2. Solve the inequality -5/2(3x − 2) < 6 − 2x.


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every step. You may add more lines if you need them.

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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:

Step-by-step explanation:

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

= 2x^4/ y^3.

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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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: 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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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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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.

Answer:

(a) x = 10

(b) y = 4

Step-by-step explanation:

For a line of the form y = mx + b, the slope is m, b is the y-intercept

A parallel line will have the same slope and a different y intercept

A perpendicular line has a slope = -1/m

But x = -4 is a line parallel to the y axis intercepting the x-axis at -4. So slope = ∞

Therefore here are equations for a parallel line and a perpendicular line

A parallel line will have the form x = k where k is a constant(positive or negative). So x = 10 is a line parallel to x = -4

A perpendicular line will be of the form y = 4 or y = -10 or whatever, i.e. without the x component. Such a line will be parallel to the x-axis so both lines are perpendicular

Regarding your questions

y = 4x + 3 has a slope of 4 and a y intersect of 3 so it will be a sloping line
x = 4 will be parallel, not perpendicular to x = -4

I have provided a graph which makes this explanation clearer. The dotted line is x = 4 and you can see it is parallel to x = -4

Answer:

Step-by-step explanation:

Answer: 8 bills of each.

Step-by-step explanation:

10x 8=80

5x8=40

1x8=8

=128

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 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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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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The solution to the equation is x = -2 or x = 5

The equation is given as

3x^2-9x=30

Rewrite properly as

3x^2 - 9x = 30

Divide through by 3

So, the equation becomes

x^2 - 3x = 10

Rewrite the equation

So, the equation becomes

x^2 - 3x - 10 = 0

Expand the equation

So, the equation becomes

x^2  + 2x - 5x - 10 = 0

Factorize the equation

So, the equation becomes

x(x  + 2) - 5(x + 2) = 0

This gives

(x + 2)(x - 5) = 0

Evaluate

x = -2 or x = 5

Hence, the solution to the equation is x = -2 or x = 5

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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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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: [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

Answer:

Infinite many solutions.

Explanation:

Equation's:

make y the subject:

eq 1

eq 2

Solve:

       y = y

5 - 2x =  5 - 2x

As both sides are equal, the system of equations have infinite solutions.

The car will move with a force of 1200 N in forward direction .

The correct option is D .

Data obtained from the question

Forward force = 2000 N

Force of air resistance = 800 N

Net force the car will use to move as illustrated below:

Net force = forward force - force of air resistance

Net force = 2000N - 800N

Net force = 1200 N forward

The net force represents the overall force acting on the car. In this case, the net force is 1200 N forward. This means that the car will experience a force of 1200 N pushing it in the forward direction.

Thus, the car will move with a force of 1200 N in forward direction .

The correct option is D .

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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 coordinates of the image is (4,-1) that is option D) is correct.

According to the question we have been given that

        the point to be rotated = (-4,1)

           center = (-3,0)

        Rotation = 180° counterclockwise.

Note that when the point is rotated 180° counterclockwise then the coordinate of the image point will be

   (x , y ) = (-x , - y)

For the coordinates of the image first we translate the center to the origin that is

    (-3,0) = (-3+3,0) = (0,0)

Now we will do same for the point that is,

   (-4 , 1) = (-4+3 , 1) = (-1,1)

Now the points are (-1,1). Thus the image will be  

   (-1,1) = (-(-1), -1) = (1,-1)

Now undoing the original translation :

  (1,-1) = (1+3,-1) = (4,-1)

Hence the coordinates of the image is (4,-1) that is option D) is correct.

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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.

The offer that will make her more money and how much more will she make is

This is further explained below.

Generally, the equation for the total made is  mathematically given as

T= flat rate +(hours worked*hourly pay)

Therefore, for the first family

T= 40 + (6+5)

T=$51

For the 2nd family

T'= 20 + (6+10)

T'=$36

In conclusion, the offer that will make her more money and how much more will she make is

T'=51-36

T'=$15

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CQ

Simone wants to babysit this weekend to make some extra money she changes a flat fee then changes per hour or part thereof that she babysits Saturday afternoon she will babysit for 6 hours she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make

Real root of ∛0.064 is 0.02133.

By considering the given expression

∛0.064

=(0.064)^1/3

= (0.021)^1/3

= 0.02133

If a mathematical equation has real roots, then its solutions or roots are real numbers. If an equation has distinct roots, we contend that all of its solutions or roots are not equal. A quadratic equation has real and distinct roots if the discriminant is greater than 0.

If there are no stationary points on the curve, then f has a single real root. If stationary points are found, you could demonstrate using the geometry of the curve that the curve can only intersect the x axis once due to the configuration of the stationary points.

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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 :)

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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a would the compound inequality have infinite solutions if a = 4

x < 4 AND x > a.

if a = 4 and we use an "or" instead of the "and" we have:

x < 4 or x > 4.

This is:

"x is larger than 4 or smaller than 4."

Then the solution of this is all the real numbers except the value x = 4.

The set of solutions can be written as:

{xI x ∈ R  \ [4]}

Where this reads:

"x belongs to the set of the reals minus the number 4".

Or we also could write it as:

x ∈ (-∞, 4) ∪ (4, ∞)

Where we have two open ends in the "4" side, so the value x = 4 does not belong to that set.

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Answer:

[tex]\frac{\text{dogs}}{\text{total}} = \frac59[/tex]

Step-by-step explanation:

We can say that the amount of cats is [tex]4x[/tex] and the amount of dogs is [tex]5x[/tex], as we know that  [tex]\frac{\text{cats}}{\text{dogs}} = \frac45[/tex]

Therefore, the total amount of animals (cats and dogs) is [tex]9x[/tex].

[tex]\frac{\text{dogs}}{\text{total}} = \frac{5x}{9x} = \frac59[/tex]