To show that every group G with identity e and such that x * x = e for all x in G is abelian, we need to prove that for any two elements a and b in G, a * b = b * a. We can use the hint provided and consider (a * b) * (a * b). By the associative property, this equals a * (b * a) * b. Since x * x = e for all x in G, we know that (b * a) * (b * a) = e. Thus, a * (b * a) * b = a * e * b = a * b. Therefore, we have shown that a * b = b * a, and G is abelian.
To prove that a group is abelian, we need to show that for any two elements a and b in the group, a * b = b * a. In this case, we are given that x * x = e for all x in the group. We use this property to manipulate (a * b) * (a * b) into a * (b * a) * b. Then, we use the fact that (b * a) * (b * a) = e to simplify the expression to a * e * b = a * b. This shows that a * b = b * a, and therefore, the group is abelian.
In conclusion, we have shown that every group G with identity e and such that x * x = e for all x in G is abelian. By considering (a * b) * (a * b) and using the property x * x = e, we were able to simplify the expression and prove that a * b = b * a. This result shows that G is abelian.
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Find the measure of the missing angle.
A box indicates a 90° angle.
So to find m<a, we can setup the equation 41 + a = 90.
Now subtract 41 from both sides to get a = 49.
y-13<6
Help please urgently!!
Step-by-step explanation:
y-13<6
y<6+13
y<19
hope it helps.
Answer:
y<19
Step-by-step explanation:
Add 13 to both sides.
y<6+13
Simplify 6+13 to 19.
y<19
How do I round 31732.441804 to the nearest dollar?
Answer and Step-by-step explanation:
To round to the nearest dollar, you are essentially rounding to the nearest whole number.
This involves looking at the tenths place.
31732.441804
The bolded 4 is in the tenths place (after the decimal), and determines if the number to the left of it rounds up or stay the same.
Since 4 is not greater than or equal to 5, it makes the number stay 2.
So, we get the answer to be $31732.
#teamtrees #WAP (Water And Plant)
New York has an elevation that us above dea level select all the answer choice's that could represent the elevation of New York City
Answer:
New York has elevation of 1,000 feet
Step-by-step explanation:
NewYork has elevation of almost 300 meters above sea level. This is lower elevation and the most lowest state is BigApple. NewYork is famous state of United States and the city is really busy. It has sea coasts which adds beauty to the city.
What is The midpoint of AB?
Answer:
(-2,0)
Step-by-step explanation:
(-2,0) is the midpoint I believe!
Hope that helps!
the mid point of AB is 1 and -1
estimate a percentage of a histogram
Answer:30 percent something like that
Step-by-step explanation:
Mariah's teacher tells her that this expression can be written as log k, where k is an integer.
3 log 3x – log 9x^4 + log x
What is the value of K?
The value of k is?
Answer: 3
Step-by-step explanation:
April buys a necklace that cost $38.25. There is a 6% sales tax. What is the total cost?
Answer:
$40.55
Step-by-step explanation:
Will give brainliest to correct! “Write the equation of the line.”
Answer: y=1/3x-2
Step-by-step explanation:
y=Mx+b
1/3 is rise over run
-2 is the y intercept
NEED HELP MATH HOMEWORK ASAP plz help
What is the solution of the system of equations?
y=x+2
y = 3x
F. (3,-1) G.(-3, 1) H. (1,3)I. (1, -3)
Answer:
the right answer is H.(1,3)
In triangle ABC, m∠A = 68° and m∠B = 9°. What is the measure of ∠C?
Answer:
103 degrees
Step-by-step explanation:
The sum of the measures of all triangles is 180 degrees. The two angles given total 77 degrees. Subtracting 77 from 180 leaves 103 degrees for the 3rd angle
CORRECT ANSWER GETS BRANLIEST, IF I SUBMIT MY TEST AND ITS INCORRECT U WILL BE REPORTED <3
Which equation has solutions at (3, 4)?
A. y=5x+2
B. y=2x-1
C. y=5x-2
D. y=2x+1
Answer:
none of them do
Step-by-step explanation:
i checked with a graphing calculator
Boden's account has a principal of $300 and a simple
interest rate of 3.6%. Complete the number line. How much
money will be in the account after 4 years, assuming
Boden does not add or take out any money?
years
2
3
and the missing year value is 1
In the double number line, the missing interest value is
(Type integers or decimals.)
Enter your answer in the edit fields and then click Check Answer.
Check Answer
Clear All
1
part
remaining
lof 11
Back
Next →
Answer:
808
Step-by-step explanation:
cause that's the answer
The regular price of a camera is 180.00 the camera is on sale for 25% off the regular price. What is the sales price of the camera in dollars and cents
Answer:
$135
Step-by-step explanation:
180 decrease 25% =
180 × (1 - 25%) = 180 × (1 - 0.25) = 135
Find the area of the semicircle.
Answer:
39.25 centimeters squared is the area of the semicircle
please can someone help me with this
Answer:
Too blurry to read
Step-by-step explanation:
The values of given bases is 1559, 3139, 648 and 170.
We are given that;
The four equations
Now,
a) 66+9t9+48 (base twelve)
[tex]= 6×12¹+6×12⁰ + 9×12²+10×12¹+9×12⁰ + 4×12¹+8×12⁰[/tex]
= 72+6+1296+120+9+48+8
= 1559 (base twelve)
b) 5117-324 (base eight)
[tex]= 5×8³+1×8²+1×8¹+7×8⁰ - (3×8²+2×8¹+4×8⁰)[/tex]
= 3272 + 64 + 8 + 7 - (192 + 16 + 4)
= 3139 (base eight)
c) 242 x 14 (base five)
[tex]= (2x5² + 4x5¹ + 2x5⁰) x (1x5¹ + 4x5⁰)[/tex]
= (50 + 20 + 2) x (5 + 4)
= 72 x 9 =648 (base ten) = 10130(base five)
d) 101010111 (base two)
[tex]= 1x2⁷ + 0x2⁶ +1x2⁵ +0x2⁴ +1x2³ +0x2² +1x2¹ +0x2⁰[/tex]
=128+32+8+2=170 (base ten)
Therefore, by algebra the answer will be 1559, 3139, 648 and 170.
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Select the correct answer.
Steven went to play video games in Games Galore arcade. Games Galore charges $1.50
for each game played. Represent the relationship between total cost, y, and number of
games played, x using a table, graph and equation. Is this relationship a proportional or
additive relationship? Explain.
Proportional
Additive
Answer:
The answer is proportional
Step-by-step explanation:
I took the test and got 5/5
The given relationship is a proportional relation.
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related linearly. If one quantity doubles in size, so does the other; if one of the variables diminishes to 1/10 of its former value, so does the other.
Given that, Steven went to play video games in Games Galore arcade. Games Galore charges $1.50 for each game played
Establishing the equation, we get,
y = 1.50x
Where 1.50 is the slope of the line, and, y is total cost and x is the number of game played.
When x = 2,
y = 1.50X2
y = 3
(2, 3)
When x = 4
y = 1.5X4
y = 6
(4, 6)
When x = 6
y = 1.5X6
y = 9
(6, 9)
Here we see that the value of y is varying from the value of x by 1.5 times.
Hence, The relation is a proportional relation.
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The government estimates 840,000 for equipment, 15,000 for software, and 40,000 per month for wages when the project will take 16 months.
Answer:
the total cost is $1,495,000
Step-by-step explanation:
The computation of the total cost is shown below:
Let us assume the months be m
Now the equation would be
= Equipment + software + wages
= $840,000 + $15,000 + 40,000m
= $840,000 + $15,000 + $40,000 (16)
= $840,000 + $15,000 + $640,000
= $1,495,000
Hence, the total cost is $1,495,000
Can the terms susc as "less than" and "more than" be used in a real situation? Can you give an example or examples?
Answer:
Yes
Step-by-step explanation:
She had more than me
I would help her but she has less than me
Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?
Item 14 Write an equation of the line passing through the point (4, 3) that is perpendicular to the line 4x−7y=9
Answer:
Step-by-step explanation:
-7y = -4x + 9
7y = 4x - 9
y = 4/7x - 9/7
perp. -7/4
y - 3 = -7/4(x - 4)
y - 3 = -7/4x + 7
y = -7/4x + 10
Three friends want to take a bus trip to the Grand Canyon. The entire trip costs $1,025 per person, plus $383 per person for the meal plan.
Answer:
4224 dollars
Step-by-step explanation:
1025 times 3 is 3075. 383 times 3 is 1149. 3075+1149 is 4224.
State if the three numbers can be the measures of the sides of a triangle.
17, 19,7
A) yes
B) no
11. Select from below the best estimate for the decimal that is equivalent to 100.5%
A. 0
B. 1
C. 100
D. 1000
Answer:
c
Step-by-step explanation:
in all honesty because if you round thats what you would get
The ages, in years, of a group of students are given in the box. Work out the mode.11 11 12 13 13 14 15 15 15 15
Explanation:
The mode is the most frequent value. We see that "15" shows up a total of 4 times, which is the most of the the unique values {11, 12, 13, 14, 15}.
Sheila is flying a kite with a string that makes a 59-degree angle with
the sand. If the height of the kite above the ground is 97 feet, how
long is the string? (Please use the exact ratio to calculate the missing
side and round your answer to the nearest hundredth.)
Answer:
113.16 feet
Step-by-step explanation:
Representing the given details appropriately with a right angle triangle. Let the length of the string for the kite be represented by x. Applying required trigonometric function, we have:
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin [tex]59^{o}[/tex] = [tex]\frac{97}{x}[/tex]
x = [tex]\frac{97}{Sin59^{o} }[/tex]
= [tex]\frac{97}{0.8572}[/tex]
= 113.1591
x = 113.16 feet
Thus, the string for the kite is 113.16 feet long.
. Chris read 25 books in 135 days. At this rate, in how many days will he read another 5 books? Another 10 books?
Answer:
5 books - 27 days
10 - 54 days
15 books - 81 days
Step-by-step explanation:
First, you need to find how many days it takes to read one book, to do this, simply divide 135 by 25 (135/5=5.4). Then, you multiply that number by the amount of books it wants to know how long it would take him to read (5 and 15 since it asks "another 10". It could also be 54 if it was asking how many for 10 books not including the 5 he would have read). 5*5.4=27, 10*5.4=54, and 15*5.4=81.
An observer in a hot air balloon spots an object on the ground. He knows that he is 150 m high and 285 m horizontally from the object. What is the angle of depression at which the observer spotted the object?
Round to the nearest tenth.
Answer:
27.8 degrees
Step-by-step explanation:
geometry multiple choice question HELPPP!!!??
Answer:
24/30
Step-by-step explanation: