Using a letter to represent the unknown number, select the equation that matches the problem.

A stick is 5 m long. A rope is 4 times as long as the stick. If the rope is divided into 2 pieces, how many meters long is each piece of rope?

Answer:

subtract 6

Step-by-step explanation:

note there is a common difference between consecutive terms, that is

45 - 51 = - 6

39 - 45 = - 6

33 - 39 = - 6

27 - 33 = - 6

21 - 27 = - 6

the rule being used to make the pattern is subtract 6

this is an arithmetic sequence for which an nth term rule can be found

Answer:

subtract 6

Step-by-step explanation:

the pattern is made by subtracting 6 from the previous number

The new exponent for the power of 10 after rewriting the number correctly in scientific notation is 2

The number written in scientific notation is given as.

0.0038 × 10^5

A number written in scientific notation is represented as.

a x 10^b

Where a is any real number between 1 and 10

So, we have

0.0038 × 10^5

Express 0.0038 as a real number between 1 and 10

This gives

0.0038 × 10^5 = 3.8 × 10^-3 × 10^5

Evaluate the products

0.0038 × 10^5 = 3.8 × 10^2

Hence, the new exponent for the power of 10 after rewriting the number correctly in scientific notation is 2

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2y+x/3=-6  is a linear equation.

An equation is written to equate two or more unknown variables and formulating a relation between them.

Equations are of various types such as:

The given equation is 2y+x/3=-6.

Here the power of both the variables is 1. Hence it can be classified as a linear equation in two variables.

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If x and y are directly proportional and we take a third of x we also have to take a third of y, which means we have to multiply y by 1/3.

Two quantities when they are in direct proportion increase or decrease by the same constant and when they are inversely proportional if one quantity increases the other quantity decreases.

We know when two quantities are directly proportional we can relate them by proportionality as x ∝ y or x = ky.

∴ if we take 1/3 of x to maintain the equality we have to multiply y also by 1/3.

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Answer:

  x = 70°

  y = 35°

Step-by-step explanation:

Given one angle of a triangle is 75° and the other two are 'x' and 'y', you want to find the possible values of 'x' and 'y' when x = 2y.

The angle sum theorem and the given relation give rise to two equations:

  75 +x +y = 180

  x = 2y

Using the second equation to substitute for x in the first equation, we have ...

  75 +(2y) +y = 180

  3y = 105 . . . . . . . . . subtract 75 and simplify

  y = 105/3 = 35

  x = 2y = 2(35) = 70

The measures of angles x and y are 70° and 35°, respectively.

The expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.

We are given that:

Team                        Number of seats

Jets                                 82,500

Dolphins                         65,326

Patriots                           66,829

The number of attendees at the jets home games = j

The number of attendees at the Dolphins home games = d

The number of attendees at the Patriots home games = p

So, the maximum number of attendees can be written by the expression:

82,500 j + 65,326 d + 66829 p.

Therefore, we get that, the expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.

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Your question was incomplete. Please refer the content below:

We are given the data as:

Team                        Number of seats

Jets                                 82,500

Dolphins                         65,326

Patriots                           66,829

Write an expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season. Let j be the number of Jets home games, d be the number of Dolphins home games, and p be the number of Patriots home games.

I don't see a solution to the given expression.

Expand [tex]3(x-2)+6: 3x[/tex]

[tex]3x=3x-6[/tex]

Subtract 3x from both sides.

[tex]3x-3x=3x-6-3x[/tex]

Simplify.

[tex]0=-6[/tex]

Considering the sides are not equal, there is no solution to the given expression.

After solving the expression 4 − (x + 2) < −3(x + 4), we get the value of x as x < - 7.

We are given the expression:

4 − (x + 2) < −3(x + 4)

Subtract 4 from both the sides, we get that:

4 - x - 2 - 4 < - 3 x - 12 - 4

- x - 2 < - 3 x - 16

- x + 3 x < - 16 + 2

2 x < - 14

x < - 14 / 2

x < - 7

Therefore, after solving the expression 4 − (x + 2) < −3(x + 4), we get the value of x as x < - 7.

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Answer: A. A one time discount of 38%.

How much will the shirt cost when given scenario (a) that gives a one time discount of 38%? : $46.50

How much will the Shirt cost when giving scenario (b) that gives a discount of 14% followed by a 24% discount? $49.02

If Tess and Alice are both on the swim team. Last practice, they each swam laps for the same amount of time, but Tess finished more laps. This weekend, they're swimming the same number of laps at a swim meet. The person that will likely finish first is: Tess.

Since Tess finished more laps first when she and Alice both swam laps at the same number of time, which in turn means that there is likelihood or tendency that Tess will finish first.

Based on this we can conclude that Tess swab faster that Alice and may likely finish the swam lap before Alice if the both swim the same number of laps.

Therefore if  this weekend, they're swimming the same number of laps at a swim meet. The person that will likely finish first is: Tess.

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We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

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The unit rate is $26.98

Unit rate can be described as the price of a single item. From the question, we are required to find the unit rate of 1 penguin

The unit rate can be calculated as follows

7 penguins = 188.88

1 Penguin= x

Cross multiply both sides

7x= 188.88

x= 188.88/7

x= 26.98

Hence the unit rate is $26.98

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The number is 11 and the equation is 4M - 23 = 21 where M is the number.

It is a mathematical statement that shows that two mathematical expressions are equal.

Example:

3x – 5 = 16

We have,

Let the number be M.

Twenty-three less than 4 times a number is 21.

Times = multiplication

less than = subtraction

We can write this as:

4M - 23 = 21

4M = 21 + 23

4M = 44

M = 44/4 = 11

Thus the number is 11 and the equation is 4M - 23 = 21 where M is the number.

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There is No Extraneous solution to the equation

The equation is

[tex]\sqrt{3x - 2}[/tex] - [tex]\sqrt{2x - 7}[/tex] = 0

We need to find the value of x,

[tex]\sqrt{3x + 2}[/tex] = [tex]\sqrt{2x + 7}[/tex]

Squaring both sides of the equation

[tex](\sqrt{3x + 2} )^{2}[/tex] = [tex](\sqrt{2x + 7} )^{2}[/tex]

3x + 2 = 2x + 7

x = 5

Now we need to put the value of x in the equation to know whether it is an extraneous solution or not.

[tex]\sqrt{(3 * 5 ) + 2}[/tex] - [tex]\sqrt{(2 * 5 ) + 7}[/tex] = 0

[tex]\sqrt{17}[/tex] - [tex]\sqrt{17}[/tex] = 0

0 = 0

Therefore we get to know that the equation has no extraneous solution.

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The maximum and minimum number of people will be 19700 and 17300 respectively.

It should be noted that it was stated that the arena can hold 18500 people.

Therefore, the equation to represent the number of people that can attend the event will be:

= 18500 +/- 1200

The maximum number of people will be:

= 18500 + 1200

= 19700

The minimum number of people will be:

= 18500 - 1200

= 17300

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The value of x is 13° and the value of y is 131°

From the question, we are to determine the values of x and y

From the given diagram, we can write that

(3x + 10)° + 90° + (2x + 15)° = 180°  (Sum of angles on a line segment)

Solve for x in the equation

(3x + 10)° + 90° + (2x + 15)° = 180°

3x° + 10° + 90° + 2x° + 15° = 180°

Collect like terms

3x° + 2x° = 180° - 10° - 90° - 15°

5x° = 65°

x = 65/5

x = 13°

Also

y + (3x + 10)°  = 180° (Sum of angles on a line segment)

Put the value of x into the equation

y + (3(13) + 10)°  = 180°

y + (39 + 10)°  = 180°

y + 49°  = 180°

y = 180° - 49°

y = 131°

Hence,

x = 13° and y = 131°

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The percentage of increase in the price of  the car is 32%

Percentage increase means adding the given percentage of  value to the original value.

To calculate this percentage increase:

            =  100{( final value - initial value )/initial value}

Given that last month online price of powered ride-on car was $250

and this month this cost is $330

Initial value = $250

Final value  = $330

Percentage increase =  100{ ( 330 -250 )/250} =100*0.32 = 32%

This the percentage increase in the price of the powered ride-on car is 32%

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Answer:

a) 10n -6

b) -5n +105

c) 7f + 1

d) -11n +48

Step-by-step explanation:

for an example let's take a) 4, 14, 24, 34

term value:

14 - 4 = 10 (coefficient)

term number:

4 = 34

4×10=40

34 - 40 = -6

coefficient and constant

therefore v = 10n -6

lol are you a Bhutanese?

The simplest form of the expression is a⁴ b¹/₂ which is option (B)   .

We have given an expression  (a²/¹ b¹/⁴)² .

On simplifying , we get

(a²/¹ b¹/⁴)² = [tex]a^{2\times2} \ \ b^{2/4}[/tex]

                 = a⁴ b¹/₂

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The complete question is given below :

What is the simplified form of (a²/¹ b¹/⁴)²?

(A) a⁴/₅ b⁹/₁₆ (B) a⁴ b¹/₂ (C) a b (D) (a b)¹⁷/₆

In mathematical terms, Number Line is defined:

A visual representation of numbers(whole, natural, decimal, integers, fraction) using a horizontal line drawn straight with equal spacing divisions that represent each number.

Numbers are marked at equal intervals ans it is used to illustrate basic numeric operators. There is no limit to a number line, which means that it expands to positive and negative infinity. The middle of the number line is represented by zero, and on the right side are all the positive values up to the positive infinity. The same for the left side where are all the negative values are listed up to the negative infinity.

Now what is given to us in the question statement are a bunch of decimals. We know decimal numbers are considered real numbers and thus can easily be plotted on the number line. In order to plot the decimal numbers, we need to mark the intervals with decimals values.

The image attached below gives a clear representation of how the numbers will be plotted.

Values closer to 0, like 0.75, and 0.705, will be plotted more towards the right, and those away from zero, like 0.44, 0.279 will be plotted more towards the left of zero.

1.008 will be plotted after 0 and 1 on the number line (towards the right of the zero).

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Answer:

4 seconds

Step-by-step explanation:

In all movement problems, the time is given by finding the ratio between the distance the object moved and the speed the object moved at.

Therefore, [tex]t = \frac{20}5 = 4\text{s}[/tex]

Answer:

The answer should be 4 seconds :)

Answer: [tex]-30x^{3} + 96x^{2}[/tex]

Step-by-step explanation:

Answer:

-30x³ + 96x²

Step-by-step explanation:

 To simplify the algebraic expression, multiply each term of (-5x + 16) by 6x².

When we multiply 6x² * (-5x), multiply the coefficient 6 & -5 and add the powers of the variables.

6x²*(-5x + 16) = 6x² *(-5x) +6x²*16

                      = -30x³ + 96x²

The n-formula is [tex]a_{n} = (n+2) a_{n-1}[/tex].

What is mean by series?

The cumulative sum of a given sequence of terms is called a series.

Given that;

[tex]a_{1} = 1[/tex]

[tex]a_{n + 1} = (n+3) a_{n}[/tex]

Now,

Find the series of numbers as;

[tex]a_{n + 1} = (n+3) a_{n}\\[/tex]

Put n = 1,

[tex]a_{1+1} = (1 + 3)a_{1} \\\\a_{2} = 4a_{1} \\[/tex]

Put n = 2,

[tex]a_{2 + 1} = (2+3) a_{2}\\\\a_{3} = 5 a_{3}[/tex]

Put n = 3,

[tex]a_{3 + 1} = (3+3) a_{2}\\\\a_{4} = 5 a_{6}[/tex]

Put n = 4,

[tex]a_{4 + 1} = (4+3) a_{4}\\\\a_{5} = 7a_{4}[/tex]

Hence, Proceed this pattern we get;

[tex]a_{n} = (n+2) a_{n-1}[/tex]

So, The n-formula is [tex]a_{n} = (n+2) a_{n-1}[/tex].

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Charlotte can obtain that which website generated more revenue by (A) revenue divided by the number of posts.

Revenue is the total amount generated without the expenses to run a business.

From the given data we can conclude that content is what the website posted.

∴ To obtain which website generated more revenue per amount of content we have to divide revenue by the number of posts.

Website A posted 110 contents and generated $30,000,

∴ Revenue per content is,

= (30000/110) dollars.

= 272.72 dollars.

Website B posted 200 contents and genarated $75,000 dollars.

∴ Revenue per content is,

= (75000/200) dollars.

= 375 dollars.

So, Website B generated more revenue per content.

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The expression the company can use to determine the money they spend on batteries in a given day would be 3000b + 2500b.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

We have been given that Machine Alpha uses 3000 batteries a day in the clocks it makes and Machine Delta uses 2500 batteries a day in the clocks it makes.

Machine Alpha = 3000b

Machine Delta = 2500b

Let b dollars represents costs of each battery.

Then the expression the company that can use to determine the money they spend on batteries in a day as;

3000b + 2500b

Hence, the expression the company can use to determine the money they spend on batteries in a given day would be 3000b + 2500b.

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Answer:

Step-by-step explanation:

(2x^(4)y^(-3))

= 2x^4/ y^3.

The solution of given system of equations is 6 and 7.

To solve the system of equations using elimination, we will equate any one variable. In this case, we will be equating variable y.

Rewriting the equations -

-6x - 6y = −42 : equation 1

-x + 2y = 8 : equation 2

Multiplying equation 2 with 3

-3x + 6y = 24 : equation 3

Adding equation 1 and equation 3 to solve the given system of equations

-6x - 6y = −42

3x + 6y = 24

We get the answer :

-3x = -18

Negative sign will be cancelled and performing division

x = 6

Keep the value of x in equation 2

-6 + 2y = 8

2y = 8 + 6

2y = 14

y = 14 ÷ 2

y = 7

Therefore, the value of x and y is 6 and 7 in given system of equations.

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[tex]4\frac{6}{12}[/tex] hours play speed, what is the total running time of the video.

What does "speed" mean in mathematics?

Running time of cassettes

at standard speed = 1 hr

at standard speed = 4 hr

at standard speed = 4 hr

given the 1/4 part of tape is recorded at standard speed, 1/3 at long-play speed , 5/12 at super long-play speed,

so the running time of standard speed = 1/4 * 1 = 1/4

at long play speed

1/3 * 4 = 4/3 hours

and at super long-play speed,

5/12 * 7 = 35/12 hours

so, the total running time of the video

1/4 + 4/3 + 35/12 = 54/12 = [tex]4\frac{6}{12}[/tex] hours

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