Use the principle of superpositinn to explain why two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

The equation that models the cost x, in dollars, of each movie download is x = $(35 ± 3)/6

From the question, we are to write an equation that models the cost x, in dollars, of each movie download

From the given information,

Steven buys 6 movie downloads and the total cost is $3 above or below

$35

That is,

6x = $(35 ± 3)

Then,

The cost x, in dollars, of each movie download is

x = $(35 ± 3)/6

Hence, the equation is x = $(35 ± 3)/6

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Answer:

2x + 12

Step-by-step explanation:

Use the distributive property of multiplication over addition.

2(x + 6) = 2 × x + 2 × 6 = 2x + 12

5.25 pack of printer paper the manager should expect to have after 30 days.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

If 140 paper are used in 80 days then

in days 80 ⇒  140 pack paper used

in day 1 ⇒ 140/80 pack paper used

in days 30 ⇒ 140/80 × 30

                  ⇒ 21/4 pack paper used or 5.25 pack paper used

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Answer:

.715 meters

Step-by-step explanation:

Answer:

{36+7[6-2(10÷)+9(2)]}÷4

Answer:

2 hours and 22 minutes

Step-by-step explanation:

Rate x Time = jobs

Mr. Comb's rate is 1 field in 5 hours or 1/5.

Mr. Ramset's rate is 1 fiend in 4.5 hours.

If we take the time and rate that it takes Mr. Comb's to mow one field and add it to the time and rate that it takes Mr. Ramset's to move one field  we can find out how long it takes them to mow one field together

RT + RT = 1 (job)

1/5T + 1/4.5T = 1  We need a common denominator.  I just multiplied 5 x 4.5  for get 22.5  Rewrite 1/5 and 1/4.5 with a common denominator or 22.5 we get the equivalent fractions that we can add together.

4.5/ 22.5T + 5/22.5T = 1  Add the fractions together

9.5/22.5T = 1  We want to solve for T, so we will multiply both sides of the equation by 22.5/9.5

9.5/22.5(22.5/9.5)T= 1 22.5/9.5

T = 22.5/9.5  When I divide these, I get 2 35/95 hours.  I need to change the fraction part of an hour to minutes.  I will use the unit multiplies 60 minutes/ 1 hour.

35hours/95 (60 minutes/1 Hour) = 22.10526331579.  I need to round this to the nearest minutes which will be 22 minutes.

1. The coefficients of the factored polynomial x² - 8x + 15  are

2. The coefficients of the  factored polynomial 2x³ - 8x² + 24x are

3. The coefficients of the  factored polynomial 6x² + 14x + 4 are

Sincw we want to factor the polynomial x² - 8x + 15 in the form (ax + b)(cx + d), we have that

x² - 8x + 15 = x² - 3x - 5x + 15

= x(x - 3) - 5(x - 3)

= (x - 5)(x - 3)

comparing  (x - 5)(x - 3) with (ax + b)(cx + d), we see that the coefficients of the polynomial are

Sincw we want to factor the polynomial 2x³ - 8x² + 24x in the form 2x(ax + b)(cx + d), we have that

2x³ - 8x² - 24x = 2x(x² - 4x - 12)

Factorizing the expression inthe bracket, we have

= 2x(x² - 2x + 6x - 12)

= 2x[x(x - 2) + 6(x - 2)

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

comparing  2x(x - 2)(x + 6) with 2x(ax + b)(cx + d), we see that  the coefficients of the polynomial are

Sincw we want to factor the polynomial 6x² + 14x + 4 in the form (ax + b)(cx + d), we have that

6x² + 14x + 4 = 6x² + 2x + 12x + 4

= 2x(3x + 1) - 4(3x + 1)

= (2x - 4)(3x + 1)

comparing  (2x - 4)(3x + 1) with (ax + b)(cx + d), we see that  the coefficients of the polynomial are

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Answer:

F= ma is the formula of Newton’s Second Law of Motion.

Newton’s Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.

Answer:

awnser value is 64

Step-by-step explanation:

4³ is an exponential multiplied by itself 3 times an added to 2

Answer:

82

Step-by-step explanation:

Follow BIDMAS: 1. Brackets, 2. Indices, 3. Division, 4. Multiplication, 5. Addition, 6. Subtraction

1. Brackets, 5+4=9

therefore the equation is now

[tex]4^3+2*9[/tex]

2. Indices

[tex]4^3=4*4*4=64[/tex]

therefore the equation is now

[tex]64+2*9[/tex]

3. Multiplication

2*9=18

therefore the equation is now

64+18

now add,

=82

therefore, [tex]4^3+2*(5+4)=82[/tex]

Answer:

(r-s)⁹

Step-by-step explanation:

The difference means to subtract, so we have r-s.

Raising this to the 9th power gives (r-s)⁹.

The length and width of the rectangle is 46 feet and 10 feet respectively.

Let the length of the rectangle be x and the width of the rectangle be y.

Now, the length of the rectangle is 4 less than 5 times its width.

Therefore,

x = 5y - 4

The perimeter of a rectangle is given as two times the sum of its length and breadth.

Perimeter = 2( length + breadth)

P = 2( x + y)

Now, the perimeter of the rectangle is 112 square feet.

Therefore,

112 = 2( 5y - 4 + y)

( 112 /2) = 5y - 4 + y

6y - 4 = 56

6y = 56 + 4

6y = 60

y = ( 60 / 6)

y = 10

Now,

x = 5y - 4

x = 5 × 10 - 4

x = 50 - 4

x = 46

So, the length of the rectangle is x = 46 feet and the breadth of the rectangle is y = 10 feet.

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Ilhan's average speed in the race is 11.03 miles per hour.

The average speed is a scalar measure of the total distance divided by the total time.

The average speed shows an object's displacement rate from one point to another.

Speed measures the rate of fastness, while the average speed shows the average rate of fastness of an object in movement.

The average speed is measured in magnitude without direction as a scalar quantity.

Beginning time for the race = 7:22 am

Ending time for the race = 8:07 pm

Time used = 12hours 45 minutes or 12.75 hours (8:07 pm - 7:22 am)

Swimming 2.4 miles

Cycling 112 miles

Running 26.2 mile

Total distance = 140.6 miles

Average speed = Distance/Time

= 11.03 miles per hour (140.6/12.75)

Thus, Ilhan's average speed in the race is 11.03 miles per hour.

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x= 6, y = 3 are the domain and range were interchanged, would the relation be a function.

What is domain ?

If the terms in range and domain were interchanged, one term 6 of domain relates with two different values of range,

x = 6, y = 2.5

x= 6, y = 3

  Since, a term of domain can't have two different values in range,

Therefore, interchanged relation will not be a function.

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The length of the missing side of the given triangle is 2√2×11.

So, the missing length of the given triangle:

The formula of the hypotenuse.

Now, substitute values in the formula:

Therefore, the length of the missing side of the given triangle is 2√2×11.

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Step-by-step explanation:

2x+13=17

2x=17-13

2x=4

x=4/2

x=2

then,

3x+1

= 3*2+1

= 6+1

= 7

Answer: 7

Step-by-step explanation:

To solve the problem you need to use algebra.

[tex]2x+13=17\\[/tex]

Subtract 13 on both sides.

[tex]2x=4[/tex]

Proceed to divide by 2 to solve for x.

[tex]x=2[/tex]

Now using your x-value, plug that into 3x+1 to get your solution.

[tex]3x+1\\3(2)+1=7[/tex]

If y varies directly with x , and y-15 when x-3, y is 60 when x is equal to 12.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

y = kx            (Where k is the constant)

Here, we have given

15 = k3

k = 15/3

  = 5

So, y = 5x

When x = 12,

y = 5(12)

  = 60

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Correct question

Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?

an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

See the pattern

1/8-0 =1/8

1/4-1/8 = 1/8

3/8-1/4 = 1/8

the explicit and a recursive formula for each sequence is an=a1+d(n−1).

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

7 + 3 * x = 52

x = 15

Step-by-step explanation:

Let's call the number x.

The sum of seven and three times a number is 52

Let's substitute x for "a number" and write it mathematically:

7 + 3 * x = 52

3 * x = 52 - 7

3 * x = 45

x = 15

thanks man you gudjkkhshsj

Answer:

first is positive

second is also positive

third id negative

forth is also negative

Step-by-step explanation:

1) and 2) It is because there is no sign before the solution.

for 3) and 4) there is a - (minus) sign before the product so the solution is negative.

The expression of the segment as the sum of the parts, gives VW = VX

The given parameters are;

VZ = VY, WY = XZ, then VW = VX

From the given drawing obtained from a similar question, we have;

VZ = VW + WY (Segment Addition Postulate)

VY = VX + XZ, by segment addition

Therefore;

By substitution property, we have;

VW + WY = VX + XZ

Which gives;

VW + WY = VX + WY (substitution)

VW + WY - WY = VX + WY - WY

VW = VX by subtraction property

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Determine whether each infinite geometric series diverges or converges. The series converges.

If the series converges, state the sum. 1+ 1/4 + 1/16 + . . . .

The sum of the infinite series is 4/3

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term })=1\\\\r=\frac{a_{2} }{a_{1} } =\frac{1/4}{1} =\frac{1}{4}\\[/tex]

Since   [tex]\vert r \vert < 1[/tex] , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{1}{1-\frac{1}{4}}=\frac{4}{3}[/tex]

The sum of the infinite series is 4/3

What is an infinite geometric series?

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The solution of the given formula V = lwh for the variable w is V/lh.

According to the given question.

We have a formula.

V = lwh

Since, we have to solve this given formula V = lwh for the variable w.

Which means we have to write separate variable w to one side from the other variables which are in the given formua V = lwh .

Thereofre, the solution of the given formula V = lwh for the variable w is given by

V = lwh

⇒ V/l = wh      (dividing both the sides by l)

⇒ V/lh = w      (dividing both the side by h)

or w = V/lh

Hence, the solution of the given formula V = lwh for the variable w is V/lh.

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Answer

3.7lb=

2.92=

lb=

6.63

Step-by-step explanation:

Six pairs of congruent angles are:

To name six pairs of congruent angles:

Given: BCDE ≅ RSTU

Then,

Now, connect diagonals BD and RT.

So,

Therefore,  six pairs of congruent angles are:

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The expression for the height is given as 3V/pir³

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the ape-x or vertex.

The formula for calculating the volume of a cone is expressed according to the equation;

V = 1/3pir³h

We are to make h the subject of the formula;

V = 1/3pir³h

Cross multiply

3V = pir³h

Divide both sides by pir³

3V/pir³ = pir³h/pir³

3V/pir³ = h

Swap

h = 3V/pir³

Hence the expression for the height is given as 3V/pir³

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Answer: 58

Step-by-step explanation:

Increment of 3

4th term is 10,

5th term is 13,

6th term is 16,

7th term is 19,

8th term is 22,

9th term is 25,

10th term is 28,

11th term is 31,

12th term is 34,

13th term is 37

14th term is 40

15th term is 43

16th term is 46

17th term is 49

18th term is 52

19th term is 55

Meaning that the 20th term is 58

Answer:

a₂₀ = 58

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = a₂ - a₁ = 4 - 1 = 3 , then

a₂₀ = 1 + (19 × 3) = 1 + 57 = 58

Answer:

it is -17/15

Step-by-step explanation:

-1/3-4/5

get the LCM .15

=(15*-1/3-1/5*15)/15

=-17/15

There are 210 ways to write 5 of the letters of the word ALGORITHM in a row if the 2 two letters must be TH

Given data

the word ALGORITHM

the first two letters must be TH

ALGORITHM has 9 letters and order of writing the letters is important, so we use Permutation to solve this

The 2 letters TH are fixed and this reduces the number of letters in the word from 9 to 7. Also, the the first two being fixed reduces the letters arrangement to be 3.

This means that we have the arrangement as follows:

7P3

= 7! / ( 7 - 3 )!

= 7! / 4!

= 7 * 6 * 5 * 4! / 4!

= 7 * 6 * 5

= 210 ways

Hence there are 210 ways to write 5 of the letters of the word ALGORITHM in a row if the 2 two letters must be TH

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