Certain polynomials with integer coefficients fall into the category of substantially prime polynomials in q[x] if and only if the ideal they create in z[x] contains a (nonzero) integer.
What are polynomials?A polynomial is an expression in mathematics that consists of indeterminates (also known as variables and coefficients) that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. x2 4x + 7 is an illustration of a polynomial of one uncertain x.
In both mathematics and science, polynomials are widely used. For instance, they are used to define polynomial functions, which can be found in a variety of contexts, from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems.
Calculations:
Let d=degP.
Then the Q-vector space V=Q[X]/(P) is d-dimensional.
The residue classes modulo (P) of X2,X3,X5,… are linearly dependent over Q, so there exist a2,a3,a5,…∈Z not all zero such that a2X2+a3X3+a5X5+⋯∈(P).
This shows that there is Q∈Z[X], Q≠0 such that PQ=a2X2+a3X3+a5X5+⋯.
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Differentiate the following equation [tex]sin^2(\frac{\pi }{6} -x)[/tex]
[tex]\sin^2\left(\frac{\pi }{6}-x \right)\implies \left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^2 \\\\\\ \stackrel{\textit{\LARGE Chain Rule}}{2\left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^1 \left[ ~~ \cos\left(\frac{\pi }{6}-x \right) ~~ \right] (-1)}\implies \boxed{-2\sin\left(\frac{\pi }{6}-x \right)\cos\left(\frac{\pi }{6}-x \right)}[/tex]
Find the total amount given the original price and tax rate. round to the nearest hundredth if necessary. original price: $123.28 tax rate: 7.5% enter the correct answer in the box.
The Total amount to pay including the tax will be $132.52
In the given question, For the Total amount, we know that we have to add the Tax rate to the Principal amount. It is mentioned that the Principal amount P = $123.28 and the Tax rate is 7.5%. Firstly we have to calculate what amount of interest is to be charged upon the Principal amount. To calculate Interest we have the formula :
=> I = (P * R)/100 , where I = Interest, P = Principal Amt, R = Interest Rate
=> I = (123.28 * 7.5)/100 => I = 9.24
We get Interest amount = $9.24
To calculate the Total amount, We have the formula: T = P + I
where, T = Total Amount, P = Principal Amount, and I = Interest Amount
=> T = 123.28 + 9.24 => T = 132.52
Hence, the Total Amount is $132.52
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If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
By using the fact that EBC and ABE are supplementary angles, we will see that the measure of angle EBF is 106 degrees.
How to find the measure of the angle EBF?First, we can notice that angles EBC and ABE are supplementary angles, which means that their measures add up to 180°.
Then we can write:
m∠EBC + m∠ABE = 180°
Replacing what we know we get:
3y + 10 + 2y - 20 = 180°
Now we can solve this linear equation for y, we will get:
5y - 10 = 180
5y = 180 + 10
y = 190/5 = 38
Then we have that:
EBC = 3*38 + 10 = 124°
ABE = 2*38 - 20 = 56°
Now, in the image it says that:
ABE = 2b = 56°
then b = 56°/2 = 28°
And ABF = 7b - 24 = 162°
Then:
EBF = ABF - ABE = 162° - 56° = 106°
We conclude that the measure of angle EBF is 106 degrees.
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The standard deviation for a data set is 0. Determine whether each conclusion about the data is true or false.
a. The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different.
b. All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value.
Statement a : "The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different" is false.
Statement b : "All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value" is true
What is standard deviation?
This is a term in statistics that represent the amount of variation in a data set or simply put the spread of the data set. Standard deviation is solved from the mean of the data, that is we get mean first before solving for standard deviation.
From the definition, if all the data is the same then the data should be equal to the mean. If the data is equal to the mean there will be no spread or variation leading to a zero standard deviation.
Hence we can conclude that statement b is true and statement a is false
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Find the distance between the two points in simplest radical form (0,-7)(-9,5)
Step-by-step explanation:
1111111111111111111111
If y=-1 is a zero of the polynomial q (y) = 4y³+ ky² - y -1, then find the vaLue of k
Answer:
Step-by-step explanation:
Since zero of a polynomial function is a value of the variable at which the function's value is 0, 0=4(-1)^3+k(-1)^2-(-1)-1, for the given polynomial q(y)=4y^3+ky^2-y-1
simplifying the above gives: 0= -4+k+0
k=4
g(x)= 3x find g(-5)
Answer: -15
Step-by-step explanation:
x=-5
g(-5)=3(-5)
g(-5)=-15
I need to know What is 3/4 x 8 1/2
Answer:
3/4 x 8 1/2 = 6.375
what’s the absolute value of the equation
|y-2|=|2y|
Just the answer please
The x-intercept of the line is -3
y-intercept: None
x-intercept and y-interceptFrom the question, we are to find the y-intercept and x-intercept of the given line
The x-intercept of a line is the point where the line crosses the x-axis on a cartesian plane
The y-intercept of a line is the point where the line crosses the y-axis on a cartesian plane
From the graph, we can observe that the line only crosses the x-axis at the point (-3, 0). That is, at the point where x = -3
Thus,
The x-intercept of the line is -3
The graph does not cut through the y-axis
Thus,
There is no y-intercept
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Find the derivative of the function using the definition of derivative. f(x) = 5x
The derivative is f'(x) = 5.
The limit definition of the derivative tells us that the derivative of a function is f is
f' (x) = [tex]\lim_{h \to \0} 0[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
For this, f(x) = 5x and f(x + h) = 5(x + h)
So:
f'(x) = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5(x+h)-5x}{h}[/tex]
= [tex]\lim_{h \to \}0[/tex] [tex]\frac{5x+5h-5x}{h}[/tex]
= [tex]\lim_{h \to \}0[/tex] [tex]\frac{5h}{h}[/tex]
= [tex]\lim_{h \to \}0[/tex] 5
= 5
So, when f(x) = 5x , we see that its derivative is f'(x) = 5.
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A scale drawing of a rectangular park is 6 cm wide and 10 cm long. The actual park is 180 meters wide. What is the area of the actual park in square meters?
The area of the actual park in square meters will be 54000m².
How to calculate the area?The length of the actual park will be:
= 180/6 × 10
= 300m
Width = 180m
Therefore, the area will be:
= Length × Width
= 300 × 180
= 54000 m²
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(2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)
Pls step by step
The evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c) is mathematically given as
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
This is further explained below.
What is the evaluation of (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c)?(2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
2^3+3 * 2^2(-a)+3*2(-a)^2+(-a)^3 +(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+2^3+3 * 2^2(-b)+3 * 2(-b)^2+(-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +(2-c)^3-3(2-a)(2-b)(2-c)
Use the Binomial Theorem.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+2^3+3 \cdot 2^2(-c)+3 \cdot 2(-c)^2+(-c)^3-3(2-a)(2-b)(2-c)
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3-3(2-a)(2-b)(2-c)
Apply the distributive property.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3+(-3 * 2-3(-a))(2-b)(2-c)
Multiply -3 by 2 .
&8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3 +(-6-3(-a))(2-b)(2-c)
Multiply -1 by -3.
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3 +(-6+3 a)(2-b)(2-c)
Expand (-6+3 a)(2-b) using the FOIL Method.
Combine the opposite terms in
8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3-24+12 c+12 b-6 b c+12 a-6 a c-6 a b+3 abc
8+6 a^2-a^3+8+6 b^2-b^3+8+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Simplify by adding numbers.
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc
Combine the opposite terms in
6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 a b c
6 a^2-a^3+6 b^2-b^3+6 c^2-c^3-6 b c -6 ac-6 ab+3 abc
Re odrder
a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2
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what is the imagine point of (0,-9) after a translation right 5 units and down 1 unit
the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).
We are given a point:
( 0 , - 9 )
We will first translate it to the 5 units right.
So, we get that:
( 0 + 5 , - 9)
= ( 5 , - 9)
Now, we will translate it 1 unit to the down.
So, we get that:
= ( 5 , - 9 - 1)
= ( 5 , - 10 )
Image will become:
( 5 , - 10 )
Therefore, we get that, the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).
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If a number is "squared" that means it
is raised to the
______ power.
1. 1st
2. 2nd
3. 3rd
4. square root
5. none of the above
Answer:
2nd power
Step-by-step explanation:
3rd is cubed and 1st is: example 3^1 = 3
square root is √
A rectangular pool is 20 feet by 30 feet. The depth of the pool is 60 inches, but the depth of the water is 3/4 of the depth of the pool. Find each measure to the nearest tenth. (Lesson 1-7)
b. the volume of water in the pool
The water in the rectangular pool which has a depth of 3/4 of the pool's depth has a volume of 2250 cubic feet.
If the depth of the water is 3/4 of the depth of the pool and the depth of the pool is 60 inches, then
depth of the water = 3/4 of the depth of the pool
depth of the water = 3/4(60 inches)
depth of the water = 45 inches = 3.75 feet
Volume is defined as the amount of space any object occupies. The volume for a rectangular prism is given by the formula:
V = lwh
where v is the volume
l is the length
w is the width
h is the height
Since the water occupies the inside of the rectangular pool, to solve the volume of the water, use the formula for the volume of a rectangular prism.
V = lwh
V = 20 feet(30 feet)(3.75 feet)
V = 2250 cubic feet
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2. Which graph represents the solution
of 6 + 3y < 9 or 4y > 3y + 2?
Help please!!!!!
Answer: It is likely B
Step-by-step explanation:
1. Subtract 6:
6 -6 + 3y < 9 -6
2. Divide by 3:
3y/3 < 3/3
3. Simplify:
y < 1
--------------------------------------
1. Subtract 3y:
4y -3y < 3y -3y + 2
2. Simplify:
y < 2
(i) So the answer is likely B
Select the car that travels the fastest. choose 1 answer: choose 1 answer: (choice a, checked) a 50 50 km/h km/hcar a (choice b) b car b travels a distance of d dd kilometers in h hh hours, based on the equation 55 h = d 55h=d55, h, equals, d. (choice c) c car c travels 135 135135 kilometers in 3 33 hours. see more
The car with the speed of 50 Km/h travels the fastest.
We have given with three choices for selecting the fastest speed from them. The three choices are
First choice is 50 Km/h.
Second Choice is car b travels a distance of d kilometers in h hours, based on the equation 55 h = d , h, equals, d.. So from this be can conclude that this car is moving with the speed of (1/55)km/h.
Third choice is car c travels 135 kilometers in 3 hours. So from this be can conclude that this car is moving with the speed of (135/3) Km/h i.e., 45 Km/h.
So, from the given choices we can conclude that the car with the speed of 50 Km/h travels the fastest.
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Alguien me puede ayudar pls
Answer:
hola
Step-by-step explanation:
is -24 greater than -24.0
Answer:
yes
Step-by-step explanation:
-24 is. a whole number so it would be greater
WILL GIVE BRAINLIEST IF ANSWERED WELL!!!
Answer:
r = S/(2πh)
Step-by-step explanation:
S = 2πrh
divided by (2πh)
r = S/(2πh)
question 4 suppose the fraction of high school students who can drive is 15% and the fraction of college students who can drive is 23%. if one-fifth of the students are college students and the rest are high school students, what is the probability that a student who can drive is a college student? select the correct probability.
The probability that a student who can drive is a college student is 0.2771 or 27.7%
It will be sooved using Baye's theorem -
P(college) = P(C) / 1/5 = 0.2
P(high school students) = P(H) = 4/5 = 0.8
P(college drives) = 0.23
P(high school drives) = 0.15
We have to find, probability that a student who drives is a college student.
That is, we have to find P(C/D).
P(C/D) = P(C ∩ S)/P(S)
Since P(C ∩ S) is an independent event.
P(C ∩ S) = P(C) × P(S)
P(C ∩ S) = 0.2 × 0.23
= 0.046
Using bayes's theorem, we will get
P(C/D) = 0.2771 or 27.7%
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The table shows a proportional relationship between x and y. Dimitrios and Katerina have to complete the table. Katerina incorrectly says the ratio is 10 a complete the table. 3 5 7 0 y 30 50 70 90 Ratio y/x
Here is the completed table:
x y y/x
3 30 10 / 1
5 50 10 / 1
7 70 10 / 1
9 90 10 / 1
What are the ratios?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s). The sign used to represent ratios are :.
The ratio of y to x : change in value of y / change in the value of x
(50 - 30) / (5 - 3) = 20 / 2 = 10 / 1
(70 - 50) / (7 - 5) = 20 / 2 = 10 / 1
(90 - 70) / (9 - 7) = 20 / 2 = 10 / 1
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∠A and \angle B∠B are vertical angles. If m\angle A=(5x+1)^{\circ}∠A=(5x+1) ∘ and m\angle B=(4x+3)^{\circ}∠B=(4x+3) ∘ , then find the value of x.
HELP
Using the vertical angles theorem, the value of x = 2.
How to Apply the Vertical Angles Theorem?Given that angles A and B are vertical angles pair, based on the vertical angles theorem, both angles are congruent to each other.
Therefore:
m<A = m<B [vertical angles theorem]
m<A = (5x + 1)°
m<B = (4x + 3)°
Substitute
(5x + 1)° = (4x + 3)°
Solve for x
5x + 1 = 4x + 3
5x + 1 - 1 = 4x + 3 - 1
5x = 4x + 2
5x - 4x = 4x + 2 - 4x
x = 2
Therefore, using the vertical angles theorem, the value of x = 2.
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[tex]\sqrt[3]{} \frac{1}{16} *(-\frac{54}{1} )[/tex]
The simplification of the expression ∛(1/16) × (-54/1) is -27√4/32.
What is defined as the Rationalization?Rationalization is the process of removing a radical as well as imaginary number from of the denominator of an arithmetic fraction. That is, in a fraction, remove the radicals so that the denominator just includes a rational number.
Step 1: Multiply the numerator and denominator by the a radical that removes the radical from the denominator.Step 2: Ensure that all radicals have been simplified.Step 3: If necessary, simplify the fraction.Now the expression is given as;
= ∛(1/16) × (-54/1)
= -54/ ∛16
Taking cube root of 16.
= -54/(4√4)
= -27/2(√4)
By the process of rationalization, multiply the numerator and denominator by the a radical that removes the radical from the denominator which is √4.
= -27×√4/2(√4×√4)
Simplifying the equation;
= -27√4/32
Therefore, the simplification of the expression is -27√4/32.
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the sum of 2 consecutive intergers is 515 how can i write this as an equation?
We get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.
We are given that,
The sum of 2 consecutive numbers is 515.
Consecutive numbers:
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1 and 2 are consecutive numbers, 34 and 35 are also consecutive numbers.
Here let the first number be x
Second number will be:
x + 1
We need to find their sum:
x + x + 1 = 515
2 x + 1 = 515
2 x = 515 - 1
2 x = 514
x = 514 / 2
x = 257
x + 1 = 257 + 1 = 258
Therefore, we get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.
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state which is greater
(5-6) times 10 or 5-6 times 10
How do I solve this? step by step please 30 POINTS!
The solution to the system of equations is (-7, 5)
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x + y = -9
3x + 5y = 4
Make y the subject in 2x + y = -9
So, we have
y = -2x - 9
Substitute y = -2x - 9 in 3x + 5y = 4
So, we have
3x + 5(-2x - 9) = 4
Open the bracket
So, we have
3x - 10x - 45 = 4
Evaluate the like terms
-7x = 49
Divide both sides by -7
x = -7
Substitute x = -7 in y = -2x - 9
y = -2(-7) - 9
Evaluate
y = 5
Hence, the solution to the system of equations is (-7, 5)
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Find the coordinate of the midpoint of the segment with the given endpoints.
-6 and -4
Answer:
-5
Step-by-step explanation:
Let's assume the you are moving horizontally along the number line. If you start at -4 and jump to -6, you have made 2 jumps to the left(-4;-5;-6). So halfway between them (the midpoint) is 1 jump (half of 2 jumps).
1 jump to the left of -4.... You land at -5.
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cant focus today lolol pls help
Answer:
18.48
7.39 divided by 0.4 is 18.475
rounded to hundredth is 18.48 because 5 or above you round up
Answer:2.909
Step-by-step explanation:hope this helps