Please help!!! I really need this!!! It's piecewise functions......

Please Help!!! I Really Need This!!! It's Piecewise Functions......

Answers

Answer 1

well, let's take a peek at the graph, hmmm it has a straight line from the origin to (5,10), and then another straight line from (5,10) to (10,5) and then another one from there up to (20,5).

well, let's simply get the equations for each of those lines then

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{0})\implies \boxed{y = 2x} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ 5 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-1}(x-\stackrel{x_1}{5}) \\\\\\ y-10=-x+5\implies \boxed{y=-x+15} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 0 }{ 10 }\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{0}(x-\stackrel{x_1}{10})\implies y-5=0\implies \boxed{y=5}[/tex]

so then hmmm let's use those, we know how f(x) is moving now, so

[tex]\stackrel{y}{f(x)}= \begin{cases} 2x&x\geqslant 0\\\\ -x+15&x\leqslant 10\\\\ 5&x\leqslant 20 \end{cases}[/tex]


Related Questions

100 POINTS!!!

The wavelength of the color red is about 6.5×10^−9 m. The wavelength of the color blue is about 4.75×10^−9 m. Show that the wavelength of red is longer than the wavelength of blue.

Pls answer asap 100 points

Answers

2.5 x 10^-7 m
Explanation:
We can substract the wavength of the violet light to the wavelength of the red light:
(6.5 x 10^-7 m) - (4.0 × 10^-7 m) = 2.5 x 10^-7 m
This is the difference between this two values of wavelength.
So the wavelength of red light is 2.5 x 10^-7m longer than violet light.

Step-by-step explanation:

To tell if something is longer than another object is to find the difference between the two objects.

If the difference is < 0, then the object is shorter

If the difference is = 0, then the objects are equal in length

If the difference is > 0, then the object is longer

[tex]6.5 * 10^{-9}[/tex] - [tex]4.75 * 10^{-9}[/tex] = [tex]1.75*10^{-9}[/tex]

The difference is > 0, so the wavelength is longer.

A line passes through (1, 3) and (4, 7). Which line would be perpendicular to this line?
a) y=-x+5
b) y=-x-2
c) y= 4x + 2
d) y=-4x-4

Answers

Answer: Any line with slope of -3/4

Reason:

Let's calculate the slope of the line through those two points

[tex](x_1,y_1) = (1,3) \text{ and } (x_2,y_2) = (4,7)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{7 - 3}{4 - 1}\\\\m = \frac{4}{3}\\\\[/tex]

The slope of the line is 4/3

Anything perpendicular to this has a slope of -3/4. I flipped the fraction and flipped the sign (from positive to negative).

So for example, the answer may be something like [tex]y = -\frac{3}{4}x+5[/tex] or [tex]y = -\frac{3}{4}x-2[/tex]. All that matters is the -3/4 out front of the x.

Side note: the original slope 4/3 and perpendicular slope -3/4 multiply to -1

Let f (x) = -4+1 Write a function g whose graph is a reflection in the y-axis of the graph of f.

Answers

If the function is reflected across the y-axis of the graph of f, the resulting function will be g(x) = 4x + 1

Translation of functions

Translation is the technique that is used to change the position of a figure on an xy-plane.

For instance, if the function f(x) is reflected in the y-axis, the resulting function will be g(x) = f(-x)

Given the function f(x) = -4x+1 if the function is reflected in the y-axis of the graph of f.f, the resulting function will be;

g(x) = f(-x)

g(x) = -(-4x) + 1

g(x) =4x + 1

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How do you factor this equation

3n³+9n²-10n

Answers

Answer:

[tex]n(3n^2+9n-10)[/tex]

Step-by-step explanation:

Well you'll notice each of the components in the equation have a factor of "n". Each of them are being multiplied by at least one "n". This means we can factor out this "n" to get the following result: [tex]n(3n^2+9n-10)[/tex]

This is just the reverse of the distributive property: [tex](a+b)c=ac+bc[/tex] except you're going from ac + bc -> (a+b)c

HELP.........................! !

Answers

Answer:

[tex] \sf \large \: −6.23[/tex]

Step-by-step explanation:

2.67−8.9

=2.67+−8.9

=−6.23


Which angles are shown in the diagram?

Answers

DAE BAC DAB BAE CAB EAC

a movie theater charges $4 for each child's ticket and $6.50 for each adult's ticket. one night, 200 tickets were sold, amounting to $1100 in ticket sales. how many of each type were sold?

Answers

A total of 200 tickets was sold whereas 120 tickets were for adult and 80 tickets for the child.

What do you mean by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

As a result, multiplying by 2, the man travels 3.5 miles in one hour.

The distance the man walks in 7 hours, multiplied by 7, comes out to be 24.5 miles. Alternatively, you might divide the man's distance traveled by 7, or X, to get 7 (x/7). It equals the time needed to travel X miles, which is 2 hours (7/2), divided by the time needed to go X miles, which is 7 hours. X, therefore, equals 24.5 miles.

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If the actual book is 9 inches wide. How tall is the actual book?

Answers

The height of the book is 18 inches tall.

How to calculate the height?

The width of an image of a book shown on a website = 1.5 inches

The length of the book shown on the website = 3 inches

The actual width of the book = 9 inches

Scale of the book image = 1 inches  = 6 inches

The actual heigth of the book:

= 3 × 6

= 18 inches.

The actual book is 9 inches wide and 18 inches tall.

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An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide

Please help me please help

Answers

Answer:

Step-by-step explanation: ok so divide by 647

f(x)=9 find the following values





2f(x) +3

Answers

Answer

this question is impossible no expert can solve this!11!1!!!

Step-by-step explanation:

none

Simplify (step by step)
(-2)(-3) - (8)(-3) + (9)(-2)

Answers

Answer:

12

Step-by-step explanation:

190 students enrolled in a freshman-level chemistry class. by the end of the semester, 4 times the number of students passed as failed. find the number of students who passed, and the number of students who failed.

Answers

The number of students passed is 152 and who failed is 38.

This problem is from the chapter of linear equation in one variable.

right here, it's far for the reason that the overall quantity of college students enrolled in the chemistry class is =190

And additionally the whole variety of students who passed is 4 instances the quantity of college students failed.

allow the total range of students who failed is x.

So, the number of students who passed is 4x.

According to question,

  4x + x=190

⇒5x=190

⇒x=[tex]\frac{190}{5}[/tex]

∴ x = 38

So, the number of students who failed is 38 and the number of students who passed is 152.

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5. Charnita Jones earns $304.80 per week as a sales assistant. Next week she will be
promoted to assistant manager. She will then earn $332.50 per week. She is single
and claims 1 allowance. How much more will she pay in federal income tax?

Answers

Charnita Jones will have to pay $5 more in federal income tax.

According to the question we have been given that Charnita Jones

As sales assistant she earned = $304.80

After promotion as assistant manager she will earn = $332.50

Number of allowance she claims = 1

We need to find how much more she will pay in federal income tax.

For that we will first calculate how much she paid when her earning was $304.80. For this we will use the table for single persons-weekly payroll period. In that table, first we will choose the row of wages from the column number 1. We look to that row where $304.80 will lie that is the row will be $300-$310. then we will look for allowance that is 1. Thus the tax she will pay will be in column of allowance 1 and in the row of   $300-$310 is $22.

In similar way we will find out the tax she will pay when she earn $332.50 which is $27.

Difference = $27 - $22 = $5

Hence she will have to pay $5 more in federal income tax.

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give at least one physical explanatgion for nay difference between the actuial number of beans in the container and theh number of beans determined by the expierment

Answers

The number of beans calculated by physical counting and by calculating the number of beans could always be different unless the bean in the jar is not identical.

Given that,
To give at least one physical explanation for nay difference between the actual number of beans in the container and the number of beans determined by the experiment.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let's assume we have 1 kg o bean in a jar but the weight of all the individual bean are not the same, that's why the number of bean in physical counting differs from the number of beans calculated from the calculation in an experiment,

Thus, the number of beans calculated by physical counting and by calculating the number of beans could always be different unless the bean in a jar is not identical.

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Ingrid types 3 pages in the same amount of time that Tanya types 4 pages. If Ingrid and Tanya start typing at the same time, how many

Answers

If the grid and tanya start typing at the same time, tanya have typed 14.67 pages.

What is the ratio?

A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.

Now it is given that,

Pages typed by Ingrid = 3

Pages typed by Tanya = 4

So, the ratio of pages, Ingrid : Tanya = 3 : 4

So,  If the grid and tanya start typing at the same time Ingrid has typed 11 pages

Thus, dividing the ratio be 3 we get,

3 : 4 = 1 : 1.33

Now for 11 pages multiplying 1.33 with 11 we get,

1.33 x 11 = 14.67

Thus, If the grid and tanya start typing at the same time, tanya have typed 14.67 pages.

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The Complete question is,

Ingrid types 3 pages in the same amount of time that tanya types 4 pages. If the grid and tanya start typing at the same time how many pages will tanya have typed when ingrid has typed 11 pages ?

the triangles are similar

Find x

Answers

62+90+x=180

152+x=180

x=28

28

If the two tringles are similar they will have equal angles

and it is also right angle try angle this means we have two angles given

90,62

the mesurement of triangle is 180 so to find x we will

90+62+x=180

x=180-90+62

x=180-152

x=28


Maddie scored 2 fewer than triple the number of points Crystal scored in their basketball game. Together the girls scored 30 points. Let
m = the points Maddie scored, and c = the points Crystal scored. Which system can be used to find the number of points each girl
scored?

Answers

The system of equations that is used to find how many points each girl scored is given as follows:

m = 3c - 2.c + m = 30.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

Variable m: number of points scored by Maddie.Variable c: number of points scored by Crystal.

Maddie scored 2 fewer than triple the number of points Crystal scored in their basketball game, hence:

m = 3c - 2.

They scored 30 points in total, hence:

c + m = 30.

Thus, the system is given by:

m = 3c - 2.c + m = 30.

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How do I get five with with two sevens one 9 and one three ans can use the same number twice.

Answers

2 Sevens take that 2 and subtracts is by 7 like this 7 minus 2 which is five

ip a standard sheet of paper measures 8 1/2 by 11 inches. find the area of one such sheet of paper in

Answers

The area of the standard sheet of paper is 93 1/2 square inches.

The standard sheet of paper is a rectangle and to find its area, multiply the length by the width.

The area of the rectangle is the region enclosed by the perimeter of the rectangle and is equal to product of length and width.

If the standard sheet of paper has a length of 11 inches and a width of 8 1/2 inches, then:

A = l * w

A = 11 x 8 1/2

A = 93 1/2 square inches

Hence, the area of the standard sheet of paper is 93 1/2 square inches.

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Which graph represents the equation.

Answers

Answer: The one that has a picture to itself

Step-by-step explanation:

Use desmos its a free online graphics calculator for graphs. etc

please look at picture this thing is due next day

Answers

Snail will have to travel shortest distance of (C) 11 cm

The shortest distance between vertex A and vertex B will be the line directly joining the two points. This line is called diagonal and is related with length, width and height by the formula -

Diagonal = ✓(l² + w² + h²), where l represents length, w represents width and h represents height. Keep the values in formula -

Diagonal = ✓(4² + 4² + 10²)

Taking square of the number

Diagonal = ✓(16 + 16 + 100)

Performing addition on Right Hand Side of the equation

Diagonal = ✓132

Taking square root

Diagonal = 11.49 cm

Therefore, the shortest distance needed to be travelled by snail is (C) 11 cm.

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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Answers

The slope of the line = rise/run = 2/3.

How to Determine the Slope of a Line?

To determine the slope of a line, we can find the ratio of the rise of the line to that of its run.

Therefore, slope (m) of a line = rise/run.

Rise = vertical distance across the line

Run = horizontal distance across the line

In the graph given, we have:

Rise is the blue line = 6 units

Run is the red line = 9 units

Slope of the line (m) = 6 units/9 units

Slope of the line (m) = 2/3

Therefore, In simplest form, the slope of the line = rise/run = 2/3.

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You average 55 miles per hour while driving to a relative's house. On the return trip, you average 50 miles per hour because of bad weather. The total driving time is 5 hours and 15 minutes. How long does each trip take?

Answers

We conclude that the frist trip takes 2.75 hours and the second one 2.5 hours.

How long does each trip take?

Remember the relation:

Distance = Speed*Time.

Here the total distance of the trip is 55mi + 50mi = 105mi

And the total time is 5 hours and 15 minutes, remember that:

60 min = 1 hour

Then; 15 min = 0.25 hours.

So the total time is 5.25 hours, with that we conclude that the average speed is:

S = 105mi/5.25 h = 20 mi/h

The first trip is 55 miles long, then the time in which it is travelled is:

T = (55 mi)/(20 mi/h) = 2.75 hours

The second trip is 50 miles long, then:

T' = (50mi)/(20 mi/h) = 2.5 hours.

We conclude that the frist trip takes 2.75 hours and the second one 2.5 hours.

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Mary and Julie are trying to raise $1000,mary raises $12 every 4 days, Julie raises $19 every six days.who reaches the goal first?explane

Answers

The person who first reaches the goal is Julie because she raise more than the amount Mary raise per day

Equation to determine who reaches the goal first

Their goal = $1000

Mary

Every 4 days = $12Amount by raised per day = $12/4

= $3

Julie:

Every 6 days = $19Amount earned per day = $19 / 6

= $3.17

Therefore, the person who reaches the goal first between Mary and Julie is Julie

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The perimeter of the polygon with the vertices. U(-2,4), V(3,4), W(3,-4). Round your answer to the nearest hundredth.

Answers

The Perimeter of the polygon = 22.43 units.

How to Determine the Perimeter of a Polygon?

Given the vertices of the polygon as:

U(-2,4)V(3,4)W(3,-4)

The perimeter of the polygon is the sum of all its sides, UV + VW + UW.

Apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] to find the length of each of the three sides of the polygon as shown below:

UV = √[(3−(−2))² + (4−4)²]

UV = √[(5)² + (0)²]

UV = √25

UV = 5 units

VW = √[(3−3)² + (4−(−4))²]

VW = √64 = 8 units

UW = √[(−2−3)² + (4−(−4))²]

UW = √89 = 9.43 units

Perimeter of the polygon = 5 + 8 + 9.43

Perimeter of the polygon = 22.43 units

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имеется 9 различных книг 4 из которых учебники. Сколькими способами можно расставить эти книги на полке так чтобы все учебники стояли рядом

Answers

Answer:

17280

Step-by-step explanation:

И для этих 4 книг, сложенных вместе, возможное расположение будет следующим: 4 х 3 х 2 х 1 = 24. Всего возможные способы расположения 9 книг будут: 720 х 24 = 17280.

What is the average rate of change of the function f(x)=x2–5x+14 on the interval from x=3 to x=5?

Answers

Answer:

3

Step-by-step explanation:

To find the average rate of change from two points: [a, b] we generally use the slope equation, which can be represented as: [tex]\frac{f(a)-f(b)}{a-b}[/tex]

So here let's first calculate f(3) and f(5)

[tex]f(3)=(3)^2-5(3)+14\\f(3)=8\\\\f(5)=(5)^2-5(5)+14\\f(5)=14[/tex]

Now let's plug these values into the equation: [tex]\frac{f(5)-f(3)}{5-3}[/tex]

To get the equation: [tex]\Longrightarrow \frac{14-8}{5-3}=\frac{6}{2}=3[/tex]

14 less twice the sum of m and 12 is at most 24.
Find all the solutions for m. Give all three
representations.

Answers

The solution to the given inequality are x  ≤ 7, and (-∞, 7).

Inequality expressions

Inequality expressions are expressions that are not separated by an equal sign.

For the statement "14 less twice the sum of m and 12 is at most 24", it is expressed as:

2(x+12)-14 ≤ 24

Simplify

2x + 24 - 14  ≤ 24

2x + 10  ≤ 24

2x  ≤ 24 - 10

2x ≤ 14

Divide both sides by 2

x  ≤ 14/2

x  ≤ 7

Hence the solution to the given inequality are x  ≤ 7, and (-∞, 7).

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Write the algebraic expression for the sum of k and l divided by the sum of d and e pill

Answers

The algebraic expression for the sum of (k) and (l) divided by the sum of (d) and (e) is: (k + I) / (d + e) =

To solve this problem, we have to state the equation using the information of the problem:

Algebraic Expression:

"the sum of (k) and (l) divided by the sum of (d) and (e)"

(k + I) / (d + e) =

What are algebraic operations?

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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{(2, 1). (-4, 5), (1, 7), (2, -3), (-1,2)}
Domain and Range​

Answers

The Domain of a relation is the set of all allowable inputs. It is all the x-values in the (x, y) points determined by the relation.

The Range of a relation is the set of the resulting outputs. It is all the y-values in the (x, y) points determined by the relation.

Now, the given relation is {(2, 1). (-4, 5), (1, 7), (2, -3), (-1,2)}

The Domain of the given relation will be

= {2, -4, 1, -1}

And the Range of the relation will be

= [1, 5, 7, -3, 2]

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