Select all the correct answers.
Consider functions f and g.
f(x) = - 2 cos (x - 1) + 3
g(x) = 2 cos (x + 3) - 3
Which statements describe transformations of the graph of fresulting in the graph of function g?
A. The graph of function f has been vertically stretched by a factor of 4.
B. The graph of function fhas been reflected over the y-axis.
C. The graph of function fhas been reflected over the x-axis.
D. The graph of function fhas been translated 3 units down.
D. The graph of function fhas been translated 4 units left.
E. The graph of function fhas been translated 3 units left.

((More than one))

The base of an exponent can be simplified by multiplying it by itself as many times as the exponent indicates. If you want to simplify the base of an exponent in an expression, it would be done by raising the base to the power of the exponent using the notation aᵇ = aa...*a (b times)

The base of an exponent is the number that is being multiplied by itself a certain number of times. The exponent is the number indicating how many times the base is being multiplied by itself.

For example, in the expression 2³, the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times, or 2 * 2 * 2. The simplified form of this expression is 8.

In general, if the base is 'a' and the exponent is 'b' then the simplified form of the expression is 'a' raised to the power 'b' or aᵇ = aa*...*a (b times)

It's also important to note that when the exponent is 1, the expression can't be simplified anymore. For example, 2¹ = 2, where 2 is the base and 1 is the exponent.

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The diagram relating to the scatterplot for the data is attached.

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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5y is the coefficient of x² in the given polynomial 5x²y.

Polynomial coefficients are the integers preceding a word. Terms are often composed of a number and a variable (for example, 2 x 2 2x2 2x2, where 2 is the number and x is the variable). The coefficient is represented by the number portion. Simply put, it is the leading term's coefficient. The polynomial degree is the largest power of the variable that occurs in the polynomial. The leading phrase is the one with the greatest power of the variable: the term with the greatest degree. The leading coefficient is the leading term's coefficient.

Here,

The coefficient of x^2 in the above polynomial 5x^2y is 5y.

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Answer: A=16 B=14 C=34

Step-by-step explanation:

It depends on the context and the audience. Both describing the solution of a system of linear inequalities in words and showing it using a graph have their own advantages.

An explanation graph is what?

A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.

Describing the solution of a system of linear inequalities in words is often useful when the system is simple and the inequalities are easy to understand. It can be a more straightforward way to explain the solution, especially when the audience is not familiar with reading graphs.

On the other hand, using a graph to show the solution of a system of linear inequalities can be more efficient and effective when the system is more complex and the inequalities are harder to understand. Graphs can provide a visual representation of the solution, which can make it easier for the audience to understand the solution and see how it relates to the original problem. Additionally, it can be easier to find the exact point of intersection between the inequalities by looking at the graph.

Both methods can be useful depending on the situation, so it's best to consider your audience, the complexity of the system, and the goal of your explanation when deciding which method to use.

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To satisfy the lengths of the two sides of the triangle given in the question, the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition.

If we know the lengths of two sides of a triangle, we can use the "triangle inequality theorem" to determine the possible lengths of the third side. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the lengths of two sides of a triangle are 5 inches and 12 inches, the length of the third side must be:

Greater than 0 inches

Less than the sum of the other two sides (5 inches + 12 inches = 17 inches)

Greater than the difference between the other two sides (abs(5 inches - 12 inches) = 7 inches)

So the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.

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On solving the provided question we can say that by percentage  40% of savings  = 40% of 20 = 40/100 X 20 = $8 140% of savings  = 140% of 20 = 140/100 X 20 = $28 his monthly allowance is =  $8 + $28 = $36

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Increase in savings $20

by percentage

40% of savings  = 40% of 20 = 40/100 X 20 = $8

140% of savings  = 140% of 20 = 140/100 X 20 = $28

his monthly allowance is =  $8 + $28 = $36

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Answer:

14

Step-by-step explanation:



the answer is  y = 16.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

E(-6, y), F(6, 5), G(14, 11), and H(8,-13),

& EF is perpendicular to GH.

now, we get,

The slope of GH is ...

G -H = (14, 11) -(8, -13) = (6, 24) = (Δx, Δy)

slope = Δy/Δx = 24/6 = 4

The perpendicular line through F will have a slope of the negative reciprocal of this, or -1/4.

The point-slope form of the equation can be written as ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

The perpendicular line through F is then ...

 y -13 = (-1/4)(x -6)

For an x-value of -6, the value of y will be ...

y = (-1/4)(-6 -6) +13 = 12/4 +13 = 16

hence, The value of y so that EF is perpendicular to GH is 16.

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F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.

Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.

There are three common types of logarithms such as:

Therefore logarithm is the mathematical expression used to answer the question.

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Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.

A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.

given, a function f(x) = √ (x² - 4x +4)

now for every input value of x we will get an output value for f(x).

we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}

when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]

                                                                            f(-3) = √25 =5

     similarly, f( -2) = 4

                            f(-1) = 3

                             f(0) = 2

                               f(1) = 1

                            f(2) =0

                           f(3) = 1

the range of function is {5, 4, 3, 2, 1, 0,1}

The range of function indicates that it is neither increasing nor decreasing.

hence the function is a monotonous function.

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Sam is 25 years old, and Harry is 5 years old.

If we multiply the age of Harry (5) five times, it will give us 25:

5×5= 25

and if we multiply Harry's age three times and then add up ten, it will give us 25:

(5×3) +10 = 25

15 + 10 = 25

25 = 25

Therefore ,perimeter of square photo frame = 63.2 centimeter.

The total length of boundary of a closed geometric shape is called perimeter. Different geometric shape has different formula for determining perimeter. For a square shaped object perimeter is the four times of its side length.

Here,

Area of a square photo frame = 250 square centimeter.

We know, area of a square photo frame = square of side length

if side length = s

area = s²

it is given that area of a square photo frame = 250 cm²

250 cm² = s²

s = √250 cm

s = 15.81 cm

side length = 15.81 cm

formula for perimeter = 4× side length

perimeter of frame = 4×15.81 = 63.24 cm

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Equality means being equal in all aspects such as status, rights irrespective of caste, colour, race, gender, etc.

Now, According to the question:

What is a equality in math?

Equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.

Example of Equality

Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division.

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The system of equations  y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].

What is algebraic equation ?

An algebraic equation is a mathematical expression that contains one or more variables, and an equal sign. The goal is to find the value or values of the variables that make the equation true. Algebraic equations can take many forms, such as linear equations, quadratic equations, polynomial equations, and more.

y = −2x + 14

x + 2y = −1

We can use the first equation to solve for y in terms of x:

y = −2x + 14

Now we can substitute this expression for y into the second equation,

x + 2(-2x + 14) = -1

x + (-4x + 28) = -1

-3x = -29

x = 9/3

Now we can substitute this value for x back into the first equation to find y,

y = -2(9/3) + 14 = -6/3 + 14 = -2 + 14 = 12

Hence , The system of equations  y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].

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The people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).

A set is like a bunch of different stuff put together; it includes elements or members, which can be anything mathematical, like numbers, symbols, shapes, variables, or even other sets.

So, we have:

N = { x ∈ U | x subscribes to News Magazine }

D = { x ∈ U | x subscribes to The Daily Informer }

As, N∩D ≠ ∅.

It looks like a decent amount of people surveyed only have a subscription to News Magazine and not any other magazines.

= Subscribe to News Magazine and not Daily Informer

= N ∩ D c

Out of the people surveyed, 4 of them only subscribe to the Daily Informer.

= Subscribe to Daily informer and not subscribe to News Magazine

= D ∩ N c

Out of the people surveyed, 4 of them only subscribe to the Daily Informer.

= Subscribe to News Magazine and not subscribe to Daily Informer or subscribe to Daily informer and not subscribe to News Magazine

= ( N ∩ D c ) ∪ ( D ∩ N c )

= ( N c ∩ D ) ∪ ( N ∩ D c )

Therefore, the people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).

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Complete question:

Let U represent the set of people in a certain community who were asked if they subscribe to an information source. Let D ={ x ∈ U | x subscribes to The Daily Informer } and N ={ x ∈ U | x subscribes to News Magazine } (Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.

a. N ∪ D

b. ( N c ∩ D ) ∪ ( N ∩ D c )

c. N c ∩ D

d. ( N ∩ D )c

e. ( N c ∪ D ) ∩ ( N ∪ D c )

Answer:51.96 dollars total

Step-by-step explanation:

go to a smart cauculator and add 8.25%  to 48

Answer:

36

Step-by-step explanation:

Answer:

Length = Width = 55

Step-by-step explanation:

Perimeter of rectangle = 2(length + width)

Let x = length; let y = width.

perimeter = 2(x + y)

The perimeter must be 220.

2(x + y) = 220

x + y = 110

y = 110 - x

length = x

width = 110 - x

area = length × width

area = x(110 - x)

area = 110x - x²

A = 110x - x²

Take the first derivative of the area function and set equal to zero. Then solve for x.

A' = 110 - 2x

110 - 2x = 0

2x = 110

x = 55

y = 110 - x = 110 - 55 = 55

Answer: Length = Width = 55

Answer:

20

Step-by-step explanation:

4 ans ten both have 20 in common and it jas ro be the first because the next is like 40

Answer:

b: 59 houses

Step-by-step explanation:

50 + 18% of 50 =

= 50 + 0.18 × 50

= 50 + 9

= 59

Answer:

b

Step-by-step explanation:

Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: The survey results from the sample as

A -240

B-210

C-50

The total number of people surveyed is 500

Now as per the given survey results the voters likely to vote for candidate A is P(A)=240/500

              =12/25

Similarly, the probability that the voters vote for Candidate A and B are

P(A)=210/500

      =21/50

P(B)=1/10

∴ If 18000 voters vote the voters likely to vote for A are

=12/25 ×18000

=8640 voters

Hence, Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.

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The probability of landing on yellow is less than the probability of landing on blue

Probability is the likelihood of a desired event happening.

Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.

Thus, we can write the probabilities as follow:

probability of orange = 1/8

probability of purple = 2/8 = 1/4

probability of yellow = 2/8 = 1/4

probability of blue = 3/8

Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement

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The approximate side length of the square is 4.2 units. Hence option B is the correct option.

What is a square?

A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.

Given that the length of half of the diagonal is 3 units.

The diagonals of the square cut each other at a right angle.

The length of OB is 3 units and OC is 3 units.

The △BOC is a right triangle at O.

The hypotenuse of △BOC is BC. The legs of △BOC are OB and OC.

According to the Pythagorean theorem,

OB² + OC² = BC²

3² + 3² = BC²

BC² = 9 + 9

BC² =  18

BC = 3√2

BC ≈ 4.2

The approximate side length of the square is 4.2 units.

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Answer:

$56.00

Step-by-step explanation:

8(5 + 2)  Distribute the 8

8(5) + 8(2)

40 + 16

56

The equation that has the solution x = -1 is D. 7x+8 = -6x - 5

To find the solution of an equation, we need to find the value of the variable that makes the equation true. In this case, we need to find the value of x that makes the equation 7x+8 = -6x - 5 true.

We can start isolating the x variable by adding or subtracting the same terms on both sides of the equation.

D. 7x+8 = -6x - 5

13x = -13

x = -1

So the solution of the equation is x = -1

We can check if this is the solution by substituting it back in the equation. If the equation is true, both sides will be equal when x is -1.

7x+8 = -6x - 5

7*-1 + 8 = -6*-1 -5

-7+8 = 6 -5

1 = 1 (true)

Therefore, D. 7x+8 = -6x - 5 has x = -1 as the solution.

The equation that represents the situation is $160.40 = $100 + $7.55h.

An equation is a statement that consists of numbers or letters and an equal to sign. The amount earned is a function  of the tip, hours worked and the pay per hour.

The form of the equation is:

Total amount earned =tip + (amount earned peer hour)

$160.40 = $100 + ($7.55 x h)

$160.40 = $100 + $7.55h

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