Show that each field is a subset of the other and that f(a, b) = f(b)(a) is a subset of f(a, b). Therefore, f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f.
To prove that f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f, we need to first understand what the expression means. Here, f(a, b) represents the field generated by a and b over the field f, i.e., the smallest field containing a and b and all elements of f.
Now, to show that f(a, b) = f(a, b) = f(b)(a), we need to demonstrate that each field is a subset of the other.
Firstly, we show that f(a, b) is a subset of f(a, b) = f(b)(a). This can be done by observing that a and b are both elements of f(a, b) and hence, they are also elements of f(b)(a), which is the field generated by the set {a, b}. Therefore, any element that can be obtained by combining a and b using the field operations of addition, subtraction, multiplication, and division is also an element of f(b)(a), and hence, of f(a, b) = f(b)(a).
Secondly, we show that f(a, b) = f(b)(a) is a subset of f(a, b). This can be done by observing that f(b)(a) is the smallest field containing both a and b, and hence, it is a subset of f(a, b), which is the smallest field containing a, b, and all elements of f. Therefore, any element that can be obtained by combining a, b, and the elements of f using the field operations of addition, subtraction, multiplication, and division is also an element of f(a, b), and hence, of f(a, b) = f(b)(a).
Hence, we have shown that f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f.
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√26+10-15 cuanto es me ayudan ?
Step-by-step explanation:
If the whole thing is in a square root, then the answer is sqrt21.
If only sqrt26 is in the square root, then the answer is -5+sqrt26.
(esto es en español) (This is in spanish transalation)
Si todo está en una raíz cuadrada, entonces la respuesta es la raíz cuadrada 21.
Si solo la raíz cuadrada 26 está en la raíz cuadrada, entonces la respuesta es -5 + raíz cuadrada 26.
Can someone help me with this problem? 3[x(-6)]
Answer:
-18x
Step-by-step explanation:
First step: remove the parentheses.
So, you'll have -3x*6.
multiply the numbers (3 x 6 = 18)
and you'll get -18x.
hope this helps!
can anyone solve this
Answer:
Step-by-step explanation:=(1+sinA)2+cos2A/cosA(1+sinA)
=1+sin2 A+2sin A+cos2 A/cos A(1+sin A)
=1+2sin A+1/cos A(1+sin A)
=2(1+sin A)/cos A(1+ sin A)
=2sec A
Answer:
see explanation
Step-by-step explanation:
Consider the left side
[tex]\frac{1+sinA}{cosA}[/tex] + [tex]\frac{cosA}{1+sinA}[/tex] ← combine into a single fraction
= [tex]\frac{(1+sinA)^2+cos^2A}{cosA(1+sinA)}[/tex] ← expand and simplify numerator
= [tex]\frac{1+2sinA+sin^2A+cos^2A}{cosA(1+sinA)}[/tex] [ sin²A + cos²A = 1 ]
= [tex]\frac{1+2sinA+1}{cosA(1+sinA)}[/tex]
= [tex]\frac{2+2sinA}{cosA(1+sinA)}[/tex] ← factor out 2 on the numerator
= [tex]\frac{2(1+sinA)}{cosA(1+sinA)}[/tex] ← cancel (1 + sinA) on numerator/ denominator
= [tex]\frac{2}{cosA}[/tex]
= 2secA = right side, thus verified
Sunning itself on a cliff 5.8 feet above sea level. The iguana dove into the water from the cliff. When the iguana reached the deepest part of its dive, its total change in elevation was 8.3 feet. What was the iguana's position relative to sea level at the deepest part of its dive?
Answer:
deepest part of dive is 2.5 feets below sea level ;
-2.5 feets
Step-by-step explanation:
Given :
Initial Position = 5.8 feets above sea level = +5.8
Deepest part of dive = x
Change in elevation between initial position and deepest part of dive = 8.3 feets
Position relative to sea level at deepest part of dive :
x = change in elevation - Initial position
x = 8.3 feets - 5.8 feets
x = 2.5 feets
Hence, deepest part of dive is 2.5 feets below sea level
PLEASE HELP! worth 50 points!! Please only put the right answer in I really need help trying to get my grade up..
Answer:
1) x = 41.8 deg
2) x = 64.2 deg
3) x = 51.3 deg
Step-by-step explanation:
Problem 1
For angle x, 4 is the opposite leg and 6 is the hypotenuse.
sin x = 4/6
x = sin^-1 2/3
x = 41.8 deg
Problem 2
For angle x, 14 is the adjacent leg, and 29 is the opposite leg.
tan x = 29/14
x = tan^-1 29/14
x = 64.2 deg
Problem 3
For angle xm 25 is the adjacent leg, and 40 is the hypotenuse.
cos x = 25/40
x = cos^-1 5/8
x = 51.3 deg
Please helpppp 15 points!!!
Answer:
105 students and 150 guests
Step-by-step explanation:
equation to find the answer are
1x + 5y = 855
x + y = 255
with
x + y = 255
x = 255 - y
now we replace x with (255 - y) into 1x + 5y = 855 to find y
1(255 - y) + 5y = 855
255 - y + 5y = 855
255 + 4y = 855
4y = 855 - 255
4y = 600
y = 150 (number of guests)
now we got y = 150, let's find x
x + y = 255
x + 150 = 255
x = 255 - 150
x = 105 (number of students)
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
Help me plz ??? Help
Answer:
16
Step-by-step explanation:
h(x) = x^3 - 2x
g(x) = 3x + 4 Find (h+g)(4)
9514 1404 393
Answer:
72
Step-by-step explanation:
h(4) = 4^3 -2·4 = 64 -8 = 56
g(4) = 3·4 +4 = 16
Then the sum is ...
(h+g)(4) = h(4) + g(4) = 56 +16
(h+g)(4) = 72
в треугольнике abc точки d и m принадежат сторонам ab и bc dm и ac параллельны докажи что треугольник bdm подобен треугольнику abc
Answer:
this is in Russian please ask in English
Step-by-step explanation:
I know what is the question but you should ask in English after translating ok
Graph a line with a slope of 1 and a y-intercept of 4.
Answer:
Step-by-step explanation:
Plot the y-intercept (0, 4). Starting at (0, 4), move your pencil point 1 space to the right, to (1, 4), and from (1, 4) up 1 space to (1, 5). Draw a straight line through (0, 4) passing through (1, 5) also.
Which postulate proves the two
triangles are congruent
A. SAS
B. ASA
C. SSS
D. HL
Answer:
SSS
Step-by-step explanation:
please help me and thank you
find the inequality of 3x-2÷4+3≥12
Answer:
x + 5 = ,3
Step-by-step explanation:
x+5-5= +3-5
x= -2
Can someone help me with these two questions plss
Answer:
c. 6
d. 3
Step-by-step explanation:
:-)
tim played 20 games of draughts he won 16 of those games.what fraction of the game did he win
b) he played 30more games he had then 68% of all his games how amny of 30 games did he win
Answers to both subparts are shown:
(A) The fraction of games Tim wins is 4/5.(B) Tim wind has 20 games when he plays 30 games.What is a fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.So, (A) fraction of the game Tim wins:
The number of games played is 20.The game won is 16.Then, the fraction will be:
16/204/5(B) Games Tim wins in 30 games.
The total number of games played is 30.The winning percentage is 68%.So, a number of games won:
30/100 × 680.30 × 6820.4Rounding off: 20Therefore, answers to both subparts are shown:
(A) The fraction of games Tim wins is 4/5.(B) Tim wind has 20 games when he plays 30 games.Know more about fractions here:
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The correct question is shown below:
(A) tim played 20 games of draughts he won 16 of those games.what fraction of the game did he win
b) he played 30 more games he had then 68% of all his games how amny of 30 games did he wi
Which pair of angles is congruent?
What is the answer to 3/8 + 2/4
Answer:
1 1/2
Step-by-step explanation:
1.) First find the common denominator of the 2 fractions (8) 4: 4
8: 4, 8
2.) then you write a new expression with the numerator left blank and the denominator as 8 shown below in the step by step explanation. /8 + /8
3.)3/8 + 2/4 multiply by 1 both numerator and denominator for the first fraction. And multiply by 2 both numerator and denominator for the second fraction. 3/8 + 4/8.
4.) Then you add those 2 fractions which I assume you already know how by adding the numerators together, and get 12/8.
5.) You simplify 12/8 and get 1 4/8. 4/8 is equal to 1/2 so its 1 1/2.
Find a slope for each line (each block is one unit):
On a coordinate plane, a point is at (1, 2) and (5, 2). Find the distance between (1, 2) and (5, 2). The points lie in the same quadrant . The distance is .
Answer:
The points lie in
✔ the same quadrant
The distance is
✔ 4 units
Step-by-step explanation:
the same quadrant
4 units
The distance between the two points (1, 2) and (5, 2) is 4 units. And both the points (1, 2) and (5, 2) lie in the same quadrant.
What is Distance between the two points?Distance between two points is the length of the line segment that connects two given points.
Formula for the distance between two points[tex]d = \sqrt{(x_{2}-x_{1} ^{2}) +(y_{2}-y_{1} ) ^{2} }[/tex]
According to the given question
We have
Two points
(1, 2) and (5, 2)
Let,
[tex](x_{1},y_{1}) = (1, 2)[/tex]
And, [tex](x_{2},y_{2} ) = (5,2)[/tex]
Therefore,
The distance between the points (1,2) and (5, 2)
= [tex]\sqrt{(5-1)^{2} +(2-2)^{2} }[/tex]
[tex]=\sqrt{(4)^{2}+0 }[/tex]
[tex]=4[/tex] unit.
Hence, the distance between the two points (1, 2) and (5, 2) is 4 units.
Since, the x coordinate and y coordinate of both the points (1,2) and (5, 2) are positive. Therefore, they both lie in the first quadrant. Hence, the points lie in the same quadrant.
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2 1/7+1 2/5 Give your answer as a mixed number where appropriate.
Answer:
3 19/35
Step-by-step explanation:
Find the least common denominator of the two.
The LCD is 35.
Now convert the fractions to a denominator of 35.
This will be it>>>
2 5/35 + 1 14/35.
Now the answer to that will be: 3 19/35
Jonas and Marisol were the only candidates for sixth grade class president. Jonas received 60 votes and Marisol received 90 votes.
Of the 90 votes cast for Marisol, 40% were girls. How many girls voted for Marisol?
Answer:
36 girls voted for Marisol
Step-by-step explanation:
1. Find the slope
>
X
18
8
10
24
0 -5
y
10
1 7
Rise =
Run =
m =
Answer:
I think the slope is y, but look for an expert opinion
Step-by-step explanation:
In solving quadratic equation, if the constant term is missing what is the best method to
use?
Step-by-step explanation:
If you are looking for its roots, try completing the square method, and factoring out the common terms. These two is what I usually use.Kyla wants to add songs to her phone to listen to while she is riding on the bus. She bought 100 songs on her account.She is planning to download an equal number of songs each week for the next 5 weeks. The number of songs left to download, y, for a certain number of weeks, c is shown in the graph.
A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0.
Part A: Determine the rate of change and the initial value (2 points) of the function show on the graph. What does each represent in the scenario (2 points)? Show/Explain the work you completed to find the rate of change and initial value (2 points).
Part B: Using the information from Part A, write the equation that would model this relationship between x and y in slope-intercept form. (4 points)
Answer:
Slope = - 20; intercept, c = 100
y = - 20x
Step-by-step explanation:
The slope (s) = Rise / Run
using the pairs : (0, 100) and (5, 0)
x1 = 0 ; y1 = 100 ; x2 = 5 ; y2 = 0
Rise = (y2 - y1) = (0 - 100) = - 100
Run = (x2 - x1) = (5 - 0) = 5
Slope = - 100 / 5
Slope = - 20
Using the slope intercept relation :
y = mx + c
m = slope ; c = intercept
y = - 20x + c
Using the point (4, 20) to find c
20 = - 20(4) + c
20 = - 80 + c
20 + 80 = c
100 = c
Hence, c = 100
Slope, m = number of songs downloaded per week
c = Total number songs at week 0
The equation expressed in slope intercept form:
General form:
y = mx + c
m = - 20 ; c = 100
y = - 20x + 100
how do you factor: 2x + -15
Answer:
It is not factorable.
Step-by-step explanation:
It is not factorable with rational numbers.
Answer:
This expression is not factorable with rational numbers.
Step-by-step explanation:
2x+(-15)=2x-15
find the area of the figure
Expand 3(y + 4).
3(y+4)=
Answer:
expanded it is x= 3(y+4)
Answer:
3*y + 3*4 = 3*m + 12
Step-by-step explanation:
What is the solution to the equation below? √x+6 = x-6
A. x=12
B. x=3
C. x=4
D. x=10
Answer:
√x+6=x-6
squarring both side
x+6=x²-12x+36
0=x²-12x-x+36-6
x2-13x+30=0
x²-10x-3x+30=0
x(x-10)-3(x-10)=0
(x-10)(x-3)=0
either
x=10
or
x=3
Answer:
D:X=10
Explanation
Find x
I need help plz :(
A. 6
B. 24
C. 12
D. 12 sqr root of 3
E. 36
Answer:
b
Step-by-step explanation:
Answer:
To determine the value of X, what you would need to do is to use a trigonometric ratio, that would make use of the value of x and the side length of 12. This can either be, sin 30 or cos 60. Both of them will enable you to solve for x.
The final value for x would be either
X = 12/Sin 30
X = 12/Cos 60
Compute these in your calculator and you will find the final value in these cases.
Can someone please check my answer for this function???
Answer:
You're wrong, it's the bottom left
Step-by-step explanation:
x^2-49 is a difference of squares so it factors into (x+7)(x-7) which obviously cancels out with the denominator leaving x-7 left. This is the line you should graph, but keep in that x+7 is still in the denominator so x cannot be equal to -7 which means that this point should be be on the line which leaves the answer to be the one on the bottom left.