Given the piecewise function shown below, select all of the statements that
are true.
-x+1₁x<0]
f(x)= -2, x=0
[x²-1, x>0]

Every proper subgroup of G is cyclic.

In abstract algebra, a subgroup is a subset of a group that is itself a group under the same operation as the original group. More precisely, a subgroup H of a group G is a subset of G that satisfies the following three conditions:

A cyclic subgroup is a subgroup of a group that is generated by a single element. In other words, a subgroup H of a group G is cyclic if there exists an element a in G such that every element of H can be written as a power of a, and H is the smallest subgroup of G containing a.

In the given question,

Let H be a proper subgroup of G. Since H is a proper subgroup, we have lHl < lGl = 77.

Now, by Lagrange's Theorem, the order of any subgroup of G must divide the order of G. That is, lHl divides lGl = 77.

Since H is a proper subgroup, we have lHl > 1. Therefore, lHl can only be 7, 11, or 77 (the divisors of 77).

Suppose lHl = 7. Then, by Lagrange's Theorem, the elements of G are partitioned into disjoint cosets of H, each of size 7. But 77 is not divisible by 7, so there cannot be a whole number of cosets. Therefore, this case is not possible.

Similarly, suppose lHl = 11. Then, the elements of G are partitioned into disjoint cosets of H, each of size 11. But 77 is not divisible by 11, so there cannot be a whole number of cosets. Therefore, this case is also not possible.

Thus, we are left with the case where lHl = 77. But this implies that H = G, which contradicts the fact that H is a proper subgroup. Therefore, this case is also not possible.

We have exhausted all possibilities for the order of H, and in each case, we have arrived at a contradiction. Therefore, the assumption that there exists a proper non-cyclic subgroup of G must be false.

Hence, every proper subgroup of G is cyclic.

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The quadratic equation represented by the table is:

y = 2x^2 - 4x + 8

Here we have a table that represents a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)^2 + k

Here we can see that the vertex is at (1, 6), replacing that we will get:

y = a*(x - 1)^2 + 6

And we  can see the point (0, 8), replacing these values we will get:

8 = a*(0 - 1)^2 + 6

8 = a + 6

8 - 6 = a = 2

The quadratic is:

y = 2*(x - 1)^2 + 6

Expanding this we will get:

y = 2*(x^2 - 2x + 1) + 6

y = 2x^2 - 4x + 2 + 6

y = 2x^2 - 4x + 8

That is the quadratic equation.

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The number of students that studied math and English in the class is 64 students.

1/5 of a class Study English and 3/5 study mathematics. The class consists of 80 Students.

Therefore, the number of students studying English and Maths in the class can be represented as follows:

number studying English = 1 / 5 (80)

number studying English =  16

number studying Math = 3 / 5 (80) = 240 / 5 = 48

Therefore, let's find the number of student that studied maths and English in the class

Student that studied math and English in the class = 48 + 16

Student that studied math and English in the class = 64

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The solution for x in the equation -7x/5 + 4 = -1/2x - 7/2 is 5, and the other solutions are listed below

Given that

-7x/5 + 4 = -1/2x - 7/2

Multiply through by 10

-14x + 40 = 5x - 35

Evaluate the like terms

-19x = -95

So, we have

x = 5

Let x be the number of adult tickets sold.

So, the number of student tickets sold is 2x.

The total number of tickets sold is 444. Therefore:

x + 2x = 444

Combining like terms:

3x = 444

Dividing both sides by 3:

x = 148

Therefore, 148 adult tickets were sold.

The slope

To read the slope off the graph, we can use the formula:

slope = (change in y) / (change in x)

Using the points, we can calculate:

slope = (-2 - 1) / (3 - 1)

slope = -1.5

So the slope of the line is -1.5.

The y-intercept value

We can look at where the line intersects the y-axis on the graph. From the graph, it looks like the y-intercept is around y = 2.5.

The y-intercept point

Using the solution in (b), the estimated y-intercept point is (0, 2).

Rearrange the equation

To rearrange the equation into slope-intercept form, we need to isolate y on one side of the equation:

5x + 3y = 15

Subtract 5x from both sides:

3y = -5x + 15

Divide both sides by 3:

y = (-5/3)x + 5

So the equation in slope-intercept form is y = (-5/3)x + 5.

The slope

b) The slope of the line is the coefficient of x in the equation when it is in slope-intercept form.

Therefore, the slope of the line is -5/3.

The y-intercept of the line

This is the value of y when x = 0.

From the equation in slope-intercept form, we can see that when x = 0, y = 5.

So, the y-intercept of the line is 5.

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Answer:
Part a:

[tex]A(x)=10x^2+53x+63[/tex]

Part b:
2nd degree polynomial.

Part c:
Check step by step.

Step-by-step explanation:

since the sides of the rectangle are (2x+7) and (5x+9), the area is given by the product of the sides:

[tex]A=(2x+7)(5x+9)=10x^2+18x+35x+63=10x^2+53x+63[/tex]

So the area as a function of X is given by:
[tex]A(x)=10x^2+53x+63[/tex]

Notice is a second degree polynomial in standard form

To ensure part c, notice we can also multiply the sides in different order. This is A*B must be B*A for the sides of the rectangle. Lets check

[tex]A=(5x+9)(2x+7)=10x^2+35x+18x+63=10x^2+53x+63[/tex]
Since we obtained the same answer in part A the closure property for multiplication is check for the polynomial.

When thinking about lines of reflection, imagine that there exists a mirror and your trying to guess the location of the mirror on the xy plane. It will have to be located on horizontal line where y is -5. So your line of reflection is y = -5.

Answer:

the answer was 31.88USD

Solving a system of equations we can see that the two numbers are-8 and -7.

Let's say that the two numbers are A and B, and we know that we can write:

A*B = 56

A + B = -15

So we have a system of equations.

Using the second equation we can write:

A=  -15 - B

And replace that in the first equation, then we will get:

(-15 - B)*B = 56

-15B - B² = 56

Now we can solve the quadratic equation:

-B² - 15B - 56 = 0

The solutions are:

[tex]B = \frac{15 \pm \sqrt{(-15)^2 - 4*-56*-1} }{2*-1} \\\\B = \frac{15 \pm 1 }{-2}[/tex]

The two possible solutions are:

B = (15 + 1)/-2 = -8

B = (15 - 1)/-2 = -7

And when B is one of these values, A will be the other one.

Then the two numbers are -8 and -7.

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Answer:

That answer is -3

Step-by-step explanation:

The way you do this is Rise/Run

so you would do y2-y1/x2-x1

In this case it's 10-1/-4-(-1)

Simplified is 9/-3 which is -3

hope this helped

The set of solutions in R³ of the equation x1 - 3x2 + 2x3 = 1 is classified as a plane, hence option d is the correct option in the context of the problem.

The equation of a plane in 3-dimensional space can be written in different forms, but the most common one is the standard form:

Ax + By + Cz + D = 0

where A, B, and C are the coefficients of the variables x, y, and z, respectively, and D is a constant term.

Comparing the equation for this problem to the standard form, the coefficients are given as follows:

A = 1, B = -3, C = 2, D = -1.

Hence option d is the correct option.

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Answer:35.09

Step-by-step explanation:From the question given above, the following data were:Opposite = 12Hypothenus = X Angle θ = 20 °

The child at the 69th percentile is 5.5279 years οld.

The age οf the children in kindergarten οn the first day οf schοοl is unifοrmly distributed between 4.81 and 5.71 years οld. We can find the tοtal prοbability οf the child being between 4.81 and 5.71 years οld by subtracting the prοbability οf the child being yοunger than 4.81 frοm the prοbability οf the child being yοunger than 5.71:

P(4.81 ≤ age ≤ 5.71) = P(age ≤ 5.71) - P(age < 4.81)

The prοbability οf the child being yοunger than 4.81 is 0 since the age cannοt be negative.

The prοbability οf the child being yοunger than 5.71 can be calculated as:

P(age ≤ 5.71) = (5.71 - 4.81) / (5.71 - 4.81) = 1

Therefοre,

P(4.81 ≤ age ≤ 5.71) = 1 - 0 = 1

This means that the prοbability οf the child being οlder than 5 years οld is:

P(age > 5) = P(5.00 < age ≤ 5.71) = 1 - P(age ≤ 5.00) = 1 - [(5.00 - 4.81) / (5.71 - 4.81)] = 0.7018

Sο the prοbability οf the child is οlder than 5 years οld is 0.7018.

Tο find the age οf a child at the 69th percentile, we need tο find the age x such that the prοbability οf the child being yοunger than x is 0.69.

Let's call the age at the 69th percentile x. Then we have:

P(age < x) = 0.69

We can sοlve fοr x as fοllοws:

( x - 4.81 ) / ( 5.71 - 4.81 ) = 0.69

x - 4.81 = 0.69 ( 5.71 - 4.81 )

x - 4.81 = 0.69

x = 4.81 + 0.69 ( 5.71 - 4.81 )

x = 5.5279

Therefοre, the child at the 69th percentile is 5.5279 years οld.

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The base of the triangle is 8 cm.

The following equation determines a triangle's area A:

A = (1/2) * b * h

Where the triangle's height (h) and base (b) are the same.

In this instance, the triangle's height is 12 cm, and its size is 48 cm²

When these values are added to the formula, we obtain the following:

48 = (1/2) * b * 12

By condensing the right side, we obtain the following:

48 = 6b

When we multiply both sides by 6, we get:

b = 8

Therefore, the base of the triangle is 8 cm.

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There are 3150 distinct ways to arrange the marbles in a row.

What is Combination ?

In mathematics, combination is a way of selecting a group of objects from a larger set, without regard to the order in which the objects are selected. Combinations are also sometimes called "unordered selections" or "combinatorial subsets".

To solve this problem, we can use the formula for permutations with repetition. We have a total of 10 marbles, but some of them are repeated. Specifically, we have:

3 yellow marbles (repeated)

3 green marbles (repeated)

2 red marbles (repeated)

2 blue marbles (repeated)

So the number of distinct ways to arrange these marbles in a row is:

(10!) ÷ (3! x 3! x 2! x 2!)

The factorials in the denominator account for the repetition of each color. We divide by them to eliminate the overcounting that would occur if all the marbles were unique.

Simplifying this expression, we get:

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)÷(3 x 2 x 1 x 3 x 2 x 1 x 2 x 1 x 1 x 1)

which equals:

(10 x 9 x 8 x 7 x 6 x 5 x 4) ÷ (3 x 3 x 2 x 2)

Simplifying further, we get:

(10 x 3 x 3 x 3 x 2 x 2 x 7 x 5) ÷ (3 x 3 x 2 x 2)

which equals:

(10 x 3 x 3 x 7 x 5)

which finally equals:

3150

Therefore, there are 3150 distinct ways to arrange the marbles in a row.

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We can say that after answering the offered question As a result, Jamie interest will have $1,746 in her account after four years. Option B is the correct answer.

Simple interest is calculated via dividing the investment by the interest rate, the duration of the loan, and perhaps other factors. In marketing, the formula is simple: return = principal + interest + hours. This method makes it easiest to calculate interest. The most common approach to compute interest is to use the percentages of the principle balance. If he borrows $100 from a buddy and promises to repay that with 5% interest, he will only pay his percentage of the total interest. $100 (0.05) = $5. When you borrow money, you must charge interest and extending when you lend it. The most often, interest is determined as an indicator of the overall of the loan balance. This percentage is known as the loan's interest.

To answer this problem, we can utilise the compound interest formula:

[tex]A = P(1 + r/n)^(nt) (nt)[/tex]

where A is the total amount

P = the initial principal ($1,500 in this example).

r represents the yearly interest rate (3.8%).

n denotes the number of times interest is compounded per year (12 for monthly)

t denotes the number of years (4 in this case)

When we plug in the values, we get:

[tex]A = 1500(1 + 0.038/12)^(12*4) \sA ≈ 1745.99[/tex]

As a result, Jamie will have $1,746 in her account after four years. Option B is the correct answer.

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Answer:

Step-by-step explanation:

We can start by finding the weight lifter's original body mass before the training session:

Let x = original body mass

Then, we know that 15% of x is equal to 78 kg - x:

0.15x = 78 - x

1.15x = 78

x = 78/1.15

x ≈ 67.83 kg

Therefore, the weight lifter's original body mass was approximately 67.83 kg.

Now, let's find the difference between the weight lifter's new body mass and his original body mass:

78 kg - 67.83 kg ≈ 10.17 kg

So, the weight lifter did indeed gain approximately 10 kg of weight after the training session. Therefore, his claim is valid.

Answer: Can't solve

Step-by-step explanation: no equation sign

Answer:

B.1/100 is your answer for your question

Answer is below.

Let's call the height of the house "h".

The ladder is propped up against the house, forming a right triangle with the wall of the house and the ground. The ladder is the hypotenuse of the triangle, and the height of the house is one of the legs.

We know that the length of the ladder is 16 feet, and the angle of elevation is 62 degrees. We can use trigonometry to find the height of the house.

The trigonometric function that relates the angle of elevation to the height and length of the ladder is the tangent function:

tan(62) = h/16

To solve for h, we can multiply both sides by 16:

16 tan(62) = h

Using a calculator, we can evaluate the tangent of 62 degrees to get:

16 tan(62) ≈ 28.6

So the height of the house is approximately 28.6 feet.

A possible graph that shows the movement of the kite over time is shown below.

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Answer: Let's call the first term of the arithmetic sequence "a", and the common difference between the terms "d".

Then, we know that the sum of the first 8 terms is 88, so we can write:

a + (a + d) + (a + 2d) + ... + (a + 7d) = 88

Using the formula for the sum of an arithmetic sequence, we can simplify this to:

8a + 28d = 88

We also know that the product of the 1st and 8th terms is 120, so we can write:

a(a + 7d) = 120

Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable.

Solving the first equation for d:

d = (88 - 8a)/28

Substituting into the second equation:

a(a + 7[(88-8a)/28]) = 120

Multiplying both sides by 28 to eliminate the fraction:

28a^2 + 154a - 960 = 0

We can factor this quadratic equation as:

(2a - 15)(14a + 64) = 0

So either 2a - 15 = 0 or 14a + 64 = 0. Solving for "a" in each case, we get:

a = 15/2 or a = -64/14

Since we're looking for the first term of the sequence, which must be positive, we can discard the negative value and conclude that the first term is:

a = 15/2

Therefore, the first term of the arithmetic sequence is 7.5.

Step-by-step explanation:

By selling a bag at rs1500 and rs2100, there is some loss and profit respectively. if the loss is twice the profit , its cost price​ is Rs 1900.

The cost price is the amount of money that a seller pays to acquire or produce a product or service. It includes all the expenses incurred in the production or purchase of the product, such as the cost of raw materials, labor, packaging, shipping, and other overhead expenses.

Based on the given inforemation , we can represent the cost price by x.

x-1500 = 2 (2100- x)

x-1500 = 4200 -2x

3x = 5700

x= 1900

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The equation is true, we have confirmed that x = 3 is the correct solution.

The equation shown in the image is:

4x + 12 = 24

To write a related multiplication equation, we can simplify the left side of the equation by factoring out the common factor of 4:

4(x + 3) = 24

By multiplying both sides of the equation by 4, we can now find x:

x + 3 = 6

x = 6 - 3

x = 3

Therefore, the solution to the original equation is x = 3. We can check this solution by substituting it back into the original equation:

4x + 12 = 24

4(3) + 12 = 24

12 + 12 = 24

24 = 24

Since the equation is true, we have confirmed that x = 3 is the correct solution.

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(C) "Your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.

You are permitted to contribute as much of your salary as you choose to the Retirement Savings Plan on a tax-advantaged basis, up to the yearly limit established by the Federal Revenue Agency (IRS).

A retirement savings plan (RSP), also known as an RRSP, is a form of financial account used in Canada to hold savings and investment assets.

When opposed to investing outside of tax-preferred accounts, RRSPs offer a number of tax benefits.

They were launched in 1957 to encourage both workers and independent contractors to save for retirement.

They are subject to a number of limitations outlined in the Canadian Income Tax Act.

Savings accounts, guaranteed investment certificates (GICs), bonds, mortgage loans, income trusts, mutual funds, corporate shares, exchange-traded funds, foreign currency, and funds sponsored by labor are examples of approved assets.

Therefore, (C) "your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.

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The items that can be discharged when filing fοr bankruptcy are:

b. credit card debt

d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)

e. sοme taxes (under certain circumstances)

g. sοme fees (depending οn the type οf fees)

Bankruptcy helps peοple whο can nο lοnger pay their debts get a fresh start by liquidating assets tο pay their debts οr by creating a repayment plan. Bankruptcy laws alsο prοtect financially trοubled businesses.

The items that can be discharged when filing fοr bankruptcy are:

b. credit card debt

d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)

e. sοme taxes (under certain circumstances)

g. sοme fees (depending οn the type οf fees)

The items that cannοt be discharged in bankruptcy are:

a. autο car lοan (if yοu want tο keep the car, yοu need tο cοntinue making payments)

c. mοrtgage lοans (if yοu want tο keep the hοuse, yοu need tο cοntinue making payments)

f. child suppοrt (this is a nοn-dischargeable debt)

Hence, the best answer frοm the chοices prοvided are:

The items that can be discharged when filing fοr bankruptcy are:

b. credit card debt

d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)

e. sοme taxes (under certain circumstances)

g. sοme fees (depending οn the type οf fees)

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Answer:

The method that might have been used to result in Garcia winning is the Instant RunOff method.

In this method, voters rank the candidates in order of preference. If no candidate has a majority of first-choice votes, the candidate with the fewest votes is eliminated, and their votes are redistributed to the remaining candidates according to the second-choice preferences of the voters who supported the eliminated candidate. This process is repeated until one candidate has a majority of the votes.

In the preference ballot provided, Garcia received the most first-choice votes with a total of 26, but did not receive a majority of the votes. Therefore, the Instant RunOff method could have been used to determine the winner by redistributing the votes of the eliminated candidates (Müller and Ivanov) to the remaining candidates. Based on the preferences of the voters who chose Müller and Ivanov as their first choice, it is possible that the redistributed votes would have favored Garcia, leading to a majority win for Garcia.

The Instant RunOff method might not be fair to the other nominees because it can result in a candidate winning with a majority of second-choice or even lower preferences, rather than being the first choice of the majority of voters. This means that the candidate who is ultimately chosen may not have broad support, and may not be the candidate that the most voters actually prefer. Additionally, the method can be influenced by strategic voting, where voters rank their choices based on who they think is most likely to win, rather than their actual preferences. This can result in outcomes that do not accurately reflect the preferences of the voters.

Answer:If Krista drank 3/16 of the water in her water bottle in the morning, 5/16 in the afternoon, and 3/16 in the evening, then the total amount of water she drank during the day is:

3/16 + 5/16 + 3/16 = 11/16

This means that the fraction of water that is left at the end of the day is:

1 - 11/16 = 5/16

Therefore, Krista has 5/16 of the water remaining in her water bottle at the end of the day.

Step-by-step explanation:

Answer:

629=500+120+9

Step-by-step explanation:

500+120+9=629

629=629

The equation of the ellipse is [tex]}(x-3)^2/4^2 + (y+1)^2/2^2 = 1} or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex].

An ellipse is a type of closed curve which is symmetrical in shape and is the set of all points in a plane such that the sum of the distances from two fixed points (known as foci) is constant. It is a type of conic section, a curve obtained by intersecting a cone by a plane. Its shape is similar to that of an oval, but it is more elongated and slender. Ellipses are found in nature, such as in the orbits of the planets, and are used in a variety of applications, such as in engineering and architecture. They are also used in mathematics, where they can be used to represent a range of equations and to study the properties of shapes.

The equation of an ellipse with center (h,k), major axis of length 2a and minor axis of length 2b is given by:
[tex](x-h)^2/a^2 + (y-k)^2/b^2 = 1[/tex]
Given: h=3, k=-1, a=4, b=2
Therefore, the equation of the ellipse is:

[tex](x-3)^2/4^2 + (y+1)^2/2^2 = 1\\or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex]

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