the sum of 3 times a number and 4 is equal to 7.

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:

(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

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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The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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Answer:

5/7

Step-by-step explanation:

because it is 5/(2+5)

Answer:

9,

Step-by-step explanation:

The probability that a person selected randomly from the survey group is not in statistics given they are in AQR is 0.75

The Venn diagram represents the given parameter

From the Venn diagram, we have the following values

n(not statistics and AQR) = 21

n(AQR) = 21 + 7

Evaluate the sum

n(AQR) = 28

The probability that a person selected randomly from the survey group is not in statistics given they are in AQR is then calculated as

P(not statistics | AQR) = n(not statistics and AQR)/n(AQR)

So, we have

P(not statistics | AQR) = 21/28

Evaluate the quotient

So, we have

P(not statistics | AQR) = 0.75

Hence, the probability that a person selected randomly from the survey group is not in statistics given they are in AQR is 0.75

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Answer: 1/3 cup of cat food

Step-by-step explanation:

[tex]\displaystyle\\\frac{2}{3}:2=\\\\ \frac{2}{3}*\frac{1}{2} =\\\\ \frac{(2)(1)}{(3)(2)}=\\\\ \frac{1}{3}\ cup\ of\ cat\ food[/tex]

Answer:

Step-by-step explanation:

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 median of the set of data is 14 1/ 2

It is important to note that the median is the middle number of a given set of data.

Given the set of data;

12, 14, 15 , 16

Let's find the median;

There are two numbers in the middle, so we take their sum, and divide by 2, we have;

Median = 14 + 15/2

Find the sum of the numerators

Median = 29/ 2

Median = 14 1/2

Thus, the median of the set of data is 14 1/ 2

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The number of miles when the cost would be the same is 40 miles.

The equation that represents the total cost for car rentals is a linear function. A linear function is a function with a single variable that is raised to the power of one. A linear function is a straight line when drawn on a graph.

Total cost = constant cost + (cost per mile x number of miles driven)

First rental : $15 + (0.50 x m)

$15 + 0.50m

Second rental : $25 + (0.25 x m)

$25 + 0.25m

When the cost is the same for the car rentals, the two equations would be equal:

$15 + 0.50m = $25 + 0.25m

$25 - $15 = 0.50m - 0.25m

$10 = 0.25m

m = 10 / 0.25

m = 40 miles

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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.

Based on the given numbers, the number that is divisible by 4 are: 152, 76, and 4,788.

The numbers that are divisible by four need to meet certain requirements and the first one is that they should end in an even number.

The numbers divisible by 4 are:

= 152/4 = 38

= 76 / 4 = 19

= 4,788 / 4

= 1,197

This shows that these numbers are divisible by 4.

In conclusion, the numbers that are divisible by 4 are 152, 76, and 4,788.

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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

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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Answer:

B'C' = 16.2 and AB = 2.8

Step-by-step explanation:

the scale factor is 3 , then sides of Δ A'B'C' are 3 times Δ ABC

B'C' = 3 × BC = 3 × 5.4 = 16.2 units

Then

the sides of Δ ABC are [tex]\frac{1}{3}[/tex] times Δ A'B'C'

AB = A'B' ÷ 3 = 8.2 ÷ 3 ≈ 2.7 units ( to the nearest tenth )

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{4x^{2} }{5y}.\frac{7y}{12x^{4} }[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{1}{5}.\frac{7}{3x^{2} }= \frac{7}{15x^{2} }[/tex]

The final expression of the given equation is [tex]\frac{7}{15x^{2} }[/tex].

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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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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The values, when substituted for x in the expression \sqrt{x} , that will result in an irrational number are:

An irrational number can be described as the type of real number  that the representation can not be seen as that of simple fraction and they are been termed as the irrational numbers.

In this case , we can come into conclusion that any number  that posses a non-terminating as well as non-repeating decimal fit in , hence values, when substituted for x in the expression \sqrt{x} , that will result in an irrational number are:

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Answer:

24.5

Step-by-step explanation:

24.5*2 is 49

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]

[tex]x-4~\geqslant~-1\implies x~\geqslant~-1+4\implies \boxed{x~\geqslant~3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{multiplying both sides by -5}}{-5(x)\underset{\stackrel{\uparrow }{notice}}{~\leqslant~}-5(3)}\implies -5x~\leqslant~-15\implies -5x= \begin{cases} -15 ~~ \textit{greatest value}\\ -16,-17,-18...-\infty \end{cases}[/tex]

let's recall that for inequalities whenever we divide or multiply or exponentialize by a negative value, we must flip the inequality sign, notice, multiplying by -5, flipped it sideways.

Also let's recall that on the negative side of the number line, the closer to 0, the greater, thus -1 is much much greater than -1,000,000.

Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

Given the functions in the question;

To evaluate f + g, replace the function designators in f + g with the actual functions and simplify

( f + g )(x) = f(x) + g(x)

( f + g )(x) = (4x + 1) + (x + 5)

Remove the parenthesis and collect like terms

( f + g )(x) = (4x + 1) + (x + 5)

( f + g )(x) = 4x + 1 + x + 5  

( f + g )(x) = 4x + x + 5  + 1

( f + g )(x) = 5x + 6  

Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

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The given function is exponential growth and the y-intercept is y=3.

Given that the given function is y=3(4ˣ).

Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.

If a is positive and b is greater than 1 then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 then it exponential decay.

The graph of the given function y=3(4)ˣ is shown in the attached image.

From the graph, it is visible that the given function is an exponential growth because a is 3 and it is positive and it is greater than 1.

Now, we will find the y-intercept by substituting x=0, we get

y=3(4⁰)

y=3(1)

y=3

Hence, the given function or situation y=3(4ˣ) as an example of exponential growth and the y-intercept is 3.

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In the equation b = a -2, which variable is the independent variable and which is the dependent variable ? Explain.

In the given equation b=a-2, a is an independent variable and b is an dependent variable.

Independent variable is variable whose values are unaffected by changes is referred to as an independent variable.

The dependent variable is defined as the variable whose evaluation of the independent variable determines the quality of the dependent variable.

For example, y=x+5

Here, According to changes in the evaluation of the variable "x," the estimation of the variable "y" also varies. The variable "y" is referred to as an dependent variable and the "x" is referred to as an independent variable.

Therefore, In the equation b=a-2, "a" is an independent variable and "b" is an dependent variable.

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Answer: 8 bills of each.

Step-by-step explanation:

10x 8=80

5x8=40

1x8=8

=128

The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

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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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