Why do translations produce parallel lines?
Choose the correct answer below.
O A. Translations do not change the y-intercept of the line, so the
original line and the transformed line are always parallel.
OB. Translations do not change the slope of the line, so the
original line and the transformed line are always parallel.
OC. Translations change both the slope and the y-intercept of
the line an equivalent amount, so the original line and the
transformed line are always parallel.
O D. Translations do not change the slope or y-intercept of
the line, so the original line and the transformed line are
always parallel.

The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.

In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.

The given sequence is as follows,

625, 125, 25, 5, 1

The first term is given as a₁ = 625

And, the ratio of the consecutive terms are,

125/625 = 1/5

25/125 = 1/5

Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.

The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.

Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.

Hence, the term for the given sequence can be written in general form as  aₙ = 625 × (1/5)ⁿ⁻¹.

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The table of values which represent the equation y = 7x - 3 is: table D.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;

For ordered pair (-2, -1), we have:

y = 7x - 3

-1 = 7(-2) - 3

-1 = -14 - 3

-1 = -17 (False).

For ordered pair (-2, -19), we have:

y = 7x - 3

-19 = 7(-2) - 3

-19 = -14 - 3

-19 = -17 (False).

For ordered pair (-2, -15), we have:

y = 7x - 3

-15 = 7(-2) - 3

-15 = -14 - 3

-15 = -17 (False).

For ordered pair (-2, -17), we have:

y = 7x - 3

-17 = 7(-2) - 3

-17 = -14 - 3

-17 = -17 (True).

In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.

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We must report the deviation to Upon request of the Federal Aviation Administration.

What is Deviation?

The deviation is a metric used to determine the discrepancy between an observed variable's value and its predicted value. The deviation can be defined as the distance from the centre point.

Concept:

Each remote PIC who deviates from a Part 107 rule shall, upon request from the FAA administrator, submit a written report of such deviation.

Who is in charge of providing the participants with information on emergency procedures while utilising a small unmanned airplane in a commercial operation? The commander of the remote pilot. A person may fly an unmanned aerial system for profit even without a Part 107 remote pilot certificate: under the immediate control of a Remote PIC.

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Answer:y=2x+3

Step-by-step explanation:

The slope intercept form is y=mx+b

m equals to slope

b equals the y-intercept

the slop of this equation is 2

The y-intercept is at (0, 3)

y=2x+3

Answer: no solution

Step-by-step explanation:

Correct, there is no solution as any values of x and y will make the equation false

a) The number of intersections between the railroad and the highway is of: One.

b) The number of intersections between the railroad and the turnpike is of: Two.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are listed as follows:

The points for the railroad are given as follows:

(-8, 0) and (0,5).

When x = 0, y = 5, hence the intercept is of:

b = 5.

When x increases by 8, y increases by 5, hence the slope is of:

m = 5/8.

Thus the equation for the railroad is of:

y = 5/8x + 5.

Then the number of intersections with the highway is of one, as they are linear functions with different slopes.

With the turnpike, the intersection is given as follows:

5/8x + 5 = x²/3

x² -1.875x - 15 = 0.

The discriminant is of:

(-1.875)² - 4(1)(-15) = 63.5.

Which is positive, hence they have two intersections.

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Answer: 1611 no votes

Explanation:

4296/8=537
537*3=1611

The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

A test consists of 10 true/false questions.

If a student guesses on each question

The probability that the student will answer at least7questions correctly.

The probability that the student answers each question correctly is 1/2, and

The probability that the student answers each question correctly is also 1/2

{Bernoalli trail}

Bernoalli trail for at least 7 times,

Probability P =  [tex]C7_{10} (\frac{1}{2}) ^{7} (\frac{1}{2}) ^{7}[/tex]

Using the formula nCr = n!(n−r)!r!

= 10!(10−7)!7!

Subtract  7 from 10.

= 10!(3)!7!

Simplify 10!(3)!7!.

Rewrite 10! as (10⋅9⋅8⋅7!)

= (10⋅9⋅8⋅7! / (3)!7!)

Cancel the common factor of 7!.

Cancel the common factor.

= 10⋅9⋅8⋅7! / (3)!7!

Rewrite the expression.

= 10⋅9⋅8 / (3)!

Multiply 10 by 9.

= 90⋅8 / (3)!

Multiply 90 by 8.

= 720 / (3)!

Expand (3)! to 3⋅2⋅1.

= 720 / 3⋅2⋅1

Multiply 3 by 2.

= 720 / 6⋅1

= 720 / 6

Divide 720 by 6

= 120

So,

We can write,

P = [tex]\frac{120}{2^{7} }[/tex]

P = [tex]\frac{120}{128}[/tex]

Therefore,

The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]

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The value of x in the intersecting line is 54.

When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles angles on a straight lines.

Therefore, angle 2x + 2 is vertically opposite to the angle 3x - 52 .

Vertically opposite angles are congruent to each other.

Vertical Angles are the angles opposite each other when two lines cross. in other words, vertical angles are formed when two lines meet each other at a point.

Hence,

2x + 2 = 3x - 52

2x - 3x = -52 - 2

- x = -54

Therefore,

x = 54

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Answer:

  19%

Step-by-step explanation:

You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.

The change from February to March is given as 7%.

The change from March to April is 500 bottles. In terms of the February quantity, this is ...

  500/4100 × 100% ≈ 12.2%

Then the total of changes from February to April is ...

  change = 7% +12.2% = 19.2% ≈ 19%.

The number of bottles manufactured increased by about 19% from February to April.

__

Additional comment

When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.

Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.

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Answer:

m = 2k/v²

Step-by-step explanation:

K = ½mv²

multiply both sides by 2

2 × k = ² × ½mv²

2k = mv²

divide both sides by (v²)

m = 2k/v²

i hope this helped

The sales tax percentage of the store manager report is 7.41%

Customers are subject to a charge known as sales tax when they buy goods and services.

It is a pass-through tax, which means you must collect it from clients and send the money to your state or local government. the seller do not contribute sales tax.

The sales tax is first calculated by

= price after tax - price before tax

= 513 - 475

= 38

sales tax percentage is calculated using the formula

= (Tax amount / Price before tax) × 100%

= (38 / 513) * 100

= 7.4074

= 7.41%

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When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

What is a annual inflation rate?

A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.

Here, we have

Given

The cost of the gallon of milk earlier was $2.81

The cost of a gallon of milk now is $3.48.

The total time period is 10 years.

r = (F/P)ⁿ⁻¹ - 1

r = {(3.48/2.81)^(1/10) - 1}×100

r = {(1.238)^(1/10) - 1}×100

r = 0.0215 ×100

r = 2.15

Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

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The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.

What is the Angle-Angle similarity theorem of triangles?

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In the given figure,

In ΔPQR and ΔPXY

∠P ≅ ∠P ----- Common Angle

∠PQR ≅ ∠PXY ----Corresponding angles.

So, ΔPQR ~ ΔPXY -----(AA test)

Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.

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Answer:

12 hours

Step-by-step explanation:

1 pair per hour ?

$699.95×20%=$139.99,  is the finance charge.

A finance charge is any fee that reflects the cost of credit or borrowing under American law.

Some forms of credit have fees and interest that accrue over time. [1] In addition to interest, it also includes additional costs, like those for financial transactions.

The Truth-in-Lending Act and Regulation Z, which were issued by the Statutory Reserve Board, contain information about the federal definition of a finance charge.

A financing charge in personal finance is just the cash amount paid to borrow money, whereas interest is the amount paid as a percentage, such as the annual percentage rate (APR).

Compared to standard dictionary definitions or accounting definitions, these definitions are more specific.

Lenders and creditors both calculate finance charges in different ways. a majority.

Hence, $699.95×20%=$139.99,  is the finance charge.

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The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.

Types of Parametric test–

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Answer:

25

Step-by-step explanation:

When you're figuring out the area of a square, you're measuring the size of its surface. You can think of it as finding how many square units make up the entire surface. For squares, the formula for determining area is A = s2, or A = side x side.=

Answer:

14 cups

Step-by-step explanation:

3 + 6 = 9
9 + 4 = 13

13 + 1 = 14

14 plus fraction

Answer: x=5

Step-by-step explanation:

Answer:

(x - 1)² = 16

Step-by-step explanation:

x² - 2x - 15 = 0

x² - 2x + 1 = 15 + 1

(x - 1)² = 16

The 56th term of the following arithmetic sequence 7,10,13,16 is 172.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Here, we have

Given

Arithmetic sequence 7,10,13,16.

We have to find the 56th term.

The common difference between terms: 10 - 7 = 3

Using the arithmetic progression formula:

nth term = first term + (n-1)* common difference

56th term = 7 +(56-1) 3

56th term = 7 + 55×3

56th term = 7 + 165

56th term = 172

Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.

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Answer:

142.6

Step-by-step explanation:

100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6

Hope that helped

The sum of any two sides of a triangle must be greater than the other thus 32 feet,21 feet, and 12 feet will be the correct so options (A),(B), and (D) are correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

As per the given,

To be a triangle of three side polygon the sum of any two sides must be greater than the third side.

If we take 32 feet,21 feet, and 8 feet.

21 + 8 = 29 < 32 so it will not form any triangle.

Thus, 8 cannot be taken. now let's take 32,21 and 12 here 21 + 12 = 33 > 32 so it will form a triangle this will be used for the project.

Hence "The right answer will be 32 feet, 21 feet, and 12 feet because the sum of any two sides of a triangle must be bigger than the other".

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Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

tan(A+B)/cot(A-B)

tan(A+B)/1/tan(A-B)

(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)

tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB

We know algebraic identity

(a+b)(a-b)=a²-b²

(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)

tan²A-tan²B/1-tan²Atan²B

Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

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The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)

A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.

Therefore, quadratic equation can be represented as follows:

ax² + bx + c

where

Hence, let's factorise x² + 18x + 45 = 0

x² + 18x + 45 = 0

Let's find the two numbers to add to get 18 and multiply to get 45

Therefore, the numbers are 3 and 15

x² + 18x + 45 = 0

x² + 3x + 15x + 45 = 0

x(x + 3) + 15(x + 3) = 0

(x + 3)(x + 15) = 0

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Horizontal compression of f(x) = -x + 4 by a factor of 0.5 will be -2x + 4.

A horizontal line that a function's graph looks to coincide with but does not really do so is said to be its horizontal asymptote. The final behavior of the function is determined using the horizontal asymptote.

Given, g(x) is a horizontal compression of function f(x) = - x + 4 by a factor of 0.5. Hence,

g(x) = -x / 0.5 + 4

g(x) = -2x + 4

Therefore, By a factor of 0.5, the horizontal compression of the function (f(x)) is -x + 4 will result in -2x + 4.

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Answer:

If there are 4 boys and they ate 3 pizzas, and each boy ate the same amount, then each boy ate 3/4 of a pizza. If you want to express this as a fraction, it would be 3/4 of a pizza per boy. If you want to express it as a decimal, it would be 0.75 pizzas per boy. If you want to express it as a percentage, it would be 75% of a pizza per boy.

Answer:

C)w-3, w-1, w, w + 1, w+3

Step-by-step explanation:

I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.

C) is the correct answer, the data points do not repeat and are spread out more than A.

You can check this by calculated each standard deviation (but only if you are crazy ;] )

Hope this helps,

:]

Diego rows 300 meters per minute

Information given in the question include

The graph shows the relationship between the time in the distant, Diego rows

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the change of the output values to the input values

the slope, m calculating using the points on the graph (1, 300) and  (2, 600)

m = (y₀ - y₁) / (x₀ - x₁)

m = (600 - 300) / (2 - 1)

m = 300 / (1)

m = 300

The number of meters Diego rows per minute is solved to be 300

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The square root of 80 is 4√5 ≅ 8.92.

What is a square root of a number?

In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.

Using Prime Factorization:

The first step in this method is to find the prime factors of 80.

80 = 2 × 2 × 2 × 2 × 5

To find the root from here, we can simplify this to

√80 = √(2 × 2 × 2 × 2 × 5)

√80 = 4√5

We can either leave it at this or find the root of 5 which is 2.23 and simplify further.

Hence, Square Root of 80 = 4√5 ≅ 8.92.

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