2(3x +4) -(x-2)
expand and simplify

The graph of each function in the piecewise function is added as an attachment

The equation of the piecewise function is given as

f(x) = 1/4x - 5  if x < 4

         x + 3 if x ≥ 4

In the above definition of the piecewise function, we have the following functions and the domains

f(x) = 1/4x - 5 at a domain of x < 4

f(x) = x + 3 at a domain of x ≥ 4

Note that:

The domain of the function is the set of input values of the graph

This in other words mean the domain of a function is the set of x values of the graph.

Next, we plot the graph of each function in the piecewise function in their respective domain

See attachment for the graph of each function in the piecewise function,

On the graph, the blue line represents f(x) = 1/4x - 5 while the other line represents f(x) = x + 3

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Possible question

Plot of the piecewise function

f(x) = 1/4x - 5  if x < 4

         x + 3 if x ≥ 4

Answer:

[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex]

Step-by-step explanation:

2y + k = 6y - ky; solve for y

2y = 6y - ky - k (Subtraction Property of Equality)

2y - (6y - ky) = 6y - ky - k - (6y - ky)  (Subtraction Property of Equality)

-4y + ky = -k (Simplify)

y(-4 + k) = -k (Factor)

[tex]\frac{y(-4+k)}{-4+k}=\frac{-k}{-4+k}: k\neq 4[/tex] (Division Property of Equality)

   [tex]y=-\frac{k}{-4+k}; k \neq 4[/tex] (Simplify)

The value of y is k/ (4- k).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.

Given:

2y + k = 6y - ky

Now, solving for y

2y -6y + ky = -k

-4y + ky= -k

y( k-4) = -k

y = -k/(k -4)

y= k/ (4- k)

Hence, the value of y is k/ (4- k).

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Answer:

first equation: Incorrect

second equation: Correct

Step-by-step explanation:

first equation:

[tex]-1 + (\frac{1}{-1}) = 1[/tex]

[tex]-1 + (-1) = 1[/tex]

[tex]-2 = 1[/tex]

negative 2 isn't the same as positive 1 which isn't true so the answer is incorrect.

second equation:

[tex](\frac{-1}{1} ) = -1[/tex]

[tex](-1) = -1[/tex]

negative 1 is the same as negative 1 so the answer is correct

The rate at which the customers enter the store in minutes per customer is 2 minutes.

Based on the given question the number of customers is 9 so they take 18 minutes to enter. If each customer takes

(18÷9) minutes = 2 minutes.

Then all the customers will be inside the shop.

Fractions: The number of parts of a full portion is known as a fraction.

It is usually best to show an explanation using the easiest fraction. That is called Simplifying, or Decreasing the Fraction.

We call the top number the Numerator, it is the number of parts we have.

We call the bottom number the Denominator, it is the number of parts the total is separated into.

Represented as : [tex]\frac{Numerator}{Denominator}[/tex]

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Answer: The common factors of 14 and 35 are 7, 1, intersecting the two sets above. In the intersection factors of 14 ∩ factors of 35 the greatest element is 7. Therefore, the greatest common factor of 14 and 35 is 7.

Step-by-step explanation:

The discrete data might consist of number of legs, number of teeth. The continuous data might consist the length of tail, and the height of dog.

The discrete data is a data whose value is obtained by counting and they can be described by an integer value. Those random variables, who take only distinct values, are called discrete random variables.

Consider the provided information; Something that will never change

So, the discrete data might consist of number of legs, number of teeth.

A continuous data is defined as a variable whose value is obtained by measuring.

The continuous data might consist the length of tail, and the height of dog.

The continuous variables are random variables, who take any value from a given continuous interval of real numbers.

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The slope of the line passing from the two points is found as infinity.

For the given question;

The two passing points of the line is given as;

(x1, y1) = (-4, 6)

(x2, y2) = (-4, 18)

The formula for calculating the slope is;

Slope  = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (18 - 6)/ (- 4 + 4)

m = 12/0

m = ∞

It means, the line is parallel to the x axis.

Thus, the slope of the line passing from the two points is found as infinity.

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g ≥ 1.8 is  the number of hours of running per day in inequality .

What are the mathematical inequalities?

Atleast means the number would be greater than or equal to given number.

g ≥ 1.8

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Answer:

Its C

Step-by-step explanation:

Answer:

Can I see the graph, please?

Step-by-step explanation:

Answer:he graph shows the relationship between the number of miles she drives, y, and the number of gallons of gasoline in her car's tank, x.

Step-by-step explanation:

The graph could be the graph of f(x) which is the correct answer would be option (B).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We are given the degree of the polynomial function f(x) to be 3; and

the roots of the equation f(x) to be 0 are -1, 0, and 4.

So we will put these values in the polynomial function of degree 3 to get:

f(x) = (x  -(-1))(x-0)(x-4)

f(x) = (x  + 1)x(x-4) = x³ - 3x² - 4x

According to this, the x-intercepts of this function on the graph will be:

(0, 0)

(-1, 0)

(4, 0)

So we will look for a graph that intercepts the x-axis at these points.

Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).

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Answer:

1.5 miles = 241,401.6 centimeters

               = 95,040 inches

1.5 miles = 2,414.016 meters

Step-by-step explanation: 5,280 feet x 12 inches = 63,360 inches

                                              2,640 feet x 12 inches = 31, 680 inches

63,360 + 31,680 = 95,040 inches in 1.5 miles

95,040 x 2.54 centimeters per inch = 241,401.6

241,401.6 centimeters / 100 = 2,414.016 meters

The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).The x-coordinates of P is 6.2 and y-coordinates of P is 1.4.

Given that,

The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).

We have to find the coordinates of the QR line segment aimed at point P along that QP to PR is a 1 to 4 ratio.

QR has the endpoints Q(8, 4) and R. (-2, -1).

Line segment QR divides at point P in ratio 1:4.

Using section formula:

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P(x,y)=[tex](\frac{mx_{2} +nx_{1} }{m+n},\frac{my_{2} +ny_{1} }{m+n},)[/tex]

Where m is 1 and n is 4. x₁=8,y₁=4 and x₂=-2,y₂=-1.

Substitute in the formulae we get,

P(x,y)=((1×-1+4×8)/1+4,(1×-1+4×4/1+4))

P(x,y)=((-1+32)/5,(-1+8)/5)

P(x,y)=(31/5,7/5)

P(x,y)=(6.2, 1.4)

Therefore, the x-coordinates of P is 6.2 and y-coordinates of P is 1.4

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The coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.

A reflection is a transformation that uses a line to reflect a figure, much like a mirror. The mirror line is also known as the line of reflection.

The given coordinates are A(7,-5), B(5,3), and C(-2,-5).

The line of reflection is y = -2.

We have to determine the coordinates of the vertices of A'B'C' for the reflection.

In this case, the x-coordinate will remain the same and the y-coordinate will vary as the points are reflected across the line y = -2.

From the line of reflection i.e.y = -2, point A(7,-5) is located down at a distance of 3 units so its reflection A' is 3 units up of line y = -2 at (7,1).

From the line of reflection i.e.y = -2, point B(5, 3) is located up at a distance of 5 units so its reflection B' is 5 units down of line y = -2 at (5,-7).

From the line of reflection i.e.y = -2, point C(-2,-5) is located down at a distance of 3 units so its reflection C' is 3 units up of line y = -2 at (-2,1).

Hence, the coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.

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Answer:

0.1 == -0.1

1/7 == -1/7

10 == -10

-7 == 7

Step-by-step explanation:

I took the test

The opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The numbers are:

0.005, 12, 0, -2

As we know, from the definition of the number, a number is a mathematical entity that can be used to count, measure, or name things.

The opposite of any number can be obtained by changing the sign of the number.

The opposite of the number 0.005 is -0.005

The opposite of the number 12 is -12

The opposite of the number 0 is 0

The opposite of the number -2 is 2

Thus, the opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

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Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.

What is consecutive integers ?

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the 1st sibling

Let x -2 = the second sibling

Let x -4 = the third sibling

Let x-6 = the fourth sibling.

If you add the four siblings together they equal 112

(x) +(x-2)+(x-4)+(x-6) = 112  Combine like terms

4x - 12 = 112

add 12 from both sides

4x - 12 + 12 = 112 + 12

4x = 124

divide 4 both side :

x = 31

The eldest sibling is 31, followed by siblings 29, 27 and 25

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Answer:

x=20 degrees

I did what your teacher did down there; I added all the exterior angles and set them equal to 360°

Just combined the like terms and got the answer!

*3x + 4x + 3x = 10x

12 - 10 - 2 = 0

90 + 70 = 160

Put them "as an equation": 10x + 160 = 360

Get rid of what's surrounding the x, so subtract 160 from both sides.

10x = 200

To get rid of whats beside the x *again*, divided 10x by 10 on both sides.

x = 20

cross multiplying

4/3(y-9/10)=5y(2/10)

expanding the bracket and collecting like terms

4y/3 - 6/5=y

4y/3 - y=6/5

((4y-3y)/3)=6/5

y/3=6/5

y=6/5x3

y=18/5

y=3.6

I hope this will help✨

The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.

The volume of an ice cream cone (V), in cubic units, is described by the following formula:

V = (1 / 3) · (π · r²) · h                                     (1)

Where:

The rate of change for the height of the cone is derived from differentiating (1) with respect to time:

V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'

V' = (2π / 3) · h · r' + (π / 3) · r² · h'

h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]

Where:

If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:

h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]

The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.

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The range of the error will be [3.65,3.75.

The accuracy range or limit where a number is rounded off or truncated is known as the error interval. This range merely depicts the possible range before rounding.

Given that :A number, x, rounded to 1 decimal place is 3.7

The mistake will be half of 0.1, which is[tex]\frac{0.1}{2} = 0.05[/tex], since the number is rounded to the nearest 0.1 unit.

3.7-0.05=3.65 will then be the lower limit of the error interval.

The error interval's upper limit will be 3.7 + 0.05 = 3.75.

The error will be 3.65≤x<3.75 milliseconds.

If the second decimal unit is more than 5, the first decimal unit will be 6, since we are rounding the first decimal unit. Similar to this, the first decimal unit will be 7 if the second decimal unit is less than 5.

The figures below, when rounded, result in 3.7.

3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74

As a result, the error range will be [3.65,3.75).

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Answer:

3 inches up per foot across

Step-by-step explanation:

rate of change = difference of y / difference of x

R = (18 - 12) / ( 6-4) = 6 / 2 = 3 inch / foot

hey you man what are you going here go to there

The following data table for two distinct linear functions utilizing identical x values for both functions is displayed:

[tex]\begin{tabular}{|c|c|c|}$\mathrm{x}$ & $\mathrm{y}=2 \mathrm{x}+7$ & $\mathrm{y}=-\mathrm{x}+4$ \\$-3$ & $2(-3)+7=-6+7=1$ & $-(-3)+4=3+4=7$ \\$-2$ & $2(-2)+7=-4+7=3$ & $-(-2)+4=2+4=6$ \\$-1$ & $2(-1)+7=-2+7=5$ & $-(-1)+4=1+4=5$ \\0 & $2(0)+7=0+7=7$ & $-(0)+4=0+4=4$ \\1 & $2(1)+7=2+7=9$ & $-(1)+4=-1+4=3$ \\2 & $2(2)+7=4+7=11$ & $-(2)+4=-2+4=2$ \\3 & $2(3)+7=6+7=13$ & $-(3)+4=-3+4=1$\end{tabular}[/tex]

The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.

As a result, the two functions' graphs will intersect at (1, 5)

First of all, we create 2 LINEAR function, i created the function f(x)=2x+5 and the function h(x)=3x+2, both are linear(without a quadratic term). Then

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. To find the y value, evaluate the equation (middle column). Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.

you replace the x for a number:

Table 1 (F(X)=2X+5)                                 Table 2 (H(X)=3X+2)

X=1----->Y=2+5=7                                     X=1------>Y=3·1+2=5

X=2---->Y=2·2+5=9                                  X=2----->Y=3·2+2=8

X=3---->Y=3·3+5=11                                  X=3----->Y=3·3+2=11

With both tables of data we can see that in the X=3/Y=11 point this two linear functions will intersect so the answer is that the two functions will intersect at (3,11)----->(X,Y)

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Answer:

A 2√6

Step-by-step explanation:

- Split the value under root into divisions of factors of 24

[tex]{ \sf{ \sqrt{24} = \sqrt{6 \times 4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times \sqrt{4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times 2 }} \\ \\ { \boxed{ \sf{ \: \sqrt{24} = 2 \sqrt{6} }}}[/tex]

3633 is the difference of these numbers.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.

Given Data

9832 - 6199

Subtracting,

= 9832 - 6199

= 3633

3633 is the difference of these numbers.

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Before the drawbridge starts to open, the horizontal component of the friction force f⃗ is zero (0)

The horizontal component of the friction force is the counter force that must overcome the friction force for a body to slide or move.

When the dancer is standing still on the drawbridge, the only force on the dances is the normal force exerted by the bridge. Thus, the horizontal frictional force acting on the dancer

This is given by:

[tex]f_{horizontal} =0[/tex]

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Answer:

170 strawberries

Step-by-step explanation:

Let strawberries be x, then:

Ann ate 5x, Ben ate 5x, and Cindy ate 7x

7x+30 = 5x+5x

7x+30 = 10x

30 = 3x

10 = x

5x = 50

7x = 70

total: 50+50+70 = 170

Answer:

[tex]g(h(x))=−6x−17

[/tex]

Step-by-step explanation:

given:

[tex] g(x) = 15 - 4x \\ h(x) = \frac{3}{2 } x + 8[/tex]

To find g(h(x)) substitute h(x) instead of every x in g(x)

therefore:

[tex]g(h(x)) = 15 - 4( \frac{3}{2} x + 8) \\ [/tex]

simplify

[tex]g(h(x)) = 15 - 6x - 32 \\ g(h(x)) = - 6x - 17[/tex]