The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers

Two steps in solving the inequality: simplify the algebraic expressions by combining like terms and isolating the target variable, then applying the mathematic operators.

-  Simplify the expression by: open the parentheses of algebraic expression, combine the terms like, and isolate the target variable.

- Use mathematic operators such as: addition, subtraction, multiplication, and division. All mathematic operations must be done on both sides. Addition and subtraction do not change the inequality. Multiplication and division with positive numbers will not change the inequality.

Multiplication and division with negative numbers will change the sign of the inequality.

Example:

Solve the inequality: 3x + 2 < 5x - 8

Step one: Subtract both sides with 5x and 2, this operation does not change the inequality sign

3x + 2 - 5x - 2 < 5x - 8 - 5x - 2

-2x < -10

Step two: Divide both sides with (-2). Since we divide with negative numbers, flip the inequality sign.

-2x/(-2) > -10/(-2)

x > 5

Hence, the solution is x> 5

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Answer:

Y=-[tex]\frac{1}{2}[/tex] + 4

Step-by-step explanation:

You will be using the equation of Y= Mx+B

First you must find the Y intercept, where the line crosses the Y axis, this is at positive four, this will be your B value. then you find the slope by picking 2 easily readable points on the graph, to do this i will choose (0,4) and (2,3), then you find the change in Y and put it in a fraction over the change in x, since this is going down the slope will have a negative infront of it, so your fraction is [tex]\frac{3-4}{2-0}[/tex] which equates to [tex]\frac{-1}{2}[/tex] so your slope is -1/2 (this is M value)

so lastly you plug it all in, Y= -1/2x+4

The slope of line equation 5y = -10 is m = 0.

There are three type of the equation of line:

- slope-intercept form.

The equation of line is: y = mx + b

Where:

m = slope

b = y-intercept

- point-slope form

The equation of line is: y - y₁ = m(x - x₁)

Where:

m = slope

(x₁,y₁)  = a point on the line

- standard form

Ax + By + C = 0

Where A, B, C are constant

The given equation of line is: 5y = -10

Convert it first to slope-intercept form. Divide both sides by 5:

5y/5 = -10/5

y = -2

Then, compare with slope intercept form: y = mx + b

Note that y = -2 can be written as:

y = 0 ·x - 2

Hence, the slope = m = 0

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Due to the lack of spatial thinking instruction in most math classes, people say geometry is hard. People should acquire geometrical ideas easily instead.

The father of geometry, Euclid was a brilliant mathematician. 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.

Everyone finds it difficult to dive into the issue of proofs. Children must realize that this issue affects everyone, even the mathematically skilled. Because they have trouble seeing how 3D, and 2D, forms, angles, and lines connect from various viewpoints, most youngsters struggle with geometry issues. Even kids who are really good at solving sum problems in math might be utterly stumped by this.

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Due to the lack of spatial thinking instruction in most math classes, people say geometry is hard. People should acquire geometrical ideas easily instead.

Euclid, the inventor of geometry, was a master mathematician. The words "ge" and "metria," both of which denote "measuring," are where geometry got its start. The way the Greeks approached geometry has been the basis for geometry for more than 2000 years.

Geometry is the study of different mathematical or real-world shapes, sizes, and figures. Geometry teaches us about numerous angles, transformations, and similarities among forms. The primary components of geometry are the point, line, and plane.

Everyone finds it challenging to explore the topic of proofs. Children need to understand that this problem impacts everyone, even those who are good at arithmetic. Most kids have problems with geometry because they have trouble recognizing how 3D and 2D shapes, angles, and lines link from different views. Even children who excel at math sum problems may be completely baffled by this.

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A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.

A statistical method called the sum of squares (SS) is used in regression analysis to determine how well the data can fit the model and how dispersed the data are. Since it is determined by adding up the squared differences, the sum of squares is how it is calculated.

A sum's square is equal to the product of its summands' squares and its double products' sums of summands in twos.

So, it is not always true that the square root of a sum is equal to the sum of the square roots.

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The correct answer is 6.432 × 10 raised to the power of 6

The derivatives of the functions are as follows:  y' = 4x^3+2x-3x^2-3 , s'(t) =[tex]2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex] ,  f'(x) = 4x^3sin x + x^4cos x

1. y' = (2x-3)(x^2+1) + (x^2-3x)(2x) = 4x^3+2x-3x^2-3

2. s'(t) = [tex](1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t) = 2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex]

3. f'(x) = 4x^3sin x + x^4cos x

1. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.

y' = (2x-3)(x^2+1) + (x^2-3x)(2x)

2. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.

[tex]s'(t) = (1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t)[/tex]

3. Begin by applying the quotient rule to differentiate the function. The quotient rule states that the derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions minus the product of the two functions divided by the square of the denominator.

f'(x) = 4x^3sin x + x^4cos x

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The distance PR, representing the distance across the river, is given as follows:

PR = 294 ft.

Similar triangles are triangles that share these two features given as follows:

The two similar triangles for this problem are given as follows:

POC and PRE.

Hence the distance PR is symbolized as follows:

PR = x.

The equivalent side lengths form a proportional relationship, given as follows:

x/(x + 160) = 230/355.

Hence, applying cross multiplication, the distance PR is obtained as follows:

355x = 230(x + 160)

355x = 230x + 36800

125x = 36800

x = 36800/125

x = 294 ft.

The diagram is given by the image presented at the end of the answer.

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Answer: The distance across the river is 181 ft.

Step-by-step explanation:

in photo

0 degrees is located in Quadrant I of the Coordinate Plane.

Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive. 0 degrees is the angle formed by the positive x-axis, and it is located in Quadrant I.

A coordinate plane is divided into four sections called quadrants, which are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.

This quadrant is defined by angles between 0 and 90 degrees and is generally associated with positive values on both the x- and y-axes.

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The true statements are,

A.) The pre-image is in quadrant III.

B.) The orientation of the vertices changed.

D.) The line of reflection is the x-axis.

It is determined by the order in which a figure's vertices are labeled. It refers to the sequence of points after a transformation has been applied to a geometric figure. The order may be clockwise or counterclockwise.

Here, we have,

from the given figure ,we get,

the true statements are,

A.) The pre-image is in quadrant III.

B.) The orientation of the vertices changed.

D.) The line of reflection is the x-axis.

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Answer: 90 sqare meters

Step-by-step explanation: you have to take 972 and divide it by 10.8 then you get your answer

The requried simplified value of the given expression is given as -a³/4b². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= [-b³]⁰/[2ba⁻⁷ × -2ba⁴]
= -1 / 4b²a⁻³
= -a³/4b²

Thus, the requried simplified value of the given expression is given as -a³/4b². Option B is correct.

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The total area of the figure when divided in rectangle, triangle and half circle is 86.13 square units.

Area is the room contained by a specific shape or location. It speaks of how much room is consumed. The area and perimeter of the shape will increase in size as it gets bigger.

Given figure comprises of a rectangle, triangle, and a half circle.

The area of the figure is thus calculated by adding the value of all the figures as follows:

A = Area of triangle + Area of rectangle + Area of semi-circle

[tex]A = \frac{1}{2} (b) (h) + (l)(b) + \frac{1}{2} (\pi r^{2} )\\[/tex]

Substitute the value of length, width, height and radius:

[tex]A = \frac{1}{2} (6) (6) + (9)(6) + \frac{1}{2} (3.14 (3^{2}) )\\\\\\A = 18 + 54 + 14.13\\\\A = 86.13[/tex]

Hence, the area of the figure is 86.13 square units.

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The number of sessions will be 5 and the cost is $249.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that for the first plan, the initial cost is $39 and the cost per session is $42 and for the second plan, initial cost is $54 and per session is $39.

The number of sessions for same cost of two plans will be calculated as,

39 + 42S = 54 + 39S

42S - 39S = 54 - 39

3S = 15

S = 5

For 5 sessions the cost will be calculated as,

Cost = 39 + 42S

Cost = 39 + ( 42 x 5 )

ost = 39 + 210

Cost = $249

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A obtuse triangle is a triangle in which one of the angles is greater than 90°.

An obtuse triangle can be mathematically defined as a triangle with one angle greater than 90°. The formula for calculating the angles of a triangle is known as the Law of Sines. The formula states that the ratio of the length of a side of the triangle to the sine of its opposite angle is the same for all sides. To calculate the angles of an obtuse triangle, we must first find the ratio of the sides to the opposite angle. For example, if we have a triangle with sides of length a, b and c, then the ratios of the sides to their opposite angles are a/sinA, b/sinB and c/sinC. Once we have found the ratios, we can use the Law of Sines to calculate the angles of the triangle. We can then determine if any of the angles are greater than 90°, which would indicate that the triangle is obtuse.

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By taking a quotient between the mass of salad fruit and the number of bowls, we will see that she needs to put 0.71 kg of salad fruit on each.

Here we know that Brooklyn wants to divide 2.84 kilograms of fruit salad equally among 4 serving bowls.

So, to see the mass of fruit salad that she needs to put in each bowl is equal to the quotient between the total mass of frit salad and 4, then we will get:

N = 2.84kg/4

N = 0.71 kg

So she needs to put 0.71 kilograms of salad fruit on each one of the 4 bowls.

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The required perimeter of the given rectangle is (C) 29 4/6 ft.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

So, the perimeter formula is:

2(l+b)

Now, calculate the perimeter as follows:

2(l+b)

2(8 1/6+ 6 2/3)

2(49/6 + 20/3)

2(89/6)

178/6

29 4/6 ft

Therefore, the required perimeter of the given rectangle is (C) 29 4/6 ft.

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Correct question:

What is the perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet?

A. 14 3/9 ft

B. 16 2/6 ft

C. 29 4/6 ft

D. 48 3/18 ft

Answer: Ayman has saved $25

Step-by-step explanation: It's basically just 5/6th's of 30, which is 25.

The y intercept of a line written in the standard form is calculated by

A linear function consists of functions where the variables has exponents of 1. The relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

To solve for the intercept in the equation y = mx + c x is set to zero

y = mx + c

y = m(0) + c

y = 0 + c

y = c

hence the intercept is equal to c when x is zero

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Magnolia ha a net aet of P142,234. 00 after liabilitie of P53,435. 00 at the end of the year. Then the  equity at year end become 88799

magnolia ha a net aet of P142,234. 00 after liabilitie of P53,435. 00 at the end of the

year. What i it equity at year end?

The ideal current ratio for a company is between 1.2 and 2, which indicates that it has two times as many current assets as liabilities to cover its debts.

If the current ratio is less than 1, the company's liquid assets are insufficient to cover its current liabilities.

equity = assets - liabilities

      = 142234-53435

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The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The slope-intercept form, standard form, and point-slope form are the three primary forms of linear equations. A mathematical expression known as an equation contains the equals sign. Algebra is a significant component of many equations. When you don't know the exact number to compute in math, you use algebra.

given

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Consider the equation 3x + 7 = 14, where 3x + 7 and 14 are two expressions that are separated by the symbol "equal."

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The expression for the students in the class is 5N + 25 + 15 = 90 or N = 10

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Let the number of students in class be N.

Therefore, from the information provided, the expression for the students in the class can be written as:

5N + 25 + 15 = 90

5N + 40 = 90

5N = 90 - 40

5N = 50

N = 50/5

N = 10

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The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.

True

The probability of getting more heads than tails is the same as the probability of getting an equal number of heads and tails, because the two outcomes are equally likely. The probability of getting an equal number of heads and tails is 1/2, so the probability of getting more heads than tails is also 1/2.

The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2, which is the same as the probability of getting an equal number of heads and tails.

The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.

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Answer: accidentally did that sorry

Step-by-step explanation:

The solution is Option C.

The functions f ( x ) and g ( x ) have the same y-intercept of ( 0 , 6 )

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 first function be represented as A

Let the second function be represented as B

Now , the value of A is

f ( x ) = 2x² + 7x + 6   be equation (1)

Now , the value of B is

g ( x ) = 2ˣ + 5   be equation (2)

Now , on simplifying the equation , we get

To find the y-intercepts of the function ,

Substitute the value of x = 0 in the equation , we get

f ( 0 ) = 2 ( 0 )² + 7 ( 0 ) + 6

On simplifying the equation , we get

y = 6

Now , g ( x ) = 2ˣ + 5

Substitute the value of x = 0 in the equation , we get

g ( 0 ) = 2⁰ + 5

g ( 0 ) = 1 + 5

g ( 0 ) = 6

Hence , the y intercepts of the functions f ( x ) and g ( x ) is ( 0, 6 )

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The domain of f(x) = 4 is the set of all real numbers.

The domain of any constant function (where the output is always the same) is the set of all real numbers. This is because any real number can be plugged into the function, and the output will always be 4.

The domain of f(x) = 4 is the set of all real numbers, including integers, rational numbers, irrational numbers, and any other types of real numbers.

The domain of f(x) = 4 is the set of all real numbers.

The domain of any constant function (where the output is always the same) is the set of all real numbers. This is because any real number can be plugged into the function, and the output will always be 4.

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A 4 polygon is a two-dimensional shape with four sides and four angles.

Polygon is a closed figure in a plane made up of straight lines or curved lines that intersect in pairs. A polygon has at least three sides and angles. The sides can be of any length and the angles can be of any measure. Polygons are classified according to the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), etc. Polygons are used in many fields, from mathematics to engineering.

It is a type of quadrilateral, which is a polygon with four sides. Examples of 4 polygons include squares, rectangles, rhombuses, and trapezoids. All 4 polygons have four sides of equal length, and all their interior angles add up to 360 degrees.

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