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4.6.3 Quiz: Transformation of Parent Functions
Question 2 of 10
If you apply the changes below to the cubic parent function, F(x) = x³, what is
the equation of the new function?
• Reflect across the x-axis.
Vertically compress by multiplying by
A. H(X)-(2x)
B. G(x)=(2x)³
C. (x)--²
D. K(x)--2x²

Answer: (7)^-2 and 1/49 are equivalent

Step-by-step explanation:

a) If it snows today, I will ski tomorrow.

Converse: If I ski tomorrow, it snows today.

Contrapositive: If I don't ski tomorrow, it doesn't snow today.

Inverse: If it doesn't snow today, I won't ski tomorrow.

b) I come to class whenever there is going to be a quiz.

Converse: Whenever I come to class, there is going to be a quiz.

Contrapositive: Whenever I don't come to class, there isn't going to be a quiz.

Inverse: Whenever there isn't going to be a quiz, I don't come to class.

c) A positive integer is a prime only if it has no divisors other than 1 and itself.

Converse: If a positive integer has no divisors other than 1 and itself, then it is a prime.

Contrapositive: If a positive integer is not a prime, it has divisors other than 1 and itself.

Inverse: If a positive integer has divisors other than 1 and itself, it is not a prime.

A mathematical conditional statement is a statement that presents a relationship between two statements, where one statement (the "condition") is only true if the other statement (the "conclusion") is also true.

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The range of the length is 3.2 meters to 3.34 meters

From the question, we have the following parameters that can be used in our computation:

Length of pipe = 3.27 meters

Relative error = 0.07 meters

Represent the range with x

So, we have

|x - Length| = Relative error

substitute the known values in the above equation, so, we have the following representation

|x - 3.27| = 0.07

Remove the bracket

x - 3.27 = 0.07 or x - 3.27 = -0.07

Evaluate

x = 3.2 or x = 3.34

Hence, the range is 3.2 meters to 3.34 meters

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The domain of the function f(x) - g(x) is given as follows:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

The domain of a function is the set composed by all the input values that the function accepts.

For a square root, the inner term cannot be negative, hence the domain of f(x) is given as follows:

x² - 3 >= 0

|x| >= sqrt(3)

x <= -sqrt(3) or x >= sqrt(3).

For function g(x), the domain is given as follows:

36 - x² >= 0

x² <= 36

|x| <= square root (36)

|x| <= 6.

-6 <= x <= 6.

The domain of the subtraction function is the intersection of the domain of both functions, hence:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

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Answer:

42/6 = 7 Minutes

Step-by-step explanation:

The shape and size remains the same represents the correct alternative.

Given is that a figure is rotated 180 degrees clockwise about the origin.

When a coordinate (x, y) is rotated by 180 degrees clockwise about the origin, the new coordinates become ( - x, - y). But only the coordinates change, the shape and size remains the same.

Therefore, the shape and size remains the same represents the correct alternative.

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The correct answer is 500 yards. The largest area for the field will be when the cube is a forecourt. With 2000 yds. of fencing, each side would be 2000/4 =  500 yds.

Long, or 500 yds.  If there were no swash also, the largest area would be given by a square configuration since adding the length and dwindling the range of a square by the same value, t will drop the area by a square with sides of length.  Now add the swash on one side. The swash acts like a glass.

As we guard in a cube on one side of the swash, imagine an identical cube on the other side. The maximum area is given when the two blocks form a square, that's when we have a cube doubly as long as wide.

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The value of the largest area of the field will be 5000 sq. ft.

From the given data,

Total pasture area of fencing =2,000 feet

The shape of the field =rectangular

As the area of the rectangle = l*b

So, we can write it as;

2000=x+2y, (As the area of surrounded by a river from one side, so we need to only fence twice of width and only one length (Side) of the rectangle.

Now applying the formula of the area of the rectangle

we will get it as:

[tex]$$\begin{aligned}& A(x)=x\left(\frac{2000-x}{2}\right)=\frac{1}{2}\left[2000 x-x^2\right] \\& A^{\prime}(x)=\frac{1}{2}[2000-2 x]=0 \\\end{aligned}$$[/tex]

Solving the value,

We will get: x=100 ft y=50 ft

So, determining the value of the largest area,

We will get it as:

A_{max}=(100)(50)=5000 Sq. ft.

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(0, -26) and (0,25 )is the focus of the hyberbola.

Any point in a hyperbola has distances from the two foci that are fixedly different from each other.

Every hyperbola has two foci (plural for focus). The hyperbola's branches are encircling both of them.

(0,-26) is inside the lower branch (0,-24) is not inside the lower branch (0,25) is inside the upper branch (0,30) is inside the upper branch

Lower branch is our main focus. We must examine the image to determine which of two potential solutions is correct. From the maxima to the focus for the lower branch is one distance. The top branch needs the same, which we must discover. Distances between points (0,30) and (0.25) are 1 and 6, respectively.

(0, -26) and (0,25).

The complete question is,

What is the depicted hyperbola's point of focus? (0, −26) (0, −24) (0, 25) (0, 30) (0, 30) BRAINLIESTT.

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In a data set, the number of observations will always be the same as the group of answer choices number of variables is the number of elements.

A data set is a collection of data. It is a set that corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.

The data set lists values for each of the variables, such as example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files.

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The expression that represents the number of seconds Jacob has been running is t - 7.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. An expression's structure is as follows: (Math Operator, Number/Variable, Math Operator). The two integers are connected by a mathematical operator.

Since Jacob started running 7 seconds after Alma, the number of seconds Jacob has been running can be represented as t - 7. So the expression that represents the number of seconds Jacob has been running is: t - 7.

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It is impossible to create a Gaussian surface that makes it easy to calculate the electric field around a charged dipole. Thus, the response is no.

According to Gauss's law, the enclosed electric charge directly affects how much an electric field's net flux is moving over a closed surface. This is given by, [tex]\phi=\frac{Q}{\epsilon_0}[/tex], where the electric flux is represented by Ф, the permittivity of free space is represented by [tex]\epsilon_0[/tex], and the enclosed charge is represented by Q.

Gauss's law must be applied for the symmetric charge distribution required for the given surface in the equation [tex]\frac{Q}{\epsilon_0}=\int\vec{E}\cdot d\vec{A}[/tex] to have a single value of the electric field.

The electric field surrounding a charged particle can be estimated using the Gaussian surface. Gauss' Law cannot be applied to the dipoles because electric dipoles lack a surface with a symmetric distribution of the electric field all around them.

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Answer: We can set up a system of equations to represent the information given:

Let x = length of Barbary River

Howler River = x + 230

Gin River = x + 150

Retinal River = x - 30

Total length = x + (x + 230) + (x + 150) + (x - 30) = 19,230

We can then use substitution and the equations above to solve for the length of each river:

x + (x + 230) + (x + 150) + (x - 30) = 19,230

4x + 350 = 19,230

4x = 18,880

x = 4720 (length of Barbary River)

Howler River = x + 230 = 4720 + 230 = 4950 mi

Gin River = x + 150 = 4720 + 150 = 4870 mi

Retinal River = x - 30 = 4720 - 30 = 4690 mi

Step-by-step explanation:

Based on the analysis, we can be conclude that (C) Driving behavior and gender are related.

The link between variables is described by correlation. It can be viewed positively or negatively, as well as strong or weak. A correlation does not prove a cause. When the variable on the x-axis rises as the variable on the y-axis rises, there is a positive linear association. An upward-sloping straight regression line illustrates this.

When one variable rises while the other falls, there is a negative linear correlation. A straight regression line with a falling slope illustrates this. When there is a relationship between variables, but the relationship is not linear, there is a non-linear correlation (straight).

Hence, according to correlation theory, Driving behavior and gender are related.

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The solution to the absolute value equation |6x – 4| = 6 is 6x - 4 = 6 and 6x - 4 = -6

An equation is an expression that shows the relationship between numbers and variables.

The absolute value of a real number x is the non-negative value of x without regard to its sign.

Given the absolute value equation:

|6x - 4| = 6

Therefore, the absolute equation can be represented by:

6x - 4 = 6 and -(6x - 4) = 6

Simplifying:

6x - 4 = 6 and 6x - 4 = -6

adding like terms:

6x = 10 and 6x = -2

x = 5/3 and x = -2/3

The solution to |6x – 4| = 6 is x = 5/3 and x = -2/3

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35% can be represented in equivalent decimal form and fraction form 0.35 and 7/20

35% is equivalent to 0.35 in decimal form. Divide the percentage by 100 to get the decimal equivalent. 35 / 100 = 0.35.

35% is equivalent to 7/20 as a fraction. A percentage must be multiplied by 100 before being simplified to become a fraction. 35/100 = 0.35, or 7/20, can be written more simply.

Although both forms are equal, they are employed in various contexts. The fraction form is more frequently used in probability and statistics while the decimal form is more frequently used in calculations.

It's also important to keep in mind that percentages are a technique to express numbers as fractions of 100. For example, 35% is the same as 35/100, or 7/20.

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Total area of the roof top garden is 272 ft² .

Rooftop planters can have soil depths ranging from six inches at the very least, to allow for little groundcovers and shrubs, to three to four feet, which is necessary for huge shade and coniferous trees. Divide the length by the width of a rectangle or square to find its area.

The square footage of the area is calculated by multiplying the length and width. Please maintain the same unit size (feet or inches). For a rectangular garden area, multiply the length by the width to get the square footage. A suitable garden is often one that is roughly 10 feet by 10 feet, if your landscape permits it (3 x 3 meters).

Given, the figure comprises of triangle and rectangle,

Area of rectangle = length × breadth

= 12 ft × 20 ft

= 240 ft²

Area of triangle = 1/2 × base × height

= 1/2 × 8 × (20 - 12)

= 1/2 × 8 × 8

= 32 ft²

Total area of the figure = Area of rectangle + Area of triangle

= 240 + 32

= 272 ft²

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Answer: 5s + 28.3

Step-by-step explanation:

The area of quadrilateral ABCD = 4√6314 sq cm. +  15√663 sq. cm

For this given question:

In ΔABD , using Heron's formula.

semi perimeter s = a + b + c / 2

s = 27 + 25 + 30 / 2

s = 41 cm

Now,

Area ( ΔABD ) = √s(s - a)(s - b)(s - c)

Area ( ΔABD ) = √41(41 - 27)(41 - 25)(41 - 30)

Area ( ΔABD ) = √41x14x16x11

Area ( ΔABD ) = 4√6314 sq cm.

Now,

In ΔBCD

semi perimeter s = a + b + c / 2

s = 32 + 28 + 30 / 2

s = 45cm

Area ( ΔBCD ) = √s(s - a)(s - b)(s - c)

Area ( ΔABD ) = √45(45 -32)(45 - 28)(45 - 30)

Area ( ΔABD ) = 15√663 sq. cm

Thus, the area of quadrilateral ABCD = 4√6314 sq cm. +  15√663 sq. cm

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For the graphed function we have:

The domain

D: {-3, -2, -1, 0, 1, 2}

And the range

R: {0.25, 0.5, 1, 2, 4, 8}

For a function y = f(x), we define the domain as the set of possible inputs and the range as the set of possible outputs.

Remember that the notation in point form is (input, output).

Now, the graphed points are:

(-3, 8), (-2, 4), (-1, 2), (0, 1), (1, 0.5), (2, 0.25)

The domain is the set of the first values:

D: {-3, -2, -1, 0, 1, 2}

And the range is the set of the second values:

R: {0.25, 0.5, 1, 2, 4, 8}

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The solutions to the equations is the point of intersection of graphs and the points are ( 0 , 2 ) and ( 1 , 1.25 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = ( -3/4 )x + 2   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = ( 1/4 )ˣ + 1   be equation (2)

Now , to calculate the solutions to the equations , plot the equations in the graph

The point of intersection of equation of lines represents the solution to the equation

Substituting the values in the equation , we get

( -3/4 )x + 2 = ( 1/4 )ˣ + 1

The first point of intersection is ( 0 , 2 )

when x = 0 , y = 2

( -3/4 ) (0) + 2 = ( 1/4 )⁰ + 1

On simplifying the equation , we get

0 + 2 = 1 + 1

2 = 2

So , the solution is ( 0 , 2 )

Hence , the equations are solved

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The sum of the fraction given for the sum of 7/8 and 1/4 will be 1 1/8.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that the sum of 7/8 and 1/4 will be:

= 7/8 + 1/4

= 7/8 + 2/8

= 9/8

= 1 1/8

Therefore, the sum is 1 1/8.

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Complete question

7/8 + 1/4. Find the sum.

According to the following Venn diagram, the number students surveyed is 2063

The term Venn diagram in math is defined as overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Here we have given that anonymous survey of college students was taken to determine behaviors regarding​ alcohol, cigarettes, and illegal drugs.

While we looking into the Venn diagram we have identified that 875 drank alcohol​ regularly, 665 smoked​ cigarettes, 207 used illegal​ drugs, 422drank alcohol regularly and smoked​ cigarettes, 113 drank alcohol regularly and used illegal​ drugs,126 smoked cigarettes and used illegal​ drugs, 97 engaged in all three​ behaviors, and 217 engaged in none of these behaviors.

Then the number of students is calculated as,

=> 875 + 667 + 207 + 97 + 217

=> 2063

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The perimeter of the triangle BCD is 17.25 centimeters.

A closed route that covers, encircles, or outlines a one-dimensional length or a two-dimensional form is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are several uses in real life for perimeter calculations.

so, perimeter of the triangle is the sum of all its side length.

Perimeter of one triangle / perimeter of another triangle= side of one triangle by side of another triangle.

let us suppose that the perimeter of triangle BCD is equal to X

27.6/x = 9.6/6

x = 17.25 cm

therefore, the perimeter of triangle BCD is equal to 17.25 centimeters.

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So, the average speed of the train is 54.09 miles per hour.

To calculate the average speed of the train for the entire trip, you need to find the total distance traveled and the total time traveled.

First, you can convert the time traveled at each speed to hours. 40 minutes is equal to 40/60=0.67 hours. So the total time traveled is 1+0.67=1.67 hours.

To find the total distance traveled, you can use the formula: distance = speed x time. At 45 mph, the distance traveled is 45 x 0.67 = 30.15 miles. At 60 mph, the distance traveled is 60 x 1 = 60 miles. Therefore, the total distance traveled is 30.15 + 60 = 90.15 miles.

Finally, you can use the formula: average speed = total distance / total time.

Average speed = 90.15 miles / 1.67 hours = 54.09 miles per hour.

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Answer:

(i) 11 years old

(ii) 30 years old

Step-by-step explanation:

K is x

In four years, he will be x+4 and his mother will therefore be 3(x+4)

Six years ago, he was x-6 and his mother was 7(x-6).

In 10 years his mother went from 7(x-6) to 3(x+4)

so their difference is 10

7x-42+10=3(x+4), since 7x-42 is 10 years less than 3x+12

7x-32=3x+12

4x=44

x=11 age of K now

in 4 years he will be 15 and his mother 45.

Six years ago he was 5 and his mother 35

Therefore, his mother was 30 when he was born.

She is now 41.

Imran is currently 10 years old. His mother's current age is 34 years old and she was 24 years old when Imran was born.

The question involves a system of equations based on the relationship between Imran and his mother's ages. We can define Imran's current age as i and his mother's current age as m. From the problem we have the following two equations:

By solving this system of equations, we can determine that Imran's current age (i) is 10 years old and his mother's current age (m) is 34 years old. To find the age of Imran's mother when he was born, we would subtract Imran's age from his mother's, i.e., 34 - 10, so Imran's mother was 24 years old when Imran was born.

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The inequality expression has no solution for a

From the question, we have the following parameters that can be used in our computation:

a > a + 4

Subtract the variable a from both sides of the equation

So, we have the following representation

a - a > a + 4 - a

Evaluate the difference

This gives

0 > 4

The above expression is false

hence, the inequality has no solution

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so we have hmmm 4 sets above, hmm let's check say the second set, the triangle with sides 5, 9, 3.  Check the picture below.

we have three sides, let's look at the two smaller sides first, 5 and 3.

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 5 - 3 = 2.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 2.

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 3 + 5 = 8.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 8.

so for those reasons the third side can't be 9, it won't work for a triangle, even 8 is not good, so it must be less.

Now, if we look at the 1st set and 4th set, we end up with the same dilemma, the longest side is too long.

If we take a looksie at the 3rd set however with small sides of 6 and 7, it gives us a third side that must be more than 1 but less than 13, so 7 fits just nicely, so that one works.

Sid has a total of 32 caps.

In mathematics →

Given is that Sid has a baseball cap collection. 75% of his caps have sports team symbols. 24 of the caps have the team symbols.

Let the total number of caps be {x}. Then, we can write -

24 = 75% of {x}

24 = (75/100) {x}

24 = 3/4 {x}

{x} = 24 x 4/3

{x} = 32

Therefore, Sid has a total of 32 caps.

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