The length of a bed would be about

The total number of functions from a set with 4 elements to a set with 3 elements is 333 × 3 = 64.

There are a total of 4³ = 64 functions from a set with 4 elements to a set with 3 elements.

A function from a set A to a set B is a rule or a correspondence that assigns to each element of A exactly one element of B. Set A is called the domain of the function and set B is called the co-domain.

Since there are 4 elements in the domain and 3 elements in the co-domain, each element in the domain can be mapped to any of the 3 elements in the co-domain.

So for the first element in the domain, there are 3 options to map it to in the co-domain. Similarly, for the second element, there are 3 options, and so on.

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A positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).

Average rate is a term used to describe the mean value of a set of data points or the mean rate of change of a function. It is calculated by adding all the values in a set and then dividing the sum by the total number of values.

The average rate of change of a function over an interval [a,b] is given by the formula (f(b) - f(a))/(b - a). Therefore, for h to have a positive average rate of change over an interval, we must have f(b) - f(a) > 0.
Substituting h(x) into this formula, we get (1/8b^3 - b^2 - 1/8a^3 + a^2) / (b - a) > 0.
Solving for b, we get b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
Therefore, h has a positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).

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Answer:

6(x+2y) + 3 + 4y + 5

6x+12y+3+4y+5

Simplified: 6x+16y+8

Step-by-step explanation:

The correct answer is C. We can add and subtract terms regardless if they have the same base.

To add polynomials, we add the coefficients of the like terms together. For example, to add 2x^3 + 5x^2 + 6x + 3 and 3x^2 + 7x + 8, we would first identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then added together, so 2x^3 + (5+3)x^2 + (6+7)x + (3+8). The result is 2x^3 + 8x^2 + 13x + 11.

To  subtract polynomials, we subtract the coefficients of the like terms. For example, to subtract 3x^2 + 7x + 8 from 2x^3 + 5x^2 + 6x + 3, we would identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then subtracted, so 2x^3 + (5-3)x^2 + (6-7)x + (3-8). The result is 2x^3 + 2x^2 - x - 5.

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Answer:

6x^3 + x^2 - 12x^2 - 18x - 6x - 6 = 6x^3 - 18x^2 - 12x - 6.

Step-by-step explanation:

simplify the expression (2x+3)(3x^2-6x+2)
First, we'll use the distributive property to expand the product of the two binomials:

(2x+3)(3x^2-6x+2) = 2x(3x^2-6x+2) + 3(3x^2-6x+2)

Next, we'll expand the product of each term in the first binomial with each term in the second binomial, using the distributive property again:

= 2x3x^2 + 2x(-6x) + 2x2 + 33x^2 + 3*(-6x) + 3*2

We can now simplify the resulting terms by combining like terms and combining the coefficients:

= 6x^3 -12x^2 + 4x + 9x^2 -18x + 6

we will combine the like terms

= 6x^3 - 18x^2 + 4x + 6

This is our final expression in standard form

The correct option is C.

A graph is a visual representation of data or a function, typically shown on a coordinate plane. It can be used to display information in a clear and concise way, and can be used to identify patterns, trends, or relationships within the data. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts. They are used in many different fields, including mathematics, science, engineering, economics, and statistics. A right angled triangle is a type of triangle in which one angle is 90 degrees. The side opposite the right angle is called the hypotenuse and the other two sides are called the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

There are several types of graphs that can be used to represent data and information, including:

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Answer:

The simple interest is calculated by multiplying the principal amount by the interest rate and the number of years.

Simple Interest = Principal x Interest Rate x Time

The simple interest on Boden's account is:

800 x 3.2% x 4 = 800 x 0.032 x 4 = $256

To find the total amount in the account after 4 years, we add the interest to the principal:

800 + 256 = $1056

So, Boden's account will have $1056 after 4 years.

Answer:

y = 37x

Step-by-step explanation:

We know

The value of y is 37 times the value of x, so our equation is

y = 37x

Answer:

9√6

Step-by-step explanation:

3√2 × 3√3

3√2×3 ×3

3√6×3

9√6

The formula for scale factor is: Scale Factor = New Length / Original Length.

Scale factory the rescue between two corresponding length, area or the volumes of two similar figure it is used to compare the size of one figure to another as well as to the enlarge of reduced to size of a figure the scale factor is expressed as a ratio such as one is to to fit the first number is the original size and the second is the new size.

This is used to determine the factor by which an object has been scaled up or down. For example, if an object was originally 8 inches long and then scaled up to 16 inches long, the scale factor would be 2, as 16 is twice the length of 8.

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The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

What is Perpendicular bisector of the segment?

A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.

The midpoint of the segment GH is the point (3,-3).

The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4

The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of the equation of the line is y - y1 = m(x - x1)

So we have

y - (-3) = (-3/4)(x - 3)

y + 3 = (-3/4)x + (9/2)

We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)

so our final equation is y = -(3/4)x + (9/2)

Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

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Bases are chemical compounds that can accept hydrogen ions (H+) when added to water. Bases have a pH higher than 7 on the pH scale. Common bases include baking soda (sodium bicarbonate), lye (sodium hydroxide), ammonia (NH3), and calcium hydroxide (CaOH2).

Bases are an important concept to understand in Grade 7 Chemistry. They are chemical compounds that have a pH higher than 7 on the pH scale and are capable of accepting hydrogen ions (H+) when added to water. Knowing the basics of bases can help students in a variety of ways, from understanding the properties of solutions to being able to identify and use different bases in lab experiments.

To begin with, understanding the properties of bases is essential in order to properly identify and use them in experiments. Bases can be divided into two categories: alkalis and acids. Alkalis are bases that are soluble in water, while acids are bases that are insoluble in water. Each type of base has its own unique properties and uses. For example, baking soda (sodium bicarbonate) is a common alkali that can be used for baking, cleaning, and even as an antacid. Meanwhile, lye (sodium hydroxide) is an acid that is used in many industrial processes, such as soap and textiles manufacturing.

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Answer:

67.1

Step-by-step explanation:

Writing the statement '49 is 73% of what number?' where x is the number we are trying to find:

[tex]49 = 73\% \: of \: x[/tex]

To find the percentage of a number, we multiply the number by the decimal equivalent of the percentage, so can be rewritten as:

[tex]49 = \frac{73}{100} \times x[/tex]

[tex]49 = 0.73x[/tex]

[tex] \frac{49}{0.73} = x[/tex]

[tex]x = 67.1 \: rounded \: to \: 3 \: signifiant \: figures[/tex]

1. steps to find the value of x

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate y:

-6x+y= -11 | times -3| becomes 18x-3y=33

18x-3y=33

-2x-3y = -7

y in the equation can be eliminated to become:

20x=40

x=40/20

x=2

steps to find the value of y:

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate x:

-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21

-6x+y= -11

-6x-9y=-21

x in the equation can be eliminated to become:

10y=10

y=-10/10

y=1

2.

1. steps to find the value of x

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate y:

-x+y=-1| times -3| to 3x-3y=3

-2x-3y = -1

3x-3y=3

y in the equation can be eliminated to become:

-5x=-4

x=4/5

Steps to find the value of y:

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate x:

-x+y=-1| multiplied by 2| becomes -2x+2y=-2

-2x-3y = -1

-2x+2y=-2

x in the equation can be eliminated to become:

-5y=1

y=-1/5

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A perpendicular bisector is a line that passes through the midpoint of two points, and is perpendicular to the line connecting the two points.

An example of a perpendicular bisector is the line between points A(2,4) and B(4,6). The midpoint of A and B is (3,5), and the equation of the line perpendicular to A and B is y= -x+10. To verify that the equation is perpendicular to A and B, we can calculate the slope of the line connecting A and B. The slope of A and B is (6-4)/(4-2) which is equal to 2. The slope of a perpendicular line is the negative reciprocal of 2, which is -1/2. Therefore, the equation of the perpendicular line is y = -(1/2)x + 10. This equation passes through the midpoint (3,5) which verifies that it is a perpendicular bisector of A and B.

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Check the picture below.

No, prime numbers are not divisible by any other number apart from one and number itself.

As given in the question,

Given numbers are prime numbers,

Condition to be asked :

Prime numbers are divisible.

Prime numbers are those numbers which are only divisible by only two numbers one and number itself.

Prime numbers has only two factors one and number itself.

Example of prime numbers are as follow :

2, 3, 5, 7, 11,.....so on.

If the number has more than two factors then the numbers are considered as composite numbers.

One is neither prime nor composite.

Therefore, prime numbers are not divisible by any other number.

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The unit rate of the pound of rice is given by the equation A = $ 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the unit rate of the pound of rice be represented as A

Now , the equation will be

The cost of 2 pounds of rice = $ 4

So , the cost of 1 pound of rice = cost of 2 pounds of rice / 2

Substituting the values in the equation , we get

The cost of 1 pound of rice A = 4 / 2

The cost of 1 pound of rice A = $ 2

Therefore , the value of A is $ 2

Hence , the equation is A = $ 2

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Yes, 2x²-√3x+9=0 is a quadratic equation.

A quadratic equation is a type of polynomial equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the equation 2x²-√3x+9=0 can be written in the form of ax² + bx + c = 0, where a = 2, b = -√3 and c = 9. Therefore, it is a quadratic equation. Quadratic equations have solutions in the form of x = (-b ± √(b² - 4ac))/2a, which is also known as the quadratic formula. In this case, if we substitute the values of a, b, and c into the quadratic formula, we can find the solutions for x in the equation 2x²-√3x+9=0.

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Complete question:

2x²-√3x+9=0 is it a quadratic equation​?

....................

In January, the number of days shown by the equation m = 4w + 3.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A pattern shown in the image.

Let m is the number of days in a month.

And w represents the number of days in the weeks.

So, algebraic equation,

m = 4w + 3.

Therefore, the equation is m = 4w + 3.

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Answer:

28.2 percent

Step-by-step explanation:

multiply 1/5 by 141

There are many methods for solving equations, but the two main methods are algebraic method and graphic method.

Algebraic methods: These methods involve using algebraic manipulation to isolate the variable on one side of the equation and find its value. This can include using operations such as addition, subtraction, multiplication, and division, as well as the use of inverse operations (e.g. undoing addition with subtraction) and properties of equality (e.g. transitive property).

Graphic methods: These methods involve using graphs to represent the equation and find the solution. This can include plotting the equation on a coordinate plane and finding the points of intersection, or using a graphing calculator or software to plot the equation and find the solution.

It's worth noting that the method used to solve an equation will depend on the complexity of the equation and the information available. Some equations can be easily solved using algebraic methods, while others may require a combination of algebraic and graphic methods or an entirely different approach.

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Answer:

0.0625 pounds are in an ounce

Step-by-step explanation:

Hope This Helps!

Answer:

Below

Step-by-step explanation:

There are 16 oz to a pound

if you have    'z' ounces    then you have   z/16  pounds

z oz   /  16 oz/lb =   z/16  lb

No, it is not possible to define all terms in geometry. The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

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No, it is practically not possible to define all terms in geometry. Points, lines, and planes are just a few of the many terms not defined in geometry.

The point, line, and plane are only adequately described by examples and descriptions, hence they are regarded as undefined words in geometry. Give the points, lines, and planes a name. Points that are on the same line are known as collinear points.

A legal document's definitions are often located at the outset, or at the start of a standalone portion like a schedule or section.

The study of different mathematical or real-world shapes, sizes, and figures is known as Geometry. You will learn about points, lines, planes, angles, parallel lines, triangles, similarity, quadrilaterals, transformations, circles, and area in geometry.

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From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.

What is the Onto function ?

Onto function can be defined as the function in which the range is equals to codomain.

We know that relation  can be defined as the relationship between sets of values and it is denoted by R.

And Function can be defined as the it is a relation where with only one output to each input.

From the given figure,

(0,-2) (0,1) (1,2) (2,1) (3,4) are the ordered pairs and here 0 is input for both -2 and 1
Hence , From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.

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Triangle ABC and Triangle are congruent, but PF is the corresponding side.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices. 

According to our question-

The matching parts of two figures that are congruent are identified by their respective vertices in the same order.

The side PF of PDF corresponds to the side AC of ABC (the first and last letters of the name or vertices) (corresponding letters in the name).

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The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(5, 1) and (-1, 3)

The slope of the line is given as,

m = (3 - 1) / (- 1 - 5)

m = 2 / (-6)

m = - 1/3

The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.

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Step-by-step explanation:

we need Pythagoras for right-angled triangles

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.

so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.

we know the length of the rectangle (15 ft).

the width is also the second leg of the attached right-angled triangle.

so, we know

13² = 5² + (leg2)²

169 = 25 + (leg2)²

144 = (leg2)²

leg2 = sqrt(144) = 12 ft

the total area is

the area of the rectangle

+

the area of the triangle

the area of the rectangle is

length × width = 15 × 12 = 180 ft²

the area of the right-angled triangle is

leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²

the total area is

180 + 30 = 210 ft²

FYI - a different way is to directly calculate the area of the trapezoid :

(base1 + base2)×height/2

height = the width of the rectangle or leg2 of the right-angled triangle.

so, we have

(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²

An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. The formula for an ordered pair is (x,y). where x and y are the coordinates.