Answer:
Step-by-step explanation:
If cos a = 0.5, then sin a could equal √(1 - cos^2 a) = √(1 - 0.5^2) = √0.75 ≈ 0.866.
describe how to use the zero product property when solving a quadractic equation by factoring
X + 1 = 0, so x = -1, and x - 24 = 0, so x = 24. Consequently, the two answers to the equation are x = -1 and x = 24.
What is equation?It is a method for illustrating a notion, a connection, or a behaviour that often involves two or more variables. Equations can be used to explain several events, including economic models and physical principles. They can also be applied to problem-solving and forecasting. Symbols, integers, and mathematical operations like addition, subtraction, multiplication, and division are used to create equations.
An essential tool for factoring quadratic equations is the Zero Factor Property. Finding two terms, one of which is a factor of the constant term and the other of which is a factor of the coefficient of the squared term, whose product is equal to the constant term, is the fundamental principle behind the Zero Factor Property. With this knowledge, the given quadratic equation can be factored into two parts that equal zero.
One must first factor a quadratic equation into two factors that are equal to zero in order to solve it using the zero factor property. To do this, one needs determine the constant term's factors as well as the coefficient of the squared term's factors. The coefficient of the squared term is always obtained by multiplying the factors, which are always different integers.
The constant term's factors are always sums of numbers that result in the constant term. Once the elements are known, the equation can be factored into two factors that are equal to zero each.
Consider the equation [tex]x^2+5x-24=0[/tex], for instance. The factors of the constant term are -1 and 24, while the factors of the squared term's coefficient are 1 and 5. The equation then reads as (x + 1)(x - 24) = 0.
At this stage, the Zero Factor Property can be used to find x. Since all factors must be equal to zero, x can be solved for by setting all factors to zero. Thus, x + 1 = 0, resulting in x = -1, and x – 24 = 0, resulting in x = 24. Thus, x = -1 and x = 24 are the two answers to the problem.
To know more about Equation click-
brainly.com/question/2972832
#SPJ1
Complete questions as follows-
How do I use the zero factor property when solving a quadratic equation by factoring?
A golf ball is hit with an initial velocity of 140 feet per second at an inclination of 45 degrees to the horizontal. In physics, it is established that the height h of the golf ball is given by the function h(x)=(-32x^2/140^2)+x, where x is the horizontal distance that the golf ball has traveled. Complete parts (a) through (g). Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 80 feet. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.
The distance that the ball has traveled when the height of the ball is 80 feet is either about 9.86 feet or about 3.64 feet.
We are given that;
Velocity= 140feet
Inclination= 45degrees
Function h(x)=(-32x^2/140^2)+x
Now,
To find the distance that the ball has traveled when the height of the ball is 80 feet, we need to solve the equation:
h(x) = 80
Substituting h(x) with the given function, we get:
(-32x2/1402) + x = 80
Multiplying both sides by 140^2 and simplifying, we get:
-32x^2 + 140x - 11200 = 0
Dividing both sides by -32 and simplifying, we get:
x^2 - (35/4)x + 350 = 0
Using the quadratic formula, we get:
x = [ (35/4) ± √( (35/4)^2 - 4(350) ) ] / 2 x ≈ 9.86 or x ≈ 3.64
Using a graphing utility, we can confirm that these are the approximate x-intercepts of the function h(x) - 80.
Therefore, by graphing the answer will be about 9.86 feet or about 3.64 feet.
Learn more about graphing functions here:
https://brainly.com/question/14455421
#SPJ1
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The entries in both columns when matched are
Equation of line of best fit: y = -x + 8Slope = -1y-intercept = 8Matching the entries in column A and BFrom the question, we have the following parameters that can be used in our computation:
The graph
When the line of best fit is drawn, we have
(8, 0) and (0, 8)
The equation is calculated as
y = mx + c
So, we have
8 = 0 * m + c
0 = 8 * m + c
This gives
c = 8
0 = 8 * m + 8
So, we have
m = -1
This means that the equation is
y = -x + 8
Using the above as a guide, we have the following:
Equation of line of best fit: y = -x + 8
Slope = -1
y-intercept = 8
Read more about scatter plot at
https://brainly.com/question/23202763
#SPJ1
PLEASE ANSWER FAST I NEED THE ANSWER
The direction and speed the plane traveling is at About 84.3° west of north at approximately 502.5 mph. Option C
How do we calculate the direction and speed of the traveling plane?We need to first find the distance between points A and C using the distance formula; Distance AC = √((x2 - x1)² + (y2 - y1)²)
If we input the figures as seen in the diagram, it becomes
Distance AC = √((-30 - 20)² + (520 - 20)²)
which is 502.49. if we round it off, it becomes 502.5
We have to find find the angle θ that the plane is traveling using the law of cosines
cos(θ) = (AB² + BC² - AC²) / (2 x AB x BC)
cos(θ) = (500² + 50² - 502.5²) / (2 x 500 x 50)
which is -0.000125
θ = arccos( -0.000125)
θ = 90.0071621563 (in degrees)
Give than the wind is blowing west, the angle should be measured west of north.
180° - 90.01° = 90°
It only mean that the plane is travelling at approximately 84.3° west of north
The answer is based on the question below;
A plane is set to fly due north, but it is pushes off course by crosswind blowing west. At 1 pm, the plane is located at point A and at 2pm, the plane is located at point C, as shown in the diagram. In what direction and at what speed is the plane traveling?
A. About 5.7° west of north at approximately 500.1 mph.
B. About 5.7° west of north at approximately 502.5 mph
C. About 84.3° west of north at approximately 500.1 mph.
D. About 84.3° west of north at approximately 502.5 mph
Point C coordinates (-30, 520)
Point A (20, 20)
Distance from A to B on a straight course is 500
B to C is 50
Find more exercises on speed the plane traveling;
https://brainly.com/question/700866
#SPJ1
Which of the following is a way to find 2/7 of a number?
Group of answer choices
Divide by 2 and divide by 7
Divide by 2 and multiply by 7
Divide by 7 and multiply by 2
Multiply by 7/2
A way to find 2/7 of a number is by Multiply by 7/2. The correct answer is D).
To find 2/7 of a number, we need to multiply the number by the fraction 2/7. Therefore, the correct answer is to multiply the number by 2/7, which is equivalent to option D: Multiply by 7/2.
Dividing by 2 and 7 or multiplying by 7 and dividing by 2 will not give us the correct answer because 2/7 is not equal to either 1/2 or 7/2. Therefore, we need to use the fraction 2/7 to calculate the desired amount.
To find 2/7 of a number, we can multiply the number by 2/7.
For example, let's say we want to find 2/7 of 42. We can multiply 42 by 2/7
2/7 x 42 = (2 x 42)/7 = 84/7 = 12
Therefore, 2/7 of 42 is 12.
To know more about Multiply:
https://brainly.com/question/19634536
#SPJ1
Find an equation of the tangent line to the graph of
y = g(x) at x = 2 if g(2) = −5 and g'(2) = 6.
(Enter your answer as an equation in terms of y and x.)
The equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.
How to find the equation of the tangent lineThe point-slope form of the equation of a line can be used to find the equation of the tangent line to the graph of y = g(x) at x = 2.
y - y1 = m(x - x1)
where m is the tangent line's slope and (x1, y1) is the point on the g(x) graph at x = 2.
Given that g(2) = -5, the point on the g(x) graph at x = 2 is (2, -5).
We are told that g'(2) = 6, which is the slope of the tangent line at x = 2.
As a result, the tangent line equation is: y - (-5) = 6(x - 2)
We get the following after simplifying and rearranging:
y + 5 = 6x - 12 y = 6x - 17
Hence, the equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.
Learn more tangent line at https://brainly.com/question/6617153
#SPJ1
Drag statements and reasons to each row to show why the slope
of the line between D and E is the same as the slope between E
and F, given that triangles A and B are similar.
0
4
D
16
3
12
E
Triangle A
F
Triangle B
For statement 5/3 = slope, the reason is Definition of slope and for statement 5/3 = 15/9 , the reason is Triangle A is similar to triangle B.
How to explain the informationIf slope of triangles are equal than Triangle A is similar to triangle Therefore, in statement 5/3 = 15/9 when we simplify
we get 5/3 = 5/3.
Then the reason for this statement is "If slope of triangles are equal" and the definition of slope in general is m = y/x.
Therefore, for the statement 5/3 = slope, the reason is Definition of slope.
Learn more about slope on
https://brainly.com/question/11228323
#SPJ1
Please solve this question!
Solution:
Notice that for each function, they are simply in the form [tex]f(k(x))[/tex], where [tex]k(x)[/tex] is some function of [tex]x.[/tex] More specifically,[tex]g(x)=f(x-2), h(x)=f(2x), \text{ and } j(x) = f(x^2).[/tex]
Thus, because the Interval of Convergence of [tex]f(x)[/tex] is [tex]-3 < x < 3,[/tex] the Interval of Convergence of [tex]g(x)[/tex] should be [tex]-3 < x-2 < 3 \implies -1 < x < 5.[/tex]
Similarly, the Interval of Convergence of [tex]h(x)[/tex] is [tex]-3 < 2x < 3 \implies -\frac32 < x < \frac32.[/tex]
Finally, the Interval of Convergence of [tex]j(x)[/tex] should be [tex]-3 < x^2 < 3 \implies 0 < x < \sqrt{3}.[/tex]
Simplify expression sec×sin(-×)+tan(-x) over 1+sec(-×)
Answer:
-tan(x)/sin^2(x).
Step-by-step explanation:
To simplify the expression:
sec(x)sin(-x) + tan(-x)
1 + sec(-x)
We can use the fact that sin(-x) = -sin(x), cos(-x) = cos(x), and tan(-x) = -tan(x) to rewrite the expression as:
-sec(x)sin(x) - tan(x)
1 + sec(x)
Next, we can multiply both the numerator and denominator by the conjugate of the denominator, 1 - sec(x), to eliminate the square root in the denominator. This gives:
(-sec(x)sin(x) - tan(x))(1 - sec(x))
(1 + sec(x))(1 - sec(x))
Simplifying the numerator by distributing and combining like terms, we get:
-sec(x)sin(x) + sec(x)tan(x) + tan(x) - sec(x)tan(x)
1 - sec^2(x)
Simplifying further by canceling out the sec(x)tan(x) terms in the numerator, we get:
-tan(x)
1 - sec^2(x)
Finally, we can use the identity 1 - sec^2(x) = sin^2(x) to rewrite the denominator and simplify further:
-tan(x)
sin^2(x)
Therefore, the simplified expression is -tan(x)/sin^2(x).
can you please help me with this
The square root can be simplified as 7√2
How to simply surd?Irrational numbers are numbers in the form of square roots, which when evaluated cannot be expressed in the form a/b e.g. √7, π, 2/√5, 3√11, etc. They are also called surd.
The opposite of an irrational number is called rational number. A rational number is a number that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g. 1/3, 2/3, √4 = 4/1, etc.
The square root can be simplified as follow:
√98 = √(49 * 2)
= √49 * √2
= 7 * √2
= 7√2
Learn more about irrational numbers on:
brainly.com/question/29489057
#SPJ1
Eulerize this graph in the most efficient way possible, considering the weights of the edges.
We can eulerize this graph in the most efficient way possible by making these vertices have even degree through adding an edge between them.
How do we Eulerize a graph?We can eulerize a graph by ensuring to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.
A good method to do this is by adding edges between pairs of vertices that have odd degree until all vertices have even degree.
In the scenario above, we can see that all vertices have odd degree except for the last vertex.
Hence , in order to make this vertex have even degree, we can add an edge from it to any other vertex with odd degree.
Learn more about vertices at:
https://brainly.com/question/1217219
#SPJ1
A machine that cost $500,000 has an estimated residual value of $20,000 and an estimated useful life of 20,000 machine hours. The company uses units-of-production depreciation and ran the machine 2,000 hours in year 1, 4,000 hours in year 2, and 8,000 hours in year 3.
Calculate its book value at the end of year 3. (Do not round intermediate calculations.)
The machine's book value at the end of year three is $164,000.
How to calculate the depreciation rate per machine hour?The total amount of hours used by the machine in the first three years is: 2,000 + 4,000 + 8,000 = 14,000 hours
To calculate the annual depreciation expense, we must first establish the depreciation rate per machine hour. The following is how the depreciation rate per machine hour is calculated:
Depreciation rate per machine hour = (machine cost - estimated residual value) / total number of machine hours estimated
Rate of depreciation per machine hour = ($500,000 - $20,000) / 20,000 machine hours
Depreciation per machine hour = $480,000 divided by 20,000 machine hours
Rate of depreciation per machine hour = $24 per machine hour
We may compute the depreciation expense for each year by using the depreciation rate per machine hour:
Depreciation expense in year one = depreciation rate per machine hour x hours used in the first year
Depreciation expense in year one = $24 x 2,000 hours
Depreciation expense for the first year = $48,000
Year 2 depreciation expense = Depreciation rate per machine hour multiplied by the number of hours consumed in year 2.
Depreciation expense for year 2 = $24 x 4,000 hours
Depreciation expense for year two = $96,000
Depreciation expense in year three = depreciation rate per machine hour x hours used in year three
Depreciation expense in year three = $24 x 8,000 hours
Depreciation expense during the third year = $192,000
The accumulated depreciation for the first three years is the sum of the following depreciation expenses:
Accumulated depreciation equals the sum of year one depreciation expense, year two depreciation expense, and year three depreciation expense.
Depreciation accumulated = $48,000 + $96,000 + $192,000
Depreciation accumulated = $336,000
To compute the machine's book value at the end of the year 3. We deduct the accumulated depreciation from the machine's cost:
Machine book value = machine cost minus accumulated depreciation
The machine's book value is $500,000 minus $336,000
The machine's book value is $164,000
As a result, the machine's book value at the end of year three is $164,000.
Learn more about depreciation here:
https://brainly.com/question/30531944
#SPJ1
Which statement is true about the given expression? 3 x 2 − 11 ( 2 y + 1 ) + 4 A. The "4" in the third term is a factor. B. The "11" in the second term is a constant. C. The "3" in the first term is an exponent. D. The "2" in the second term is a coefficient.
Answer: D
Step-by-step explanation:
It's not A because the 4 is a constant, not a factor.
It's not B because the 11 is not constant because its a negative, therefore being subtracted.
It's not C because 3 is not an exponent, it is simply a term.
The answer is D because 2 is a coefficient, because it is a number infront of a variable.
In investing $6,500 of a couple's money, a financial planner put some of it into a savings account paying 5% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 13% annual simple interest. The combined interest earned for the first year was $637. How much money was invested at each rate?
The pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
What is Simple interest?Borrowers are required to pay the lender's basic interest as a fee in exchange for a loan.
Compound interest is not taken into account in the calculation; just the initial principal is taken into account.
Simple interest applies to all loans, not just specific ones.
Also highlighted is the type of interest that banks provide their customers on their savings accounts.
So, we presumptively have $x invested in the savings account.
Consequently, $ was invested in the development plan.(6150 - x).
S.I. = (Prt)/100 is the formula for simple interest on a sum of money (P), compounded at a rate (r), over a time period (t).
We figure out the interest on both investments:
Contribution to a savings account:
Amount invested (P) = $x.
Rate of interest (r) = 6%.
Time for investment (t) = 1 year.
As a result, interest was received= (Prt)/100 = $(x*6*1)/100 = $ (6x)/100
We are aware that $477 in interest has been paid in total.
Thus, we can write the following equation using the interest from both investments added:
(6x)/100 + {9(6150 - x)}/100 = 477
or, 6x + 55350 - 9x = 47700,
or, 55350 - 47700 = 3x,
or, 3x = 7650,
or x = 7650/3 = 2550.
As a result, investments in:
Savings account = $x = $2550.
Development plan = $(6150 - x) = $(6150 - 2550) = $3600.
Therefore, the pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.
Know more about Simple Interest here:
https://brainly.com/question/25793394
#SPJ1
Correct question:
In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?
Using elimination method (linear combination), what would the resulting equation be after adding both equations together?
Answer:
The resulting linear equation is 3d = 12, so d = 4 and e = 0.
Based on this equation, estimate the rating of chips whose cost is $1.10.
Round your answer to the nearest hundredth.
The rating of chips whose cost is $1.10 is obtained replacing the value of x on whichever's equation is correct by 1.10.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
Missing InformationThe problem is incomplete, hence the procedure to estimate the rating of chips whose cost is $1.10 is presented.
Learn more about the numeric values of a function at brainly.com/question/28367050
#SPJ1
6. Cones A and B both have volume 487 cubic units, but have different dimensions.
Cone A has radius 6 units and height 4 units. Find one possible radius and height
for Cone B. Explain how you know Cone B has the same volume as Cone A.
The dimensions of cone B is radius, 6.8 units and height 7 units.
What are the possible dimensions of cone B?
The possible dimensions of cone B is calculated as follows;
Volume of cone = ¹/₃πr²h
Volume of cone A = ¹/₃π(6²)(4) = 150.8 units³
Volume of cone B = 487 units³ - 150.8 units³ = 336.2 units³
The dimensions of cone B is calculated as;
¹/₃πr²h = 336.2 units³
r²h = 321
Let the height of cone B = 7, then the radius of the cone is calculated as;
7r² = 321
r² = 321/7
r² = 45.86
r = √45.86
r = 6.8 units
Learn more about dimensions here: https://brainly.com/question/27404871
#SPJ1
If the spinner does not land on yellow, what is the probability it will land on blue?
Answer: 2/4 or 1/2
Step-by-step explanation: Based on the spinner shown, there are 5 equal sections, 1 of which is yellow and 2 of which are blue. If the spinner does not land on yellow, it will land on one of the 4 other sections, 2 of which are blue.
Therefore, the probability of landing on blue given that it does not land on yellow is 2/4 or 1/2.
Match each equation on the left to its solution on the right.
The solutions to the equations are marked and matched
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
4 + x = -8x - 5
Adding 8x on both sides , we get
9x + 4 = -5
Subtracting 4 on both sides , we get
9x = -9
Divide by 9 on both sides , we get
x = -1
b)
2 ( 5x + 2 ) = 10x - 4
On simplifying the equation , we get
10x + 4 = 10x - 4
Subtracting 10x on both sides , we get
4 ≠ 4
So , it has no solution
c)
7 + 2x = 2x - 7
Subtracting 2x on both sides , we get
7 ≠ -7
So , it has no solution
d)
-3x + 3 = 3 ( 1 - x )
-3x + 3 = 3 - 3x
x = all real numbers
Hence , the equations are solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
URGENT!! I WILL GIVE
BRAINLIEST!!!!!!!!!!!! AND 100 POINTS
Answer:
the function is decreasing.
the slope is -3/4 and the y-intercept is 7.
the function is linear and continuous.
y = -3/4 x + 7 3 this function.
Step-by-step explanation:
"the function is linear and discrete" is false. there are no interruptions or steps in the curve. it is a continuous curve.
the usual function form of a line is
y = ax + b
"a" being the slope, "b" being the y-intercept.
that is why the other statements are false.
1. The law of demand predicts that
a. the more consumers purchase a good, the greater the demand for the good
b. consumers are willing to buy more of a good at a lower price than at a higher price
c. as prices go up, the quantity of a particular good that consumers will buy also rises
Od. consumers are willing to buy more of a good at a higher price than at a lower price
2. The function of price in a market system
a. is a way of adjusting the balance between the forces of supply and demand
b. acts as an incentive to producers to either increase or decrease the quantity supplied
c. is a means of rationing the available supply among those who demand it
d. all of these
3. A key advantage of the corporate form of business organization is
a. that the business lives on even if the owners of the business die
b. limited liability of stockholders
c.
the ability to raise significant amounts of financial capital
d.
all of these
Two identical baseballs are dropped. The first is dropped from a height of 121 feet and the second is dropped from a height of 225 feet. Find the two height functions and compare their graphs.
h1(t) = −16t2 + 121 is a vertical translation of h2(t) = −16t2 + 225.
The y-intercept of h1 is 4 ft greater than that of h2.
h1(t) = −4t2 + 121 is a vertical translation of h2(t) = −4t2 + 225.
The y-intercept of h1 is 104 ft less than that of h2.
h1(t) = −16t2 + 121 is a vertical translation of h2(t) = −16t2 + 225.
The y-intercept of h1 is 104 ft less than that of h2.
h1(t) = −4t2 + 11 is a vertical translation of h2(t) = −4t2 + 15.
The y-intercept of h1 is 4 ft greater than that of h2.
The correct answer is:
[tex]h1(t) = -16t^2 + 121[/tex] is a vertical translation of [tex]h2(t) = -16t^2 + 225.[/tex]
The y-intercept of h1 is 104 ft less than that of h2.
What is a y-intercept?
A function or relationship's graph meets the y-axis of the coordinate system at a point known as a y-intercept, sometimes known as a vertical intercept.
The height function for an object dropped from a height of h0 is given by:
[tex]h(t) = -16t^2 + h0\\\\h1(t) = -16t^2 + 121\\\\h2(t) = -16t^2 + 225[/tex]
To find the y-intercept of h1, we set t = 0 in the equation[tex]h1(t) = -16t^2 + 121:[/tex]
[tex]h1(0) = -16(0)^2 + 121 = 121[/tex]
Therefore, the y-intercept of h1 is 121 feet.
To find the y-intercept of h2, we set t = 0 in the equation [tex]h2(t) = -16t^2 + 225:\\\\h2(0) = -16(0)^2 + 225 = 225[/tex]
Therefore, the y-intercept of h2 is 225 feet.
The difference in their y-intercepts is:
225 - 121 = 104
Therefore, the y-intercept of h1 is 104 feet less than that of h2.
To know more about y-intercept visit,
https://brainly.com/question/25722412
#SPJ1
PLEASE HELP ME! I WILL BE GIVING 50 POINTS!
The box plot that represents the data is given as follows:
Bottom plot.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The ordered data-set for this problem is given as follows:
2, 2, 4, 7, 7, 14, 16, 18.
The minimum and maximum values are given as follows:
Minimum of 2.Maximum of 18.The data-set has an even cardinality, hence the median is given by the mean of the two middle elements as follows:
Median = (7 + 7)/2 = 7.
(which removes the top two options).
The quartiles are given as follows:
First quartile -> median of 2, 2, 4 and 7 -> 3.Third quartile -> median of 7, 14, 16, 18 -> 15.Meaning that the last plot is correct. (the one that is already marked).
More can be learned about box plots at https://brainly.com/question/12343132
#SPJ1
if rice is 0.75 x it with 9379372
Answer:
7034529
Step-by-step explanation:
Assuming you mean to multiply 0.75 by 9379372, the result would be:
0.75 x 9379372 = 7034529
What meaning of the statement this?
Yes, The statement given in the problem is correct.As, <a> satisfies all three conditions- identify, Closure and inverse, it is a subgroup of G.
What is a subgroup in maths?A subgroup in mathematics is a subset of a group that, with regard to the same operation, is also a group. To put it another way, a subgroup is a smaller group that is a part of a bigger group.
Technically, let H be a subset of G and let G be a group that is subject to some operation (such as addition, multiplication, or composition). H is referred to be a subgroup of G if it forms a group on its own with regard to the same operation.
For given statement,
Let G is a group, and let a is the element of G. The set of all powers of a, denoted as<a>, is a subgroup of G, and it is the subgroup generated by a.
To show that <a> is a subgroup of G, we need to verify that it satisfies three conditions:
Identity: The identity element e of G is also in < a >, as [tex]$a^0 = e$.[/tex]Closure: For any two powers of [tex]a, $a^m$ and $a^n$, their product $a^m \cdot a^n$ is also in $\langle a \rangle$, as $a^m \cdot a^n = a^{m+n}$.[/tex]Inverse: For any power of [tex]a, $a^n$, its inverse $a^{-n}$ is also in $\langle a \rangle$, as $a^{-n} = (a^n)^{-1}$.[/tex]As, All the three conditions were satisfied by <a> , it is a subgroup of G
Moreover, it is the subgroup generated by a , as it is the smallest subgroup of G that contains a. This means that < a > includes all the powers of a, as well as their products and inverses, and nothing more.
Learn more about subgroups here:
https://brainly.com/question/31266268
#SPJ1
What is the American dollar exchange rate for Mexican pesos?
(Subject: Economics)
Answer:
1 Mexican Peso = 0.0552 US Dollar Hope this helped! Have a great day! :)
Step-by-step explanation:
Answer:
1 United States Dollar is equivalent or equal to 18.24 (Mexican peso)
En un cuadrado de 10 cm por 10 cm pinta de
forma creativa el 30 % de su área y encuentra
la fracción correspondiente.
The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Approximately how many students received a
score between 70.5 and 80?
Answer:
The correct answer is B.
Approximately 200 students received a test score between 70.5 and 80.
Line F has a slope of −6/3, and line G has a slope of −8/4. What can be determined about distinct lines F and G?
The lines will intersect.
Nothing can be determined about the lines from this information.
The lines are parallel.
The lines have proportional slopes.
how many zero pairs are in (-5) + (-8)
The total number of zero pairs in the expression (-5) + (-8) is 2.
How to find the number of zero pairs?We must pair the negative numbers so that their sum is equal to zero in order to determine the number of zero pairs in this expression. To put it another way, we need to find pairs of numbers whose sum is the same as their additive inverse.
We are combining two negative numbers in the expression (-5) + (-8).
In this case, we can pair the (-5) with a (+5), since (-5) + (+5) = 0, and we can also pair the (-8) with a (+8), since (-8) + (+8) = 0.
As a result, the expression (-5) + (-8) contains two zero pairs: one for (-5) and (+5) and one for (-8) and (+8).
Therefore, there are a total of 2 zero-pairs in the expression (-5) + (-8).
know more about algebraic expressions visit :
https://brainly.com/question/31238826
#SPJ1