The proof of every positive integer k that divides the order of g, there exists a subgroup h of g of order k is shown below:
What is Subgroup?A subgroup is a group nested inside another group. The subgroup test is used on subsets of a group to determine if they are subgroups. A proper subgroup is a subgroup that does not contain all of the original group, while a trivial subgroup contains only the identity.
Suppose k ∣ g ⟹n=dk:
If h(g)=⟨g⟩ is cyclic then
clearly K:=|⟨g^d⟩|=k .
Suppose now we have
1≠H≤h(g),
|H|=k and
let r>0 be the minimal natural number s.t.
g^r ∈ H , then
1=(g ^ r)^k = g^(r k)
⟹n ∣ r k ⟹ r k=ns =d ks ⟹ r= ds ⟹ s ∣ d
and from here we have
g^ r=(g^ d)^ s ∈K
Also, |H|=||K|
we get equality and thus uniqueness of K.
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Write an equation of the line that passes through (−6, 0) and (0, −24)
Answer:
y=4x+24
Step-by-step explanation:
1: find slope
[tex]\frac{0+24}{-6-0}[/tex]
[tex]\frac{24}{-6}[/tex]
4
2:plug into point-slope form
y-0=4(x+6)
y=4x+24
Answer:
y = -4x - 24
Step-by-step explanation:
slope = -4
Please help me with this! I’m so lost :((
Answer:
# 1 reb #2 is cfs
hope i could help...........
A group of workers can plant 8 1/4 acres in 5 1/2 days.
What is the unit rate in acres per day?
Write your answer as a fraction or a mixed number in simplest form.
What is the distance between points A and B?
Answer:
A
Step-by-step explanation:
I am 99.9% certain that this answer is A. It asks the Difference between point A and B. Difference = subtraction. So, C and D is automatically out of the Picture. I calculated A and A makes the most sense.
For there are 48 apples and 60 bananas and 96 oranges each basket must contain the same number of each type of frut Search instead for there are 48 apppes and 60 banas and 96 onanges each basket must contain the same number of each type of frut
This question is incomplete
Complete Question
For there are 48 apples and 60 bananas and 96 oranges each basket must contain the same number of each type of fruit. Find the greatest number of baskets you can have
Answer:
The greatest number of baskets you can have is 12 baskets.
And each baskets would contain:
4 apples, 5 bananas and 8 oranges
Step-by-step explanation:
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Then the greatest common factor is 12.
Therefore, the greatest number of baskets you can have is 12 baskets.
Each baskets would have
For apples
48 apples
48 apples / 12 baskets = 4 apples per basket
For bananas
60 bananas
60 bananas/12 baskets = 5 bananas per basket
For Oranges
96 Oranges/ 12 baskets = 8 oranges per baskets
Atticus is examining the equations: 4x + 2y = 10 and y = -2x + 5. He states that the equations are equivalent. Is he correct why or why not?
Answer:
He is correct
Step-by-step explanation:
Put the first equation into y = mx + b by isolating y:
4x + 2y = 10
2y = -4x + 10
Divide each side by 2:
y = -2x + 5
So, putting the first equation into y = mx + b got us the same equation as the second one, y = -2x + 5.
Since they are the same, the equations are equivalent.
Atticus is correct.
Tickets to the museum cost 7.50 each. Students receive a 15% discount on admission. What is the cost of a student ticket?
Answer:
138
Step-by-step explanation:
Please help!!! Urgent for homework
Answer: 7 and 8
Step-by-step explanation:
Square root and squared cancel out
Answer:
a=7
b=32
Step-by-step explanation:
The first one (a) is 7 because if you square a square root, you get the number inside the root. Also, technically a square root has an exponent of (1/2) so when you have a power-to-a-power (power rule of exponents) you multiply the exponents. So ([tex]7^{1/2}[/tex])^2 is 7.
For (b) you have to take it in two parts. Square the square root and you get 2. Square the 4 in front, you get 16. Multiply those two numbers (16 and 2) together and you get 32.
Edit: Check on your calculator, you get the same answers I got! :)
simply (5^1/3)
A. 5^3
B. 1/5
C. 5
D. 5^9
Answer:
A
Step-by-step explanation:
Anyone know the answer
Answer:
Infinite solution
Step-by-step explanation:
if you use distribute property on 3(x-5), it will equal to 3x-15.
What is the equation of the line that has a slope of 3 and goes through the point (3, 4).
Use the point-slope formula and then solve for y.
y - y_1 = m(x - x_1)
y_1 = 4
x_1 = 3
m = 3
y - 4 = 3(x - 3)
y - 4 = 3x - 9
y = 3x - 9 + 4
y = 3x - 5
Done.
slope intercept form
through: (2, 4) and (1, -3)
Answer: I attached a graph below, hope it helps.
Step-by-step explanation:
A line can be written in the form y = mx + b where m is the slope and b is the y intercept.
Since the slope is given as 4, the equation will be y = 4x + b
Plugging in the point (2,1) to the equation we get 1 = 4(2) + b or 1 = b + 8
Solving for b gives b = -7 so the equation will be y = 4x - 7
What is the slope of the line represented by the equation y = 4/5x-3
Answer:
m = 4/5
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define Equation
y = 4/5x - 3
Step 2: Break Function
Identify Parts
Slope m = 4/5
y-intercept b = -3
Please help due in less than 3 hours!!!!!!!! When Anne biked down the canyon, she averaged 30 miles per hour. At this rate, how long did it take her to bike 1 mile?
Answer:
2 min.
Step-by-step explanation:
1h is 60 min so divide 60 by 30 and you get 2
Answer:
It took Anne 1/30 of an hour to bike 1 mile.
Step-by-step explanation:
Unit Rate - 30 miles/ 1 hour
[tex]\frac{30 miles}{1 hour} = \frac{1 mile}{? hour}[/tex]
Based on the visual above, we need to find the proportion.
30 miles divided 30 equals to 1 mile.
What is 1 hour divided by 30? Remember: whatever is done to the numerator must be done to the denominator!
1 divided by 30 equals 1/30. Since the unit is hour, the answer is 1/30 of an hour.
Pleaseeee helppppppppp
Answer:
C
Step-by-step explanation:
Calculate the sum of the INTERIOR angles of a 16-gon.
Jayden drove 280 miles in 7 hours. On average, how fast did he drive, in miles per hour?
Answer:
23
Step-by-step explanation:
i honestly have no idea
Tina's car needs to be repaired. As auto repair shop charges Tina $42.30 for replacement parts and $22.50 per hour of labor.
If Tina gets charged a total of $109.80, how many hours of labor were spent on the repair?
O 5 hours
O 4 hours
O 3 hours
O 2 hours
ASAP!!! ILL MARK BRAINIEST!!!The expression on the left side of an equation is shown below. 3 x + 9 = box If the equation has no solution, which expression can be written in the box on the other side of the equation? –9 –3 3 x 3 x + 9
Answer:
C. 3x
Step-by-step explanation:
The first two choices give 1 solution each.
The last choice gives an infinite number of solutions.
Choice C. gives no solution.
3x + 9 = 3x
Subtract 3x from both sides.
9 = 0
Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.
Step-by-step explanation:
Answer:
C AKA 3x
Step-by-step explanation:
took the test
HELP ASAP
HELP ASAP
HELP ASAP
What is the value of X?
Answer:
61 degrees
Step-by-step explanation:
180 - 58 = 122
Since both sides are congruent, 122/2 = 61
Answer:
61
Step-by-step explanation:
Since ED and EF are congruent, Angle D = Angle F meaning angle F is also x degrees.
From here, we can use the total sum of angles in a triangle = 180 to calculate x:
180 = 58 + x + x
180 = 58 +2x
122 = 2x
x= 61 degrees
find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
The central angle in radians is given by θ = s/r, where s is the arc length and r is the radius of the circle
For given question,
we need to find the radian measure of the central angle of a circle of radius r.
The central angle intercepts an arc of length s.
Let θ be the central angle in radians.
We know that the arc length of circle of radius r is,
s = r × θ
where s is the arc length
r is the radius of the circle
θ is the central angle measured in radians
From above equation,
we have, θ = s ÷ r
Therefore, the central angle in radians is given by θ = s/r, where s is the arc length and r is the radius of the circle
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solve each system of equation by elimination
{y=-x+1
{y= 4x-14
Answer:
(3, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -x + 1
y = 4x - 14
Step 2: Rewrite Systems
y = 4x - 14
Multiply everything by -1: -y = -4x + 14Step 3: Redefine Systems
y = -x + 1
-y = -4x + 14
Step 4: Solve for x
Elimination
Combine equations: 0 = -5x + 15Isolate x term: -15 = -5xIsolate x: 3 = xRewrite: x = 3Step 5: Check
Define equation: y = -x + 1Substitute in x: y = -3 + 1Add: y = -2Vince weighs 160 pounds, and his friend Nadir weighs 140 pounds. Nadir calculated that his weight on another planet would be about 56 lb. Approximately what would Vince weigh on the other planet?
40 lb
64 lb
76 lb
90 lb
Answer: 64 lbs
Step-by-step explanation:
I divided 56/140 and got 0.4. Then multiplied 0.4 by 160 and got 64. SOunds about right to me.
You can double check by multipling 0.4 by 140 and you get 56.
Answer:
64lb
Step-by-step explanation:
i mean i got it right on my quiz on egde 2020
Quadrilaterals ABCD and EFGH are shown in the coordinate plane. Quadrilaterat ABCD will be reflected across the x-axis and then rotated 90 clockwise about the origin to create quadrilateral A^ prime B^ prime C^ prime D^ prime . What will be the y -coordinate of B?
Answer:
Step-by-step explanation:
180 degree rotation about point C prime composition reflected across line m
Transformation involves changing the position of a quadrilateral by reflecting and/or rotating it.
The y-coordinate of B" is 3
The coordinates of vertex B of quadrilateral ABCD is:
[tex]\mathbf{B = (-3,7)}[/tex]
The rule of reflection across the x-axis is:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
So, we have:
[tex]\mathbf{B' = (-3,-7)}[/tex]
The rule of 90 degrees clockwise rotation across the origin is:
[tex]\mathbf{(x,y) \to (y,-x)}[/tex]
So, we have:
[tex]\mathbf{B" = (-7,3)}[/tex]
Hence, the y-coordinate of B" is 3
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answer this please its for math :)
Answer:
bac
Step-by-step explanation:
Given trapezoid ABCD whose bases are segment AB and segment CD, what is mZB?
Answer:
x = 19
<B = 125°
Step-by-step explanation:
The sum f angle <D and angle <A is equal to 180° because these angles are supplementary
75° + 5x + 10 = 180° add like terms
85 + 5x = 180 subtract 85 from both sides
5x = 95 divide both sides by 5
x = 19
Same rule goes for angle <C and angle <B
<B + 55° = 180 subtract 55 from both sides
<B = 125°
Pls help..............
Answer:
y = 12x + -10
Step-by-step explanation:
sorry if its wrong i tried
sum of ab, a+b and b+ab is
Step-by-step explanation:
ab+a+b+b+ab
=2ab+a+2b
=a+2b+2ab
We can only add the same term numbers together.
hope it helps!
1) Factorise fully 8y^3 - 6y
[tex]8y^3-6y\\2y(4y^2-3)[/tex]
Factor 2 out because both 8 and 6 can be divided by 2.
Factor y out because there are same y's in a polynomial.
Answer:
2y (4y^2-3)
Step-by-step explanation:
8y^3 - 6y
Over here, we need to first look for the value they have in common
and u can identify that its "y". Now look for a no. that u can multiply both the no.s inside with. In this case, it two...but usually u need to pick the biggest value u can multiply both the no.s with.
So, now we need to put the common value outside the bracket-
2y (......)
2y * 4y^2 can give u 8y^3, therefore this will be the first value inside the bracket, the next value will be 2y*-3 coz it will give u -6y [Be careful of the signs].
So the ans would end up being-
2y (4y^2-3)
{u can comment if u have doubts :))}
What is 93.6 divided by 30
Answer:
The correct answer is 3.12.
Step-by-step explanation:
93.6 ÷ 30 = 3.12
Therefore, the answer is 3.12.
Hope this helps! :D