The graph represents the piecewise function

The Graph Represents The Piecewise Function

Answers

Answer 1

The piece-wise function is defined as follows:

[tex]f(x) = x^2, 0 \leq x < 3[/tex].[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex].[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex].

What is a piece-wise function?

A piece-wise function is a function that has multiple definitions, depending on the input.

In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:

[tex]f(x) = x^2, 0 \leq x < 3[/tex]

For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:

[tex]m = \frac{9 - 4}{3 - 6} = -\frac{5}{3}[/tex]

[tex]f(x) = -\frac{5}{3}x + b[/tex]

Goes through (3,9), hence:

[tex]9 = -\frac{5}{3}(3) + b[/tex]

b = 14.

So

[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex]

For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:

[tex]m = \frac{10 - 4}{10 - 6} = \frac{6}{4} = \frac{3}{2}[/tex]

Then:

[tex]f(x) = \frac{3}{2}x + b[/tex]

When x = 10, f(x) = 10, hence:

[tex]10 = \frac{3}{2}(10) + b[/tex]

10 = 15 + b

b = -5.

Hence:

[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex]

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Related Questions

Which point is on the graph of f(x) = 3.4x

Answers

Answer:

D(1,12)

Step-by-step explanation:

See attached graph.

Use the periodic compound interest formula to solve.
Suppose that $11,000 is invested at 5.8% compounded quarterly. Find the total amount of this investment after 6 years.

Answers

Answer:

$15,539.67

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Given:

P = $11,000r = 5.8% = 0.058n = 4 (quarterly)t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]

[tex]\implies \sf A=11000(1.0145)^{24}[/tex]

[tex]\implies \sf A=15539.67451...[/tex]

Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.

How to do proportional relationships in math 7th grade ?? Please explain ?!!

Answers

Answer:

Try searching online

Step-by-step explanation:

go to your browser then search up
How to do proportional relationships in math 7th grade ?? Please explain ?!!

Find the midpoint of the segment with the following endpoints. (10, 6) and (4, 9)

Answers

Answer:

(7,7.5)

Step-by-step explanation:

midpoint formula:

(10+4)/2=7

(6+9)/2=7.5

(7,7.5)

choose the graph of the linear equation 30x+75y=300

Answers

Answer:

there ya go :)

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?

Answers

Using the cosine ratio, the expression that can be used to determine the  side length of the given rhombus is: x = 10/cos 30.

What is the Cosine Ratio?

The cosine ratio that can be used to solve a right triangle is, cos ∅ = adj/hyp.

x represents the side of the rhombus as shown in the image attached.

Hypotenuse = x Adjacent = 10 in.∅ = 30

cos 30 = 10/x

x(cos 30) = 10

x = 10/cos 30

Thus, the equation that would be used to determine the side length is: x = 10/cos 30

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Answer:

A

Step-by-step explanation:

10/cos 30°

factorise 3 squared+ 5x +12​

Answers

factorise 3 squared+ 5x +12

A(n)______ is a number sentence that shows how two or more expressions are not equal

Answers

Answer:

Inequality is the answer

Answer: Inequality ✅

Step-by-step explanation:

Hii, do you need to know the answer to your question? No problem!

The answer to your question is "inequality".

An inequality is a number sentence that shows how two or more expressions are not equal.

An example of that is [tex]\sf 4x+4\geqslant3x-5[/tex].

So 4x+4 is greater than or equal to 3x-5, but they're not 100% equal (such is the case in equations).

--

Hope that this helped! Best wishes.

--

HI PLEASE ANSWER THIS QUESTION THANK YOU SO MUCH!

Mr. Avanzado has an underground in his house. What unit ofmeasure will he use to find its volume?

A. mm3
B. cm3
C. dm3
D. m3
2.What is the best unit of measure to use in finding the volumeof a rectangular pencil case?

A. mm3
B. cm3
C. dm3
D. m3
3.What is the formula to be used in finding the volume of a cube?

A. V = s x s or s2
B. V = s x s x s or s3
C. V = l x w x h
D. V = s + s + s
(NO TROLLS PLEASE)

Answers

1.  

2. cm³

3.

What is Unit?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

1. Volume is measure in

2.  volume of a rectangular pencil case in cm³

3. V = s x s x s or s³

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a suvery shows that 55℅​

Answers

Answer: No. The intervals defined by the margin or error overlap

Step-by-step explanation:

If we think about it, with the worst margins, 55% could be 48% and then the 45% would be 52%, showing there is no clear yes or no and it is possible that the intervals could overlap

In the diagram below, AB is parallel to Co What is the value of y?

Answers

Answer:

D

Step-by-step explanation:

interior angles = 180

180-72

If it is already 110F degrees below zero, and the temperature drops another 40 F degrees, how cold is it now?

Answers

Answer:

-150

or 150 degrees below 0

Step-by-step explanation:

The temp is -110. Dropping another 40 degrees means subtracting 40.

-110 - 40 = -150


Match each inequality to the number line that represents its solution:

Answers

Step-by-step explanation:

I have solve all the questions and your work is to match with that option

Solve the inequality. –6 < 2 x – 4 < 4

Answers

Step-by-step explanation:

-6<2x-4<4

-2<2x<8

-1<x<4

x = (-1,4)

Which ordered pairs make both inequalities true? Check all that apply

Answers

Answer:.

Step-by-step explanation:

sally sweeps 20 floors in 4 hours , at the same rate , how many floors can sally sweep in 6 hours ?

Answers

Answer:

35 Floors in 6 Hours

Step-by-step explanation:

20 / 4 = X Floors Per Hour

floors per hour = 5

6*5 = 35 Floors

fill in the blank
83 x 391 - 83 x ____ = 83 x (391 - 15)

Answers

Answer:

83 x 391 - 83 x 15 = 83 x (391 - 15)

Step-by-step explanation:

BODMAS is stands for Bracket Of Division Multiplication Addition and Subtraction.

left hand side:

83 × 391 - 83 × ____   = 32453 - 83 × ____

right hand side:

83  × (391 - 15) = 83 × 376 = 31208

equating both sides

32453 - 83 × ____ = 31208

32453 - 31208 = 83 × ____

1245 ÷ 83 = 15

hence the answer is 15.

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Shea and Chris drive to work.
Shea drives 30 miles in 1.25 hours.
Chris drives 62 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km

Answers

Answer:

11.2 km/hr

Step-by-step explanation:

Shea's speed: 48km/1.25hr=38.4 km/hr

Chris's speed: 62km/1.25hr= 49.6 km/hr

Vav= 49.6-38.4= 11.2 km/hr

On a piece of paper, graph y-5>2x-10. Then determine which answer
choice matches the graph you drew.
A
B
C
D
(21)
(0.5)
OA. Graph A
B. Graph B
C. Graph C
D. Graph D
(0.5)
((3.1)
(0.5)
(3.1).
(0.5)

Answers

Answer:

Graph B

Step-by-step explanation:

When graphing inequalities:

< or > : draw a dashed line≤ or ≥ : draw a solid line< or ≤ : shade under the line> or ≥ : shade above the line

Given inequality:

[tex]y-5 > 2x-10[/tex]

Rearrange the given inequality to make y the subject:

[tex]\implies y-5+5 > 2x-10+5[/tex]

[tex]\implies y > 2x-5[/tex]

Therefore, we need to draw a dashed line and shade above it.

To draw the line:

Replace the > with = to find two points on the line:

[tex]\implies y=2x-5[/tex]

[tex]x=0 \implies y=2(0)-5=-5 \implies (0,-5)[/tex]

[tex]x=3 \implies y=2(3)-5=1 \implies (3,1)[/tex]

Plot the two found points: (0, -5) and (3, 1)

As the inequality is  y > 2x - 5

Draw a dashed straight line through the two points.Shade above the line.

The inequality equation is solved and the solution is plotted on the graph

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y - 5 > 2x - 10

On simplifying , we get

Adding 5 on both sides , we get

y > 2x - 5

where 2 is the slope and 5 is the the intercept

Now , let the first point be P ( 0 , -5 )

when x = 0 and y = -5

-5 > -5

And , the graph of the inequality is plotted

Hence , the inequality is solved

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Question 12 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
A. -5
B. 3
C. 2
☐D. O
E. 1
F. -3
5

Answers

1 is the values are in the range of the function graphed below. Option E is corect.

What is the difference between domain and range?

The domain denotes all potential x values, while the range denotes the domain's possible y values.

The domain is the value of x which lies between the -2 ≤ x  ≤ 1.While the range shows the value of y which is equal to  1.

Hence, option E is correct

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What is the solution to this system of equations? x + y = 2 and y - z = -3 and x + y - z = 0

Answers

Answer:

x = 3

y = -1

z = 2

Step-by-step explanation:

if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2.  if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.

What is the median of the following data set?
(3, 4, 2, 8, 5)
02
03
04
06

Answers

Answer:

4

Step-by-step explanation:

The median is the middle number when the list is sorted from least to greatest or greatest to least.

We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.

red was rotated to form blue
describe the rotation

Answers

Red was rotated to form blue as the figure was turned in different directions.

What is rotation?

A rotation simply means a transformation that turns a figure about a fixed point called the center of rotation.

An object and its rotation are simply the same shape and size, but the figures may be turned in different directions. In this case, red was rotated to form blue.

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Which equation can be used to solve for xxx in the following diagram?




Choose 1 answer:
Choose 1 answer:

(Choice A)
A
2x = 4x2x=4x2, x, equals, 4, x

(Choice B)
B
2x + 4x = 1802x+4x=1802, x, plus, 4, x, equals, 180

(Choice C)
C
2x + 4x = 902x+4x=902, x, plus, 4, x, equals, 90

(Choice D)
D
2x + 4x = 1502x+4x=1502, x, plus, 4, x, equals, 150

Answers

The equation that can be used to determine the value of x is Option B.

What is an Equation ?

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

From the diagram ,

A straight line has an angle of 180 degree.

Therefore from the figure

To determine the value of x

2x + 4x = 180

6x = 180

x =30 degree

Thus the equation that can be used to determine the value of x is Option B.

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(5+4) +10=5+(4+10)
A. True
B. False

Answers

Answer:

A. True

Step-by-step explanation:

One of the ways to check this is solving each side of the equation.

(5+4)+10=5+(4+10)

Remember PEMDAS.

Parenthesis first.

(9)+10=5+(14)

Now, you can drop the parenthesis and add the numbers together.

9+10=19

5+14=19

19=19

This is a true statement.

Hope this helps!

If not, I am sorry.

true as they both add up to 19

4. Liam can work at most 20 hours a week but he needs to earn at least $125. His dog-walking job pays
$7 per hour and his job as a car-wash attendant pays $11 dollars an hour. How can he earn $125?
Graph a system of linear inequalities that represents this situation. Using the graph, what are two
possible solutions to the system of inequalities?

Answers

Two possible solutions are: (4.5, 8.5) and (8, 6.3)

How to graph the inequality?

Let x represents hours dog walking and y represents hours washing cars.

So, we have:

Earnings = Rate of dog walk * x + Rate of car wash * y

This gives

Earnings = 7x + 11y

He wants to earn at least $125.

This means that:

7x + 11y ≥ 125

See attachment for the graph of the inequality

From the attached graph, two possible solutions are: (4.5, 8.5) and (8, 6.3)

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Please help!! Consider the equation x/5 -2=11, where x represents the
number of basketball players that have signed up for a
new league. What is a possible scenario that would be
modeled by this equation? Consider how many teams in
the league and the number of players on each team this
equation could describe

Answers

Answer:

x=65

Each NBA team can have a maximum of 15 players, 13 of which can be active each game.

65/5=13 so it's safe to say tgat 5 team can be crated

Step-by-step explanation:

x/5-2=11-->transposing x/5=11+2---->x=13×5--->x=65

verification 65/5-2=11--->13-2=11

Factor: 117n + 90

Show your work don’t solve for n

Answers

Factoring Expressions

To factor an expression, we can identify common factors between each terms, and take them out.

Solving the Question

117n + 90

Both terms have the common factor of 9. Factor this out:

= 9(13n + 10)

13 and 10 do not have a common factor. Therefore, this is the final factored expression.

Answer

9(13n + 10)

Examine the following graphs of two functions. Two functions. One is linear passing thru (1, 2), (3, 4), (6,7) and (8, 9). 2nd function is quadratic passing thru (3, 4), (5, 0), (7, 4) & (8, 9). © 2018 StrongMind. Created using GeoGebra. Which two values of x best represent where the two functions are equal? Enter your answer as two numbers, separated by a comma, like this: 1, 2

Answers

The two values of x best represent where the two functions are equal will be (12,11)

What is a graph?

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data;

Linear function passing through;

(1, 2), (3, 4), (6,7) and (8, 9)

Quadratic function passing through

(3, 4), (5, 0), (7, 4) & (8, 9)

Let x be two values of x best represent where the two functions are equal;

The value of the x is obtained from the graph where the two line meets.

The value of x willl be (12,11)

Hence, the two values of x best represent where the two functions are equal will be (12,11)

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Shelby bought 2 cans of paint and 3/4 of a pint of special paint additive formulated to reduce mildew. Before painting her house, she divided the additive equally between the 2 cans of paint. How much additive did she put in each can?

Answers

She put 2/4 in each can
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