The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1
When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).
If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.
Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1
Let f(x) = x^6 + 3x^4 + 3x^2 + 1 and g(x) = x^3 + 3x^2 + 3x + 1
We can write these polynomials as:
f(x) = x^6 + 3x^4 + 3x^2 + 1
f(x) = (x² + 1)^3
The factors of polynomial f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and (x² + 1)^3
And g(x) = x^3 + 3x^2 + 3x + 1
g(x) = (x + 1)^3
And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1
Therefore, the HCF of the polynomials f(x) and g(x) = 1
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For each of these variables, which of the mean, median, or mode would be the best choice to describe the typical behavior of the variable? Why?
Sales prices of houses
Age of 1st graders
Heights of women
In the case of Typical behavior of the sales prices of houses median is the best term. In the case of Ages of 1st graders mean is the best way of central tendency and for Heights of women mode is the best measure.
First of all we have to know the Mean, median and mode. The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
In the case of typical behavior of the variable sales price of houses, the Median will be the best measure of central tendency because the median will not get affected by the higher/lower prices of houses.
The age of each kid will be almost the same. In order to represent the typical behavior of the variable Age of 1st graders, the mean will be the best measure of central tendency.
Incase of Heights of women, the mode will be the best measure of central tendency as it will describe the height that most of the females have.
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1) state whether the dilation with the given scale factor would be a reduction or an enlargement
k=4
k=1/2
k= .75
k=5/2
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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5x+8-5-x=3
It keep show other questions
Answer:
x = 0
Step-by-step explanation:
5x+8-5-x=3
assuming you are looking for x5x + 8 - 5 - x = 3
4x + 3 = 3
4x = 0
x = 0
----------------------------
check5 × 0 + 8 - 5 - 0 = 3
8 - 5 = 3
3 = 3
the answer is goodWhat does Y=3x + 15 look like on a graph
Answer:
Step-by-step explanation:
y = 3x + 15 represents a straight line whose y-intercept is (0, 15) and which has the steep positive slope m = 3.
Answer:
it looks like that
Step-by-step explanation:
Express 60 as the product of its prime numbers
Answer:
60 = [tex]2^2[/tex] * 3 * 5
Step-by-step explanation:
The process of prime factorization is when one breaks up a number such that it can be represented as the product of many prime numbers. One does this by dividing the prime number by its smallest prime factor. Then one will divide the composite factor by its smallest prime factor, and so on. All of the resulting prime numbers are prime factors of the original number.
60 = 2 * 30
30 = 2* 15
15 = 3 * 5
60 = [tex]2^2[/tex] * 3 * 5
Can somebody help me with this question?
Answer:
answer is 6 btw does ~ means congruent
Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buts two new pair of pants.
There are 9 possible outcomes to buy two new pair of pants.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Given:
we have the following Styles
Boot cut (B), Skinny (S), and Relaxed fit (R).
So, if her buys two paints then the possible combination he can take as
Boot cut x Boot cut
Skinny x Skinny
Relaxed fit x Relaxed fit
Boot cut x Skinny
Boot cut x Relaxed fit
Skinny x Relaxed fit
Skinny x Boot cut
Relaxed fit x Boot cut
Relaxed fit x Skinny
Hence, there are 9 possible ways.
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What is the value of x if the points A 4 3 and B x 5 are on the circle with Centre O 2 3?
The value of x with points A ( 4, 3 ) and B ( x ,5 ) on the circle and O(2,3) as centre is equal to 2.
As given in the question,
Points A(4,3 ) and B ( x, 5 ) are on the circle.
Centre of the circle is represented by O( 2,3)
OA and OB represents the radius of the circle.
This implies
OA = OB
Using distance formula we get,
√ ( 2 - 4 )² + ( 3 - 3 )² = √ ( 2 - x )² + ( 3 - 5 )²
⇒ √ 4 + 0 = √ 4 - 4x + x² + 4
⇒4 = 4 - 4x + x² + 4
⇒4 - 4x + x² = 0
⇒ ( x - 2 )² = 0
⇒ x - 2 = 0
⇒ x = 2
Therefore, the value of x for the given point of the circle is equal to 2.
The above question is incomplete , the complete question is :
What is the value of x , if the points A(4, 3) & B(x, 5) are on the circles with Centre O(2, 3), find the value of x.
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The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
If 85% of the workers in a factory factory are male and the number of female is 36. find the total number of workers in a factory
The total number of workers in the factory is = 240.
It is given that,
Male = 85%
Female = 36
If we assume that the total workers account for 100%, then we know that Female workers account for 15% of the workforce (as 100-85= 15).
Now,
=> 15% = 36
If, 1% = 36/15
then, 100% = 36/15*100
= 12*20
= 240.
Therefore, the answer is 240.
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Tiles with the numbers 1 through 9 are placed in a bag. What is the probability of choosing an even number that is greater than or equal to 4?
have anyone figured it out yet? pleaseee i need answer
The probability of choosing an even number that is greater than or equal to 4 is 0.3333 or 33.33%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Tiles with the numbers 1 through 9 are placed in a bag.
The total outcomes will be
Total outcome = 9 {1, 2, 3, 4, 5, 6, 7, 8, 9}
The probability of choosing an even number that is greater than or equal to 4 will be
Favorable event = 3 {4, 6, 8}
Then the probability will be
[tex]\rm P = \dfrac{3}{9}\\\\P = 0.3333\\\\P = 33.33 \%[/tex]
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Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A, a 50%
chance of getting a job offer from company B, and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
The probability of Johnny not getting a job offer from either company is 0.8
Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A,
A = 0.6
a 50% chance of getting a job offer from company B,
B = 0.5
and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
Suppose, probability of an event A occurring is P(A)
and that of is B IS P(B)
P(A) = 0.6
and
P(B)= 0.5
probability of either or P(AUB)=0.3
Now we need to find the probability of neither nor, which is
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = P(A) + P(B) -P(A∪B)
= 0.6 + 0.5 - 0.3
= 0.8
Now the events are mutually exclusive, so
Therefore, the probability of neither nor is 0.8
The probability of Johnny not getting a job offer from either company is 0.8
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Step 4: Calculating the right recipe for Jerome
Twenty-two people are running in tomorrow’s road race and Jerome thinks they will each want two cups of energy drink.
How many cups of energy drink does Jerome need to make?
Answer:
44
Step-by-step explanation:
If there are 22 people running and they each want two energy drinks, then Jerome needs to make 44 cups. 22 times 2 is 44
Write and Solve an equation to determine the missing dimension of the prism with a volume of 160cm. Height is missing the numbers given are 10cm and 2cm
Can someone help me in number 3?
Answer:
1.5 kilograms
Step-by-step explanation:
You need to convert grams to kilograms, this means you must divide the mass value by 1000 to find your answer.
1,500/1,000 = 1.5
Answer:
For 1500 grams in kilogram we get 1.5 kg
Step-by-step explanation:
to convert a gram into a kilogram we have to divide the gram term by 1000
In APQR, PR = 23 mm, QR = 39 mm, and
m/R = 163º.
Use an inverse trigonometric ratio to find m∠A. You know the lengths of the ... In △PQR, PR = 23 mm, QR = 39 mm, and m∠R = 163°.
Find the value of X.
Answer:
im not sure but I think its 8.3
6x + y = 20
x - 4y = -5
The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]
The given equations are
[tex]6x+y=20\\x-4y=-5[/tex]
We need to find the value of [tex]x[/tex] and [tex]y[/tex]
First let's take equation [tex]2[/tex] and we can simplify it
[tex]x-4y=-5\\x=-5+4y[/tex]
Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is
[tex]6x+y=20\\6(-5+4y)+y=20[/tex]
We can open the bracket and simplify
[tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]
Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]
[tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]
The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.
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Bilquis finds some nickels and quarters in her piggy bank. How much money (in
cents) does she have if she has 7 nickels and 5 quarters? How much money
does she have if she has n nickels and q quarters?
Answer:Bilquis finds some nickels and quarters in her piggy bank. How much money (in
cents) does she have if she has 7 nickels and 5 quarters? How much money
does she have if she has n nickels and q quarters?
Step-by-step explanation:
Answer: 157 cents ($1.57)
Step-by-step explanation: Nickels are worth 5 cents each, so 5 cents times 7 nickels equals a total of 35 cents. After that, we have 5 quarters which cost 25 cents each, so 25 cents times 5 quarters equals a total of 125 cents. Combine these two products, and you get 157 cents. Or, if you want it in dollars, you can divide 157 by 100 cents (there are 100 cents in a dollar) and end up with $1,57.
The 7th term of a geometric progression is 48 the 8th term is -16 find the common ratio
Answer:
48 = 768* (r)^2
thus, r = 0.25
solving for a(7)
a(7) = 768 * (0.25)^(5)
a(7) = 0.75
Step-by-step explanation:
Answer:
r = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The common ratio r is calculated as
r = [tex]\frac{a_{8} }{a_{7} }[/tex] = [tex]\frac{-16}{48}[/tex] = - [tex]\frac{1}{3}[/tex]
Can you help me with this
a) The ordered pair so that the set still remains the function is (-5, 17)
b) The ordered pair so that the set does not remain the function is (-26, 15).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
A Relation is said to be a function if the input value or the x- value is unique and have their corresponding output.
But if the input value repeats then it may no longer be a function.
First, Add a ordered pair so that the set still remains the function as
(-5, 17)
and, Add a ordered pair so that the set does not remain the function as
(-26, 15).
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Explain why (-5)2 -52 is true.
Step-by-step explanation:
(-5)2-52-10-52-62hope it helps.
Answer:
(-5)2 -52-10-52-62hope it is helpful to you
HELP PLZ I NEED TO GET THIS TEST DONE AND IM SO LOST can someone help me with the answers?
Answer:
I answered question 9
Step-by-step explanation:
What is the Oder of rotation? What is the angle of rotation? Express in degrees and as a fraction of a turn?
Answer:
Order of rotation is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure.
Step-by-step explanation:
We have the counter and the clockwise rotation where counter you move back in in 90 degrees and clockwise you move forward
Graph the solution to this inequality on the number line.
1/3x-3<-1 5/6
Help please asap
Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.
what is inequality ?A relationship between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. Different inequalities are employed to contrast values of all sizes. By changing the two sides until only the variables are left, one can solve many straightforward inequalities. But a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
given
the inequality for x 1/3 x - 3 -1 5/6 must first be resolved.
2 plus 3 on both sides
Simply multiply both sides of 1/3x by 3x31/2,
and then graph x31/2 on a number line.
Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.
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1. Choose your answer inside the box.
vertex
face
net
solid figures
sphere
cone
edge
rectangular prism
cube
square
pentagonal prism
pyramid
cylinder
rectangle
1. Flat parts of the solid figure.
2. The line where two faces meet.
3. The point where three edges meet.
4. Closed figure that can be folded into a closed 3-dimensional figure. It is a pattern
you can form into solid figures.
5. A polyhedron whose bases are congruent polygons and whose lateral faces are
parallelograms.
6. A polyhedron whose base is a polygon. The lateral faces are triangles
7. A solid figure with a curved surface of points that are all of the same distance from
the other
8. A solid figure with curved surfaces and one circular base
9. A solid figure with curved surfaces and that has two circular bases that are
congruent and parallel
10. A polygon with four equal sides and angles.
Answer:
I AM sure u will find answers in googl
let me go check
Step-by-step explanation:
FaceEdgeVertexNetPrism PiramidSphereConeCylinder SquareRussell randomly surveys seventh graders in his schools and finds 6 of 30 attend summer camp. if there are 200 seventh graders in his school, about how many are expected to attend summer camp.
Answer:
40
Step-by-step explanation:
Reflect shape A in the line y = -x. (See picture)
Answer:
See picture below
Step-by-step explanation:
Your mortgage payment is $954. 32/month. Using proportions, what is the minimum yearly amount you must have in realized income to keep your housing expenses in the acceptable range? $Fill in the blank text field 1
The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What is meant by mortgage payment?Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount in the principal part. Borrowing money has a cost, which is interest. Both the interest rate and the loan balance affect how much interest you pay.
You repay your mortgage loan through monthly payments. This will often be a monthly payment that aids in your gradual mortgage repayment. There will also be taxes, insurance premiums, and loan interest due.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]$& \frac{\text { Mortgage }}{\text { Acceptable Rate\% }} * 12 \\[/tex]
substitute the values in the above equation, we get
[tex]$& =\frac{954.32}{0.27} * 12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What do you mean by mortgage payment?Generally speaking, mortgage payments are made up of principal, interest, taxes, and insurance. The sum in the principle component is deducted from your outstanding loan balance. Interest is a cost associated with borrowing money. The amount of interest you pay depends on both the interest rate and the loan balance.
Monthly payments are made to pay down your home loan. This will frequently be a monthly payment to help you slowly pay down your mortgage. Taxes, insurance premiums, and loan interest will all need to be paid.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]\frac{Mortage}{Acceptable rate } *12[/tex]
substitute the values in the above equation, we get
[tex]\frac{954.32}{0.27} *12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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If Patrick scored 33 marks out of a possible 55 marks, what % did he get?
Answer:
60%
Step-by-step explanation:
33/55 = 0.6 which is 60%