Express the function graphed on the axes below as a piecewise function.104-10-8-6-4-2246810-6

Express The Function Graphed On The Axes Below As A Piecewise Function.104-10-8-6-4-2246810-6

Answers

Answer 1

Step 1

Find the equation of both lines using

[tex]\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{y-y_1}{x-x_1}[/tex]

Where,

[tex]\begin{gathered} y_1=-9 \\ y_2=\text{ -2} \\ x_1=\text{ -6} \\ x_2=1 \end{gathered}[/tex]

Hence,

[tex]\frac{-2-(-9)}{1-(-6)}=\frac{y-(-9)}{x-(-6)}[/tex][tex]\begin{gathered} \frac{7}{7}=\frac{y+9}{x+6} \\ y+9\text{ = x+6} \\ y\text{ = x+6-9} \\ y\text{ = x-}3 \end{gathered}[/tex]

For the second line we will have

[tex]\begin{gathered} \frac{-4-(-8)}{1-5}=\text{ }\frac{y-(-8)_{}}{x-5} \\ \frac{4}{-4}=\frac{y+8}{x-5} \\ -1(x-5)\text{ = y+8} \\ -x+5\text{ = y+8} \\ y\text{ =- x+5-8} \\ y\text{ = -x-3} \end{gathered}[/tex]

Step 2

Hence expressed the graphed solution as a piecewise function

[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ \square \\ -x-3,-1

Related Questions

Type the number of the spelling rule that applies to the word.

noisy

Answers

Answer:

Step-by-step explanation:

if a word ends in a consonant plus "y" , we change "y" to "i" and add "es" to form the plural; "er" for comparative and "est" for superlative

noisiest and noisier

Answer:

Step-by-step explanation:

5

Factor out the greatest common factor. Simplify the factors, if possible.2(c + y)2 - 14(c+y)2 - 6(c+y)4Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. 2(c+y) 3 – 14(c + y)2 - 6(c +y)4 =(Type your answer in factored form. Simplify your answer.)OB. There is no common factor other than 1.

Answers

The greatest common factor of a polynomial is the largest expression that divides all of the terms of the polynomial. In this case, we have:

[tex]2(c+y)^3-14(c+y)^2-6(c+y)^4[/tex]

First, find the GCF of the coefficients of the terms. The coefficients are 2, 14 and 6, their GCF is 2.

On the other hand, notice that the factor (c+y) is a common factor for all three terms. Find the greatest power of (c+y) that divides all the terms. Since the lowest power of (c+y) in the expression is 2, then, the greatest power of (c+y) that divides all the terms is (c+y)^2.

The GCF of the expression is the product of the GCF of the coefficients and the GCF of the factors with variables.

Then, the GCF of the expression is:

[tex]2(c+y)^2[/tex]

Factor out 2(c+y)^2 from the expression:

[tex]2(c+y)^3-14(c+y)^2-6(c+y)^4=2(c+y)^2\lbrack(c+y)-7-3(c+y)^2\rbrack[/tex]

Therefore, the answer is option A and the expression inside the box should be:

[tex]2(c+y)^2((c+y)-7-3(c+y)^2)[/tex]

What is x in this equation
2(x-7)=-4

Answers

x = 5

2x - 14 = -4

2x = -10

x = 5

Answer: 5

Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets.  Then because I did this I had to do the opposite to the other side. -4÷2

Then I just filled in the gaps 5-7=-2

Airfare from Atlanta, GA to Nashville, TN was decreased from $250 to $180. By what percentage did the cost of the airfare change

this is junior high math

Answers

Step-by-step explanation:

100% = $250

1% = 100%/100 = 250/100 = $2.50

the price decreased by

250 - 180 = $70

how many % are $70 ?

as many as how many times 1% ($2.50) fits into $70 :

70 / 2.50 = 28%

it changed (decreased) by 28%.

Help ASAP!! Which algebraic expression is equivalent to the expression below?

Answers

The algebraic expression is equivalent to the expression below is 36x+110

Simplifying expressions using the distributive law.

According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently.

For instance, given the standard expression C(D + E). Using the distributive law;

C(D + E) = CD + DE

Using this rule to the given expression shown below;

11(4x + 10) - 8x

Apply the distributive property;

11(4x + 10) - 8x

11(4x) + 11(10) - 8x

44x + 110 - 8x

Collect the like terms

44x + 110 - 8x

44x-8x+110

36x+110

This gives the resulting equation of the linear function after expansion

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Find the perimeter and area of the figure, rounding to the nearest tent. Use 3.14 for pie 7 ft 25 ft 4 ft Perimeter = 89.12 feet Area = feet squared

Answers

According to the picture, you can find the area of the figure by susbtracting the area of the segments of the circles to the area of the rectangle. We can observe that these segments are a quarter of a circle, together they would be a complete circle, then to find the area of the figure we can substract the area of one of the circles to the area of the rectangle.

1. Find the area of the circle:

[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(4)^2 \\ A=16(3.14) \\ A=50.24 \end{gathered}[/tex]

2. Find the area of the rectangle:

To do it, you need to find the length and the width first, do it this way:

[tex]\begin{gathered} l=25+4+4=33 \\ w=7+4+4=15 \end{gathered}[/tex]

Now, find the area of the rectangle:

[tex]\begin{gathered} A=l\cdot w \\ A=33\cdot15 \\ A=495 \end{gathered}[/tex]

3. Find the area of the figure:

[tex]\begin{gathered} A=495-50.24 \\ A=444.76 \end{gathered}[/tex]

The area of the figure is 444.76 feet squared.

Marsha is filing her federal income tax return with the Single filing status. She had an adjusted gross income of $56,800 last year and is trying to decide whether to take the standard deduction of $5700 or to itemize deductions. Last year she had $4900 in medical expenses, $3100 in state and local income taxes paid, $1940 in mortgage interest paid, $530 in charitable contributions, and $1200 in non-reimbursed work expenses

Answers

Marsha must claim for itemized deductions.

Given,

Last year's gross income is $56,800.

Medical expenses = $4900

State and local income taxes paid = $3100

The mortgage interest paid = $1940

Charitable contributions = $530

Non-reimbursed work expenses = $1200

Standard deduction = $5700

The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670

And the Standard deduction is $5700.

Which is, $11,670 - $5700 = $5970 lesser.

Therefore, Marsha must claim for itemize deductions rather than the standard deductions.

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When the summer started, Janie needed to fill her empty pool. At first, she used a garden hose to fill the pool, but this was taking too long. She got tired of watching the pool fill so slowly, so she turned off the water and went for a walk. She spotted a truck in the neighborhood that was filling pools and flagged them down to come fill her pool too. They were able to fill the pool at a faster rate. Which graph best represents this situation?

Answers

The statement mentions that the pool started empty, which implies that the graph must start at the point (0,0).

Then, the pool slowly filled, so the amount of water in the pool remained constant when Janie turned off the water and went for a walk.

Finally, thanks to a truck in the neighborhood the pool filled up quickly, and when it was filled the amount of water remained constant.

Therefore, the graph that best represents this situation is the one shown in option B.

with grade > * 0.2 Add, subtract, multiply, and divide whole numbers: word problem
A group of tourists needs rental cars to get around the city. There are 3,376 tourists in
the group. If each rental car holds 8 people, how many cars will the group need?

Answers

Using division, we know that the number of cars needed by 3,376 tourists is 422.

What is division?The division is splitting into equal parts or groups.The division allows us to divide or 'share' numbers to find an answer.Division sign (÷) is a symbol consisting of a short horizontal line with a dot above and another dot below, used to indicate mathematical division.The division of any number by zero is undefined. In this case, the result can be written as infinity. For example, 15/0 = ∞, i.e. undefined.We can represent the division with ÷, slash (/), or a horizontal line ( _ ). We can use these symbols at our convenience when dealing with different types of computations or division questions.

So, the total number of groups of tourists = 3376

One car holds 8 people.

To find the number of cars needed. Hence,

The number of cars needed = 3376/8= 422

Therefore, using division we know that the number of cars needed by 3,376 tourists is 422.

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11. Find m/Q. The diagram is not to scale.
Q/ R
77°
47°

Answers

Q=56 because a line is 180 so 77 + 47 =124 and then you take 180-124=56 so Q=56

What is the slope of the line shown?

Answers

Answer:

-11/6

Step-by-step explanation:

you can use rise over run to find your answer

PLEASE HELP QUICK!!!!!!!

Answers

Answer:

D

Step-by-step explanation:

Translation 4 units right and 1 unit up

Can someone please help me

Answers

May's total profit given the revenue, fixed cost and variable cost is $250.

What is the total profit?

Profit is when the difference between revenue and total cost is positive. A loss is earned when the difference between revenue and total cost is negative.

Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. Variable cost changes based on the level of output.

Total cost = variable cost + fixed cost

$9,000 + $300 = $9,300

Profit = revenue - total cost

$9,950 - $9,300 = $250

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At his comic book store, Korey's Comics, Korey sells approximately $3,250 in comic books each month.
But as a comic book dealer, Korey only pays $1,285 for these comic books. Korey's monthly operating expenses, including labor, are $875. Calculate Korey's monthly net income.

Answers

Answer:

Korey's monthly net income is $1090

Step-by-step explanation:

The spending is the cost plus expenses:

1285 + 875 = 2160

Net income is the difference of money made and spent:

3250 - 2160 = 1090

suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. what effect will this addition have on the correlation and the slope of the least-squares regression line?

Answers

A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.

Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).

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Which of the following could be the first step when solving the equation 4-3(x+6)=28

Answers

Answer:

I don't know the options, but the first step would definitley be distributing the -3 over the parantheses --> -3x - 18

Need help solving this problemNote for part A I got 4/22 and it was incorrect

Answers

First, we need to find the total frequency. This is given by adding all the given frequencies. That is,

[tex]\begin{gathered} f_{\text{total}}=4+6+7+5 \\ f_{\text{total}}=22 \end{gathered}[/tex]

and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,

[tex]f_{\text{rel}}=\frac{f_{\text{ interval}}}{f_{total}}[/tex]

Therefore, the answers are:

a) 4/22 but written in simple form:

[tex]\frac{2}{11}[/tex]

b)

[tex]\frac{5}{22}[/tex]

PLEASE HELP SOON!!!! Pre-calc, Trig, Calculus studentsss

Answers

Answer:

Step-by-step explanation:

If <1 and <2 are
supplementary angles with
m <1 = 10x +5 and m <2= 6x-1, what are the measure-
ments of both angles?

Answers

Step-by-step explanation:

The sum of measure of supplementary angles = 180°

The measure of angle 1 is given as 10x + 5 and the measure of angle 2 is given as 6x - 1

10x + 5 + 6x - 1 = 180 add like terms

16x + 4 = 180 subtract 4 from both sides

16x = 176 divide both sides by 16

x = 11

To find the measure of each angle, relace x with 11

angle 1,

10*11 + 5 = 115

angle 2,

6*11 - 1 = 65


*IMAGE ATTACHED* (What’s the perimeter of the shaded figure below?

Answers

Answer:

The perimeter is 12 units.

Step-by-step explanation:

The answer would be 12 units because each side is 1 unit. If you count all the sides together, you get 12 units.

Answer: 12 units

Step-by-step explanation:

       The perimeter is the length around a 2D shape. We will count the units that make up this shape's outline. See attached. Please note that as long as you count every side for this shape, it doesn't matter the order you count.

       The perimeter is 12 units, the last option.

What sets does -√3,1 and 0 belong to

Answers

√2 and -√3 belong to the set of Irrational Numbers.

1 belong to the following sets:

• Rational

,

• Whole

,

• Natural

,

• Integers

0 belongs to the following sets:

• Rational

,

• Whole

,

• Integers

enter 2 Expressions that represent the retail price of the clothes you see for your variable and exclusive clothing boutiques quadruples the price of the items it purchases for resale.

Answers

Explanation

Step 1

Let

c represent the original price

if the boutiques quadruples the price of the items it purchases for resale.​then

[tex]\begin{gathered} \text{new price=4}\cdot c \\ percentage \\ 4=4\cdot\frac{100}{100} \\ 4=\frac{400}{100} \\ 4=400\text{ per cent} \end{gathered}[/tex]

400 percent

Step 2

expressions

[tex]\begin{gathered} \text{new price=4}\cdot c \\ \text{new price= 400 percent of C} \end{gathered}[/tex]

4c and 400%c

I hope this helps you

4/y+2 = 10/5y
solve for y

Answers

Answer:

y = - 1

Step-by-step explanation:

[tex]\frac{4}{y}[/tex] + 2 = [tex]\frac{10}{5y}[/tex]

multiply through by 5y to clear the fractions

20 + 10y = 10 ( subtract 20 from both sides )

10y = - 10 ( divide both sides by 10 )

y = - 1

angles in a triangle

Answers

Answer:

i = 74

j = 47

Step-by-step explanation:

to find "i" add 16 & 90 which is 106. subtract 106 from 180 to get 74.

to find "j" add 43 & 90 which is 133. subtract 133 from 180 to get 47

The PayDay loan company lends you $500. After 2 weeks pay you pay back $520. What is the simple interest rate? Note that the times is a fraction of a year.

Answers

Answer:

Explanation:

• Loan Amount = $500

,

• Time = 2 weeks

,

• The amount paid pack = $520

We want to determine the simple interest rate.

First, find the amount paid as interest:

[tex][/tex]

the following data are from a simple random sample. 5 8 10 7 10 14 a. what is the point estimate of the population mean? b. what is the point estimate of the population standard deviation?

Answers

The point estimate of the population mean is 9

The point estimate of the population standard deviation is 2.83

Part a

Point estimate of population mean:

Given the sample data is 5,8,10,7,10,14

Number of samples, n is 6

Population mean=[tex]\frac{\sum x }{n}[/tex]

                           =(5+8+10+7+10+14)/6

                           =54/6

                           =9

Point estimate of mean=9

Part b

Point estimate of population standard deviation:

Mean=9

Data (x)     (x-mean)^2

5                16

8                1

10               1

7                 4

10               1

14               25

Total           48

Standard deviation=√(x-mean)^2/n

                               =√48/6

                               =√8

                               =2.83

Hence, the point estimate of population standard deviation is 2.83

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quick sell outlet sold a total of 40 televisions, each of which was either a model p television or a model q television. each model p television sold for $p and each model q television sold for $q. the average (arithmetic mean) selling price of the 40 televisions was $141. how many of the 40 televisions were model p televisions? (1) the model p televisions sold for $30 less than the model q televisions. (2) either p

Answers

Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.

Price plus quantity equals revenue.

Let x be the quantity of sold TVs of model p.

40 - x units of the model q TV would have been sold.

Profits from model p TV sales are

px

Sales of the type q TV bring in money.

(40 - x)q

Total income equals px plus (40 - x)q

The average price calculation formula is written as

Total revenue / total number of TVs sold equals average price.

The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that

141 = (px + (40 - x)q)/40

141 × 40 = px + (40 - x)q

5640 = px + (40 - x)q

p = q - 30

5640 = x(q - 30) + (40 - x) (40 - x)

q

30x + 40q - xq = 5640

5640 = - 30x + 40q

Since q = 120,

5640 = - 30x + 40 × 120

5640 = - 30x + 4800

5640 - 4800 = - 30x

840 = - 30x

x = 840/- 30 = - 28

Q cannot equal 120 since x cannot be negative.

Again,

5640 = px + (40 - x)q

If q = 30 + p, then

5640 = px + (40 - x)(30 + p)

5640 = px + 1200 + 40p - 30x - px

5640 = 1200 + 40p - 30x

Therefore,

If p = 120, then

5640 = 1200 + 40 × 120 - 30x

5640 = 6000 - 30x

30x = 6000 - 5640

30x = 360

x = 360/30

x = 12

Therefore, out of 40 televisions 12 tv are of model p

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101x^2+231x-334=-2 find the A,B,C

Answers

The roots of the equation is 1 and 3.28

The given equation is a quadratic

To find the roots of a quadratic equation, the formula is

[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]

The equation is 101x^2+231x-334=-2  we need to find the A,B,C

101x^2+231x-332 = 0

here a is 101, b is 231, and c is -332

[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]

[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]

Therefore, the roots of the equation is 1 and 3.28

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A groundskeeper needs grass seed to cover a circular field 290 ft in diameter a store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square ft. What is smallest number of bags there groundskeeper must buy to cover the circular field

Answers

Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.

The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in  Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms  possible and their areas, perimeters, and volumes, among other things.

Diameter of the field = 290 feet, radius = 145 feet

Area of the circular field =[tex]\pi r^{2}[/tex]

=>[tex]\pi[/tex]×145×145 =66018.5 square feet.

No of bags to be brought = 66018.5/400=165bags,

Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.

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Which of the following values are solutions to the
inequality 9 ≤ 3x +4?
I. - 7
II. 8
III. 2

Answers

Answer:

II. 8

III. 2

Step-by-step explanation:

Solving an inequality

9 ≤ 3x +4

Subtract 4 from each side

9-4 ≤ 3x +4-4

5 ≤ 3x

Divide each side by 3

5/3 ≤ 3x/3

5/3 ≤ x

x must be greater than or equal to 5/3

I. - 7  this is not greater than or equal to 5/3

II. 8   this is  greater than or equal to 5/3

III. 2 this is  greater than or equal to 5/3

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