distances are the same by counting the grid squares.
use the model for projectile motion, assuming there is no air resistance. a shot fired from a gun with a muzzle velocity of 1200 feet per second is to hit a target 3400 feet away. determine the minimum angle of elevation of the gun. (round your answer to two decimal places.)
Answers
The minimum angle of elevation of the gun is approximately 4.42 degrees (rounded to two decimal places).
To solve this problem, we can use the model for projectile motion assuming no air resistance. The equation we need is:
range = (velocity^2 * sin(2 * angle)) / gravity
where range is the horizontal distance the projectile travels (3400 feet),
velocity is the muzzle velocity (1200 feet per second),
angle is the angle of elevation we want to find,
and gravity is the acceleration due to gravity (32.2 feet per second squared).
We can rearrange this equation to solve for the angle:
\(angle = arcsin((range * gravity) / (velocity^2 * 2)) / 2\)
Plug in the given values:
\(angle = arcsin((3400 * 32.2) / (1200^2 * 2)) / 2\)
angle = arcsin(0.153) / 2
angle ≈ 0.077 radians
Now convert radians to degrees:
angle = 0.077 * (180 / pi)
angle ≈ 4.42 degrees.
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The tax rate as a percent, r, changed an item can be determined using the formula c/p-1=r, where C is the final cost of the item and P is the price of the item before tax Louis rewrite the equation to solve for the final cost of the item: c=p(1+r). What is the final cost of a $40 item after an 8% tax is applied
Answers
Answer:
\( c= 40(1+0.08) = 40*1.08= 43.2\)
The final cost would be $43.2
Step-by-step explanation:
For this case from the notation given we know that the final cost is given by C and the formula is:
\( C= p(1+r)\)
Where C is the final cost, p the price of the item before tax and r the tax on fraction. And for this case we want to find the final value with 8% of tax so we can do the following operation:
\( c= 40(1+0.08) = 40*1.08= 43.2\)
The final cost would be $43.2
solve the inequality:
||x-3|-2|≤1
Answers
Answer:
-1 ≤ x ≤ 5
Step-by-step explanation:
-1 ≤ x ≤ 5 is the answer
10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
Answers
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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Fill in the table using this function rule.
y = 6x + 5
Answers
Answer:
x=3, y=23
x=6, y=41
x=8, y=53
x=9, y=59
Step-by-step explanation:
x=3, y=6(3)+5
y=18+5
y= 23
x=6, y=6(6)+5
y=36+5
y= 41
x=8, y=6(8)+5
y=48+5
y=53
x=9, y=6(9)+5
y=54+5
y=59
A rich relative dios and you inherit $120,000. How much will you have for your retirement of age 60) if you invest the inheritance in an account paying 2.0% annual interest compounded monthlyassuming that you are 18 years old now?O A. 569,287,040,00OB. 5481,030.54O C. $287.040,00OD $1,700,400.00previow answors
Answers
To answer this question we will use the following formula for compounded monthly interest:
\(A=A_0(1+\frac{r}{12})^{12t},\)where A₀ is the initial amount, r is the annual interest as a decimal number and 12 is the number of years.
Notice that:
\(60-18=42.\)Therefore, substituting t=42, r=0.02, and A₀=120000 we get:
\(A=120000(1+\frac{0.02}{12})^{12\cdot42}\text{.}\)Simplifying the above result we get:
\(\begin{gathered} A=120000(1.001\bar{6})^{504} \\ \approx120000\cdot2.314747889 \\ \approx277769.75 \end{gathered}\)Answer: $277,769.75.
Find the length of the third side. If necessary, round to the nearest tenth.
24
14
Answers
Answer:
The answer is 19.49
Step-by-step explanation:
Hope this help you
Answer:
19.5
Step-by-step explanation:
19.49= 19.5
because of the nearest tenth
What is the density of a brownie the shape of a cube weighing 15 grams measuring 5 cm on a side?
Answers
Answer:
0.12 g/cm³
Step-by-step explanation:
Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:
V = s³ = (5 cm)³ = 125 cm³
Then the density is ...
ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³
The density of the brownie is 0.12 g/cm³.
Complete the inequality to represent the following: 13 times a number x
is less than or equal to 200.
Answers
The value for the Inequality 13x ≤ 200 is x ≤ 15.384.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
13 times a number x is less than or equal to 200.
Now, Writing the Inequality Mathematically
13x ≤ 200
x ≤ 200 / 13
x ≤ 15.384
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2x+3y=-12
2x+t=-16
X=. Y=
Help plz
Answers
To make this problem solvable, I have replaced the 't' in the second equation for a 'y'.
Answer:
x = -9
y = 2
Step-by-step explanation:
Solve the system:
2x + 3y = -12 [1]
2x + y = -16 [2]
Subtracting [1] and [2]:
3y - y = -12 + 16
2y = 4
y = 4/2 = 2
From [1]:
2x + 3(2) = -12
2x + 6 = -12
2x = -18
x = -18/2 = -9
Solution:
x = -9
y = 2
A passenger train has 812 people seated. Each train seats 70 people. So there are 11 train cars filled. How many people are in car not full
Answers
What is 14/15 over 4/7 equal to
Answers
Answer:
\(\frac{0.93}{0.57}\)
Step-by-step explanation:
Simplify both of the fractions so \(\frac{14}{15}\) to get 0.93 and \(\frac{4}{7}\) to get 0.57.
Then you put them back into fraction form.
So what s the meaning for X and Y
Answers
The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates. (x,y) has the meaning of a complex number: x is the real part and y is the imaginary part: x+yi. (x,y) has the meaning of a plane's vector from origin of coordinates.