Given m ∥ n, find the value of x.

(x,y) --> (x, y-2)

=======================================================

Explanation:

Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.

We'll come back to choice B.

Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.

-------------

To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.

Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.

For example, the point (5,12) moves to (5,10).

Notice that dilation is not being applied for choice B.

With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.

Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.

Answer:B) (x, y) → (x, y − 2)

Step-by-step explanation:

All the correct expression are;

⇒ 2x + 6 = 2

⇒ 2(x - 4) = 6x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We have to check all the expression which has x = - 2 as a solution.

So, For first expression;

⇒ 2x + 6 = 2

Put x = -2;

LHS = 2×- 2 + 6

       = - 4 + 6

       = 2

       = RHS

Hence, This expression has a solution x = - 2

For second expression;

⇒ 2(x - 4) = 6x

Put x = -2;

LHS = 2×(- 2 - 4)

       = 2 × - 6

       = -12

RHS = 6x

       = 6×-2

       = - 12

Hence, This expression has a solution x = - 2

For third expression;

⇒ 3x + 1/2 = 1/4x + 6

Put x = -2;

LHS = 3×-2 + 1/2

       = - 6 + 1/2

       = - 11/2

RHS = 1/4x + 6

       = 1/4 × - 2 + 6

       = - 1/2 + 6

       = 11/2

Hence, This expression does not a solution x = - 2.

So, For fourth expression;

⇒ 7 - 3x = 5x + 11

Put x = -2;

LHS = 7 - 3×-2

       =  7 + 6

       = 13

RHS = 5x + 11

       = 5×-2 + 11

       = - 10 + 11

       = 1

Hence, This expression does not a solution x = - 2.

So, For fifth expression;

⇒ 3x + 15 = 2x + 9

Put x = -2;

LHS = 3×- 2 + 15

       = - 6 + 15

       = 9

RHS = 2x + 9

       = 2×-2 + 9

       = - 4 + 9

       = 5

Hence, This expression does not a solution x = - 2.

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10.1 g of fluorine is required to produce 20.0 grams of FeF3

first, we have to balance the equation:

2Fe+3F₂⇒2FeF₃

The molar mass of FeF₃ is 112.84g/mol. so the num of mol(n) of FeF₃ present in 20.0g of mass is calculated as shown below:

n=20.0g/112.84g/mol

n=0.1772mol

According to the balanced equation on the macroscopic scale, 2 mol of FeF₃ is produced from 3 mol of F₂.

so, 0.1772 mol of FeF₃ is produced from X mol of F₂. where X is calculated as shown below:

X=3 mol/2mol*0.1772 mol

X=0.2658 mol

Hence, 0.2658 mol of F₂ is required. The molar mass of F₂ is 38.0g/mol

so, the mass of 0.2658 mol of F2 is calculated as:

m=0.2658 mol*38.0g/mol

m=10.1g

Hence, 10.1 g of fluorine is required.

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Answer: The fourth data set (bottom right corner).

Step-by-step explanation: In the graph shown the dots represent a value in the data set. In the graph, there are 4 data sets above 2 meaning that there should be 4 values of 2 in the data set. A quick scan will show that the only logical answer is the fourth set since this is the only set with 4 2s. You can repeat this process for the rest of the dots to check your work.

Answer:

2x+12

Step-by-step explanation:

We can re-write (2x+8)+4 using the associative property of addition. The associative property states that you can move around the parenthesis in an addition problem.

We can write (2x+8)+4 as 2x+(8+4).

2x+(8+4) = 2x+12.

The value of the sequence aₙ₊₁ is -5.5

The definition of the sequence is given as

8.0, 6.5, 5.0, 3.5, . . .

The above definitions imply that we simply subtract 1.5 from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ₊₁ = aₙ - 1.5

From the question, we have

aₙ = -4.0

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

aₙ₊₁ = -4.0 - 1.5

Evaluate

aₙ₊₁ = -5.5

Hence, the value of aₙ₊₁ is -5.5

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Answer:

3.Ans
4 is the thousands place value in the number 524,897,123.

The value of the digit 4 would be 4,000,000.

Calculation: 4 x 1,000,000 = 4,000,000


4.Ans

The product of (6*5)*10^3 is 3000. This product has 3 zeroes.

So on solving the provided question, we can say that by equation , y = 5/8x; it makes a vertical line.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Let y be the number of gallons of fertilizer produced by combining x tsp of fertilizer powder.

5 litres of liquid fertilizer are created by combining 8 tsp of fertilizer powder.

Therefore, the amount of liters of liquid fertilizer produced by combining 1 tsp of fertilizer powder = 5/8

gallons of LF by mixing x tsp of powder fertiliser  = 5/8x

the required equation is => y = 5/8x

so by graph it makes a vertical line.

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Answer:

44.3

Step-by-step explanation:

47 - 2.7 = 44.3

Taking away 2.7 from 47 gives us 44.3.

Hope this helped!

Answer:

[tex] \sqrt{1693} [/tex]

Para encontrar as coordenadas do vértice de uma função do tipo y = x² - 2x - 3, podemos seguir os seguintes passos:

Calcular o valor da coordenada x do vértice: para isso, precisamos encontrar o valor de x quando o coeficiente do x na função é igual a zero. Neste caso, temos x² - 2x - 3 = 0. Então, para encontrar x, podemos factorizar esse polinômio e encontrar as raízes: (x-3)(x+1) = 0. Isso nos dá x = 3 ou x = -1. Como estamos procurando o vértice, que é o ponto mais alto ou mais baixo da parábola, descartamos x = -1 e ficamos com x = 3.

Calcular o valor da coordenada y do vértice: agora que temos o valor de x, podemos substituí-lo na função original e calcular o valor de y. Neste caso, temos: y = (3)² - 2(3) - 3 = 9 - 6 - 3 = 0.

Portanto, as coordenadas do vértice da função y = x² - 2x - 3 são (3, 0).

Answer:

Step-by-step explanation:

(x) = x²-2x-3.

a=1 b=-2 c=-3.

Xv = -b/2a = -(-2)/2 = 1.

Yv = -Δ/4a Δ =(2²-(4.(-3))) = 16 -16/4 = -4

Vertex ( 1 , -4 )

Differentiating

f(x) = x²-2x-3.

f '(x) = 2x-2

2x-2 = 0

x=1. Xv = 1.

f(1) = x²-2x-3.  

1-2-3 = -4. Yv = -4.    

The limits to the function are given as follows:

a) lim x -> -5 f(x) = 10.

b) lim x -> 5 f(x) = -5.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

As the function in this problem does not have discontinuities at the values of x = -5 and x = 5, the limits are in fact given by the numeric values at these points.

The limits are given as follows:

a) lim x -> -5 f(x) = 10. -> as the graph passes through the point (-5,10).

b) lim x -> 5 f(x) = -5. -> as the graph passes through the point (5,-5).

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Answer:

36 -12 = 24

Step-by-step explanation:

24 / 12 × 100

= 2 × 100

= 200 %

Answer:

-79

Step-by-step explanation:

First Identify the sequence

-28 to -45 is -17

-45 to -62 is -17

This is an Arithmetic Sequence because it is constant

(Constant ; same throughout)

Two Formulas:

a60=28 -45 -62

or

an= -17(60)-11

The increase in Lupita's retirement savings from June to July to the nearest percentage is 44%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred.

It is given that the initial amount of money Lupita had in June is $115

In July the amount of money Lupita saved increased to $165

We are asked to find this increase in money as a percentage.

Increase in percentage

= {(Final amount of money - Initial amount of money) / Initial amount of money } × 100

=  {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%

Therefore the increase in amount of money saved as percentage is 44%.

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Answer:108-8 1/4=89 3/4 Jaden has 89 3/4 measures they still need to learn

Step-by-step explanation:

Answer: 89 3/4

Step-by-step explanation: Jaden played 18 1/4 of the measures and the total of Fur Elise is 108 measures. If you do 108 - 18 1/4 it would be 89 3/4. We did this because the total was 108 and we wanted to know how much of fur elise is left after we played 18 1/4.

The equation of the line in slope intercept form is y = - 1 / 2 x + 4.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2, 3) and the y-intercept is 4.

Hence,

y = mx + 4

let's find slope using (2, 3)

3 = 2m + 4

3 - 4 = 2m

2m = -1

divide both sides by 2

m = - 1 / 2

Therefore, the equation of the line is y = - 1 / 2 x + 4.

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The slope of a line perpendicular to the original line is then the negative reciprocal of 4/3, or -3/4.

Reciprocity is a reciprocal exchange of goods, services, or privileges between two parties. It is often used in business transactions and in politics to create beneficial relationships and agreements between parties.

The slope of a line perpendicular to 4x-3y=12 is calculated by finding the negative reciprocal of the slope of the original line. To find the slope of the original line, we need to rewrite the equation in the form y = mx + b, where m is the slope.
In this case, we can rewrite the equation as:
3y = 4x - 12
Yielding the slope of the original line as m = 4/3.
The slope of a line perpendicular to the original line is then the negative reciprocal of 4/3, or -3/4.

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The width of the base is __57.625__ feet

The length of the base is __57.625__ feet

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Perimeter of the rectangular base of a monument is 230.5 feet.

width is equal to its​ length

Perimeter of rectangle = 2 (length + width)

230.5 = 2 (length + length)

4 length = 230.5

length = 230.5/4

length = 57.625 feet

thus, width = 57.625 feet

Hence,

57.625 feet is the length of rectangular base.

57.625 feet is the width of rectangular base.

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24 more footballs were donated than helmets in the given ratio problem.

Ratio refers to the quotient of two values. The expression a:b or a/b can be used to represent the ratio of a to b. A is the antecedent and b is the consequent in both scenarios. Every time we make comparisons, ratios appear.

For simplicity, they are typically expressed in the simplest terms. In a school with 1,000 students and 50 teachers, there are 20 students for every teacher.

The golden ratio of classical architecture is an example of an aspect ratio, which is the ratio of a rectangle's width to height. A proportion is an equation that results from setting two ratios equal to one another.

Lets 3x be the no. of helmet and 7x be football distributed.

total pieces = 3x + 7x

3x + 7x = 60

10x = 60

x = 60/10

x = 6

3x = 3(6) = 18

7x = 7(6) = 42

Difference = 42 - 18

                  = 24

Thus, 24 more footballs were donated than helmets in the given ratio problem.

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On solving the provided question we can say that from the provided quadrilateral ABCD, ∠ BAD and ∠BCD are supplementary, ∠ABC and ∠ADC are supplementary.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

from the provided quadrilateral ABCD,

∠ BAD and ∠BCD are supplementary,

∠ABC and ∠ADC are supplementary.

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Therefore , the solution of the given problem of circumference of the given figure is 15.7 ft.

The circumference of a circle or other curved geometric object refers to length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.

Here,

in the given question

first find the length of the diameter

in the figure

Perpendicular = 3ft

Base = 4ft

using Pythagoras rule

(hypotenuse)

(base)2 + (perpendicular)2

(hypotenuse)2=42+32

(hypotenuse)2=16+9

(hypotenuse)2=25

hypotenuse = √25

hypotenuse = 5

in the given figure hypotenuse diameter of the circle

radius(r) =

diameter

== 2.5

circumference of the circle is given by

circumference = 2πr

circumference = 2*3.14 * 2.5

circumference = 15.7ft

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Answer: 40.5 cm.

Step-by-step explanation:

first the formula for a parallelogram is base times height and we know the height is 4.5 cm and the base is twice the height and 4.5+4.5=9 and then 9x4.5= 40.5

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value.

When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.

given

2000 pounds make up a ton.

Snowmobile owned by John weighs 600 pounds or 0.3 tons.

The difference between Mike's snowmobile's 500 and 600 pound weights is 100 pounds.

= 600 - 500 = 100 pounds

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

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The 10th term of the arithmetic sequence is T₁₀ = a + 9d. a is the first term and d is the common ratio.

What is a sequence?

A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined as the number of items.

An arithmetic sequence follows a pattern.

Arithmetic progression or arithmetic sequence is a number sequence in which the difference between subsequent terms is constant.

The formula for nth term of the sequence is

Tn = a + (n - 1)d

Where a is the first term, d is the common ratio, and n is the number of terms.

Putting n = 10 in Tn = a + (n - 1)d

T₁₀ = a + (10- 1)d

T₁₀ = a + 9d

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42 , 16 values of sin and cos

Let's review some information regarding the sin function before learning the sin formula. The sine function, often known as the sin function, is a periodic function in trigonometry. The ratio of the hypotenuse's length to the perpendicular's length in a right-angled triangle is another way to describe the sine function. Sin is a periodic function that has a period of 2 and a domain and range of (, ), respectively. To determine the sides of a triangle, use the sin formula.

The Sin Formula: What Is It? The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse

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The linear function's missing data values are x = 0 and y = 1, which is the right response (B).

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = mx + b, where m and b are real values.

Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b.

When given as a graph, information about a function is assumed to be linear if the graph is a line.

If the function's details are provided in algebraic form, then f(x) = mx + b indicates that the function is linear.

According to our question-

Using two specified pairs of points from the table, (-9, 3) and (-6, 2), one may calculate the slope as follows:

Let

x₁ = -6, y₁ = 2

x₂ = 95, y₂ = 3

Slope (m) equals (3 – 2)/(-9 – (-6))

Slope (m) equals 1/-3, or 1/3.

By substituting (x, y) = (-9, 3) and m = -1/3 into y = mx + c, it is possible to find c:

⇒ 3 = -1/3(-9) + c

⇒ 3 = 3 + c

⇒ 3 - 3 = c

⇒ c = 0

Change y = mx + c to m = -1/3 and c = 0.

⇒ y = -1/3x

Now, calculate the values of the missing data using the equation:

Please use y = 0.

Hence, x would be:

⇒ 0 = -1/3x

⇒ x = 0

Replace x with -3,

Y then would be:

⇒ y = -1/3(-3) (-3)

⇒ y = 1

Hence, The linear function's missing data values are x = 0 and y = 1, which is the right response (B).

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Answer:

----------------------------

Given expression:

Simplify it in steps:

Answer:

[tex] \sf \: - g - 6[/tex]

Step-by-step explanation:

The expression is,

→ -2 + 2g - (3g + 4)

Let's simplify the expression,

→ -2 + 2g - (3g + 4)

→ -2 + 2g - 3g - 4

→ (-3g + 2g) + (-2 - 4)

→ (-g) + (-6)

→ -g - 6

Hence, the answer is -g - 6.

Answer:

slope = - [tex]\frac{8}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope- formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line

m = [tex]\frac{-4-4}{4-(-1)}[/tex] = [tex]\frac{-8}{4+1}[/tex] = [tex]\frac{-8}{5}[/tex] = - [tex]\frac{8}{5}[/tex]