Sentences to Algebraic EquationsTranslate the following sentence into equations and solve them.1. The quotient of a number and six is five. Find the number.

The first six common multiples of 6 and 8 are :

24,48,72, 96, 120 and 144.

The first six common multiples of 12 and 18 are :

24, 36, 72, 108, 144, 216.

In order to resolve this, we shall use the multiples idea.

(A) The two numbers given are 6 and 8.

Six is the first multiple of which there are the following: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, and 144.

multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, and 144.

Therefore, common multiples are: 24, 48, 72, 96, 120 and 144.

(B) The two numbers given are 18 and 12.

The first few multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, and 240.

Similarly, the multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and 270.

Therefore, common multiples are: 24, 36, 72, 108, 144, 216.

Hence we get the required common multiples.

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Answer:

height = x + 6

Step-by-step explanation:

Volume = length x width x height

V = 10x³ + 67x² + 30x − 72

length = 5x - 4 and width = 2x + 3

So length x width =  (5x - 4 ) x (2x + 3)

Using the FOIL method:

= (5x)(2x) + (5x)(3) + (-4)(2x) + (-4)(3)

= 10x² + 15x - 8x - 12

= 10x² + 7x -12

So to find height, divide Volume by (length x width)

10x³ + 67x² + 30x − 72  ÷ 10x² + 7x -12

Use polynomial long division. See image ( I did the best I could to capture the process)

The answer is x + 6

To verify
Multiply (5x-4) (2x + 3) (x + 6) = 10x³ + 67x² + 30x − 72

Step-by-step explanation:

equation format: y = mx + b where m is slope and b is the y intercept.

From the points given we find that it is a horizontal line, which means slope or m = 0. So we know so far:

y = 0x + b or y = b

The y-intercept occurs where x = 0. This occurs at y = -7. So the equation for these two points:

EQUATION: y = -7

(Plotted graph attached)

The definition of the functions implies that the value of x if f(x) = g(x) is 3

The equations of the functions are given as

f(x) = -2x + 4

g(x) = 2x - 8

This means that, we have the following equation

f(x) = g(x)

Substitute the known values in the above equation

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms in the above equation

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides by 4

x = 3

Hence, the value of x such that the equations are equal is 3

The graph of the functions can be plotted using a graphing tool

See attachment for the graph of the functions

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The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.The following is a definition of a coordinate plane: The intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line, creates a coordinate plane, also referred to as a rectangular coordinate plane grid.

The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])

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The length of the ruler is approximately 304.8 millimeters .

Length is used to measure distance.

Given that there are approximately 25.4 millimeters in 1 inch.

Therefore the length of the ruler = 25.4 × 12 = 304.8 mm

Hence the length of the ruler is approximately 304.8 millimeters .

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Answer:

304.8

Step-by-step explanation:

12*25.4 = 304.8

It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.

A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

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Answer:

72

Step-by-step explanation:

Formula: P (n,r) = n! ÷ (n - r)!

n = Total number of objects in a set

r = The number of items you choose

!/Factorial = Product of all positive numbers less than or equal to the given positive number

9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

7! = 1 x 2 x 3 x 4 x 5 x 6 x 7

P (9,2) = 9! ÷ (9-2)!

362,880 ÷ 5,040 = 72

Scale factor means ratio of the sides of the triangle then the measures of the indicated sides, and the scale factor of CB and AB exists ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.

A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Each pair of given polygons are similar.

Similarity statement for the given polygons:

In ΔDEF and ΔABC,

∠D = ∠A (Angle)

∠E = ∠B  (Angle)

Therefore, ΔDEF  ΔABC (by AA similarity)

If two triangles are similar, then their sides are proportional.

[tex]$\Rightarrow \frac{D F}{A C}=\frac{D E}{A B}$[/tex]

[tex]$\Rightarrow \frac{2.4}{3.6}=\frac{2}{2 x}$[/tex]

By using cross multiplication, we get

⇒ 2.4 × 2x = 2 × 3.6

simplifying the above equation, we get

⇒ 4.8x = 7.2

⇒ x = 1.5

Therefore, the value of x = 1.5.

Substitute x = 1.5 in CB and AB,

CB = 3x – 0.6 = 3(1.5) – 0.6 = 3.9

AB = 2x = 2(1.5) = 3

Scale factor means ratio of the sides of the triangle.

⇒ DF/AC = 2.4/3.6 = 2/3

Therefore, the correct answer is option a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.

The complete question is:

Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.

[tex]$\overline{C B}$[/tex] and [tex]$\overline{A B}$[/tex]

a) ΔDEF -  ΔABC; x = 1.5; CB = 3.9; AB = 3;

b) ΔDEF - ΔCBA; x=3 ; C B=3 ; A B=3.9 ; 2/3

c) ΔDEF -  ΔCBA; x=1 ; C B=3.9 ; A B=3 ; 2/3

d) ΔDEF -  ΔABC; x=1.5 ; C B=3 ; A B=3.9 ; 3/2

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[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]

Answer:

  5/9

Step-by-step explanation:

You want the reduced fraction equivalent to the ratio 40L : 72L.

A ratio is reduced by removing the greatest common factor from all parts of the ratio. Here, that factor is 8L.

  40L : 72L = (8L)(5) : (8L)(9) = 5 : 9 = 5/9

The ratio is 5/9.

__

Additional comment

The greatest common factor can be found several ways. The easiest is for you to make use of your knowledge of multiplication tables:

  40 = 5·8

  72 = 9·8

8 is a common factor. Since 5 and 9 have no common factors, 8 is the greatest common factor of 40 and 72.

Demonstrating that the limit doesn't exist

What is Limits?

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.

The limit exists only if the value of the limit along every direction that leads to (1,1) is same.

So by calculating,

                             lim   xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2

                             x->1

calculating the limit along the line x = 1

Similarly,

              lim   xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2

             x->1

calculating the limit along the line y = 1

And the last limit you calculated is along line y=x.

To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.

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The value of 3.5 divided by 85 will be 0.4118.

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.

Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.

The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.

In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.

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Answer:

see explanation

Step-by-step explanation:

A

(f + g)(x)

= f(x) + g(x)

= x² + 3x + 2x + 2 ← collect like terms

= x² + 5x + 2

B

(f - g)(x)

= x² + 3x - (2x + 2)

= x² + 3x - 2x - 2 ← collect like terms

= x² + x - 2

In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.

The conjugate is the same expression but with the signal between the numbers changed.

So we have:

So the new denominator of the fraction is 2, therefore the correct option is D.

Notice from the graph that data are mostly to the right.

Answer: Option C The distribution is tailed.

Lines of symmetry, a line that divides a figure into two mirror parts, for example:

As we can see, the only line of symmetry that we can draw in our figure is:

Answer: One

Answer:

7/9

Step-by-step explanation:

Answer:

7/9

Step-by-step explanation:

I took the quiz

We will operate as follows:

The net sales of Shauna's company when she calculated the sales for her company using the figures is $66700.

The total of a company's net sales is its gross sales less any returns, allowances, and discounts. Externally, net sales calculations are not always obvious. They can frequently be taken into account when calculating top-line revenues that are shown on the income statement.

The total number of units sold is multiplied by the price per unit for the purpose of calculating gross sales. The term "returns" or "sales returns" refers to products that customers have sent back in exchange for reimbursement.

The nets sales based on the information given will be:

Gross sales = $72900

Less: Retuned sales = $3750

Less Discount = $2450

Net sales = $66700

Therefore, the net sale is $66700.

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By solving the equation, we get the cost of sheet metal =$20 per sq. feet

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.

Given equation 8.2x-3.7x = 90

or, 4.5x = 90

or, x = 90/4.5 = 20

Hence, the cost of sheet metal is $20 per sq. feet

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Answer:

I'm pretty sure it would be 8 though forgive me if I'm wrong

The student that has the higher standing in the class is Jill

The given parameters are:

Number of students = 200

Jill's position =80th

Nathan's position = Percentile rank  of 80

The above means that

Nathan's position = 80 percentage of the number of students in the class

Substitute the known values in the above equation

So, we have the following equation

Nathan's position = 80 percentage of 200

Rewrite as

Nathan's position = 80 percentage * 200

Express as percentage

Nathan's position = 80% * 200

Express 80% as decimal

Nathan's position = 0.80 * 200

Evaluate the product

Nathan's position = 160

So, we have

Jill's position =80th

Nathan's position = 160th

By comparing the positions, 80th is greater than 160th

Hence, Jill has the higher standing in the class

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3x + 5y = 15 is the equation of the line in standard form that passes through the point (5,0) and (0,3).

The formula for equation of line is expressed as;

y = mx + b

Where m is the slope and b is the y-intercept.

Given the data in the question;

Point 1 ( 5,0 )

Point 2 ( 0,3 )

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 3 - 0 )/( 0 - 5 )

Slope m = ( 3 )/( -5 )

Slope m = -3/5

Now, we plug the slope and coordinates of one the point into the equation of line to determine the y-intercept b.

y = mx + b

0 = (-3/5)5 + b

Solve for b

0 = -15/5 + b

0 = -3  + b

b = 3

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-3/5)x + 3

Convert to standard form; Ax + Bx = C

Multiply each term by 5

y = (-3/5)x + 3

5y = 5(-3/5)x + 5(3)

5y = -3x + 15

Reorder the equation

3x + 5y = 15

Therefore, the equation of the line is in standard form is 3x + 5y = 15.

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Answer:

f(2)=8(12-x)-5

=8(12-2)-5

f(2)=8(10)-5

=75

Given:

The ratio of the area between a small square of land and a large square

of land is 3: 7.

Total area of the two squares of land (in sq. meter) is 4000.

Required:

The area of each square of land.

Answer:

We have the ratio of the area between a small square of land and a large square of land is 3: 7.

Let

be the area of the square of land.

Then their ratio is given by,

Also given that the total area of the two squares of land (in sq.meter) is

4,000.

The area of

Therefore,

Therefore,the area of small square (in sq. meter) is,

and the area of large square (in sq. meter) is,

Final Answer:

The area of small and large square respectively (in sq. meter) is,1200 and 2800.

Answer:

x = 5

Step-by-step explanation:

Hello!

According to the question, what's the value of 4x-6=x+9

4x-6=x+9

Collect like terms

x - 4x = -6 - 9

-3x = -15

Divide both sides by the coefficient of x which is -3

-3x/-3 = -15/-3

x = 5

When checking

4x-6=x+9

(4)(5)−6 = 5+9

14=14

True

First graders in an elementary school number 92. We use mode.

Given that,

Determine which statistic would be most appropriate to characterize the middle of the next set of data: the mean, median, or mode.

First graders in an elementary school number 92. The first graders' heights are fairly similar to one another because they are all roughly the same age.

We have to find which statistic—the mean, median, or mode—does the first-graders' height best represent.

First graders in an elementary school number 92.

Depending on which their birthday walls, the first graders might be six, seven and eight on the last day of the second year.

Therefore, We use mode.

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Answer:

25.7

Step-by-step explanation:

7/13=x/48. By cross multiplication 13 x=326 = 25.7