Need some help with math

Need Some Help With Math

Answers

Answer 1

The line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

Describe Graph?

A graph is a mathematical representation of a set of objects, called vertices or nodes, and the connections between them, called edges or arcs. Graphs are commonly used to model relationships between entities in various fields such as computer science, mathematics, physics, social sciences, and many others.

To determine the line that the angle has been reflected across, we need to find the line of reflection, which is the perpendicular bisector of the segment joining each point and its corresponding image.

We can start by finding the midpoint of the segment joining A and A', which is the point that is equidistant from these two points and lies on the line of reflection. The midpoint of AA' is:

Midpoint of AA' = ((x-coordinate of A + x-coordinate of A')/2, (y-coordinate of A + y-coordinate of A')/2)

Midpoint of AA' = ((4 + (-5))/2, (5 + (-4))/2)

Midpoint of AA' = (-1/2, 1/2)

Next, we can find the midpoint of the segment joining B and B':

Midpoint of BB' = ((x-coordinate of B + x-coordinate of B')/2, (y-coordinate of B + y-coordinate of B')/2)

Midpoint of BB' = ((1 + (-2))/2, (2 + (-1))/2)

Midpoint of BB' = (-1/2, 1/2)

We can see that the midpoint of AA' and the midpoint of BB' are the same point, which means that the line joining these midpoints is the perpendicular bisector of both segments, and therefore the line of reflection.

So, the line of reflection is the line passing through the points (-1/2, 1/2) and (-2, -1), which can be found using the slope formula:

slope of line of reflection = (y2 - y1) / (x2 - x1)

slope of line of reflection = (-1 - 1/2) / (-2 - (-1/2))

slope of line of reflection = (-3/2) / (-3/2)

slope of line of reflection = 1

We now have the slope of the line of reflection, and we can find its equation by using the point-slope form:

y - y1 = m(x - x1)

Using the point (-1/2, 1/2) and the slope 1, we get:

y - 1/2 = 1(x + 1/2)

Simplifying, we get:

y = x + 1

Therefore, the line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.

To know more about reflection visit:

https://brainly.com/question/30811218

#SPJ1


Related Questions

Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.

Answers

Arc length doesn’t matter. Area does.

Area of a square: bh = 6x6 = 36 inches squared

Area of a circle: 3.14(r^2) = 3.14(36)= 113 inches squared

Mai’s paper is much larger.

A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The arc length of radius 6 inches is equal to,

Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches

The area of the circular paper = πr² = π×6×6 = 113.097²

The area of the square with a side of 6 inches = 36 in²

Therefore, the area of the circular paper is more than the area of the square.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ2

A3ft board weighs 2 pounds. How much
does a 12 ft board weigh?

Answers

Answer:

8 pounds

Step-by-step explanation:

3 ft board = 2lb

12 ft board is 4 times more so

2x4 = 8 lb

A cable extends from the top of a radio tower to a point 360 feet from the base of the tower. If the
cable is 850 feet long, how tall is the tower?

Answers

Step-by-step explanation:

we have a right-angled triangle :

the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.

then the ground distance (360 ft) and the height of the tower are the 2 legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

in our case

850² = 360² + height²

height² = 850² - 360² = 592,900

height = 770 ft

the tower is 770 ft tall.

Answer:

770 feet

Step-by-step explanation:

Given

Cable = 850 feet longExtends from radio tower to a point 360 feet from the base of a tower

Solving

Using the Pythagorean Theorem, we can find the height(distance from base)² + (height)² = (length of cable)²height² = (850)² - (360)²height² = 722,500 - 129,600height² = 592,900height = √592,900height = 770 feet

Please Help I don't understand at all !!!!!!! I'll give 50 brainly points

Students collected data and created an equation to model the spread of a winter cold among the students, teachers, and other staff. They decided this was best represented by the exponential function C(d) = 1*3d where d is the time in days since the cold began to spread.

How many people initially had the cold? _______ people

How many people would have the cold after 2 days? ______ people

Answers

Answer:

0 People initially had the cold.

6 People will have it after 2 days.

Step-by-step explanation:

To find out how many people had it initially, plug 0 in for x (implying 0 days later.)

C= 1*3(0)

C= 1*0

C=0

Nobody had the cold initially.

To find out how many people had it after 2 days, plug 2 in for x. (implying 2 days later.)

C= 1*3(2)

C= 1*6

C=6

Therefore 6 people had the cold after 2 days.

I hope this helps!

Regular expressions - recognizers of words in a language 1. Σ={a,b,c} where L={ all words in which a 's must follow the symbol b} 2. Σ={a,b,c} where L={ all words that have at least one occurrence of the string abc in them } Write a grammar for the following - grammars are generators of words in a language 3. Σ={a,b} where L={ all words that start with c and end with c and have only a's and b

s in between 4. Σ={a,b,c} where L={ all words using symbols a,b,c in which every b follows the symbol a} Is the following grammar ambiguous? Prove your statement. Why do we not want an ambiguous grammar for a programming language?

Answers

1. The regular expression for the language L={ all words in which a's must follow the symbol b} is \(^(b*(ab*)*)*a*$\).

2. The regular expression for the language L={ all words that have at least one occurrence of the string abc in them } is .*abc.*.

3. The grammar for the language L={ all words that start with c and end with c and have only a's and b's in between} is S -> cXc, X -> ε | aX | bX.

4. The grammar for the language L={ all words using symbols a,b,c in which every b follows the symbol a} is S -> ε | aSb | aA | c, A -> ε | aAb | aA | c. The grammar is ambiguous.

1. The regular expression \(^(b*(ab*)*)*a*$\) specifies that the word should start and end with any number of 'b' and 'a' in any order, and only 'a' should follow 'b'.

2. The regular expression .*abc.* matches any word that contains the substring 'abc' at least once.

3. The grammar S -> cXc, X -> ε | aX | bX generates words that start with 'c', followed by a sequence of 'a' or 'b', and ends with 'c'. Only 'a' and 'b' symbols are allowed in between.

4. The grammar S -> ε | aSb | aA | c, A -> ε | aAb | aA | c allows for words that can have multiple occurrences of 'a' followed by 'b', 'a' followed by 'a' or 'b', or just the symbol 'c'. This grammar is ambiguous because a single sentence can have multiple parse trees or interpretations.

An ambiguous grammar in a programming language can lead to different interpretations of code, resulting in confusion, inconsistencies, and difficulties in parsing and understanding the code.

Unintended or unexpected behavior can arise due to ambiguity, making it challenging to write reliable and predictable programs. To ensure clarity, correctness, and ease of interpretation, it is crucial to have an unambiguous grammar for a programming language.

To know more about regular expression refer here:

https://brainly.com/question/20486129

#SPJ11

Given hexagon LMNOPQ is congruent to hexagon L'M'N'O'P'Q'. What is the measure of OP?

6 in
7 in
45 in
51 in

Given hexagon LMNOPQ is congruent to hexagon L'M'N'O'P'Q'. What is the measure of OP?6 in7 in45 in51

Answers

Answer:

51in

Step-by-step explanation:

Just set the equations of line OP and line O'P' equal to one another, then solve for x.

ie: 3(2x+3)=(8x-5)

To solve for x, distribute first. Then, subtract 6x from each side. Then, add 5 to each side.

ie: 6x+9=8x-5

ie: 14=2x

Now divide by 2.

ie: 7=x

Now that you have your x value, plug it back into one of the equations and solve for the measure of line OP. To check you answer, plug 7 for x into the equation where they are set equal, then solve them both and if the end result is true (51=51) it is correct.

Paul ate 42 out of the 68 skittles in the bag.
How would this ratio be expressed in decimal
form?

Answers

9514 1404 393

Answer:

  \(0.6\overline{1764705882352941}\)

Step-by-step explanation:

The decimal form of a ratio is found by dividing the numerator by the denominator. You will find this reduces to the fraction 21/34, which has a 16-digit repeat when expressed as a decimal.

Using a calculator with suitable precision, you can see all of the repeating digits:

  \(0.6\overline{1764705882352941}\)

Evaluate the expression when a=6 and b=4. b - 3a

Answers

-14 is the value of the expression b - 3a at a =6 and b = 4.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

Learn more about expression here:

https://brainly.com/question/23246712

#SPJ1

4 4/5 x 3 2/6 I don’t understand this pls help

Answers

Answer:

change to improper fraction

24/5 × 20/6=16 (you cross multiply)

Answer:

= 46 14/15

Step-by-step explanation:

Find the greatest common factor of the numerator and denominator:Factor out and cancel the greatest common factor:Multiply the fractions:Simplify the arithmetic:Simplify the arithmetic
Hope You Enjoy !

Write as an algebraic expression.
14 fewer than the product of 3 and a number

Answers

Answer:

3 x X - 14

Step-by-step explanation:

Is your algebra expression.

Answer:

3x-14

Step-by-step explanation:

Product of 3 and number is 3*x

For " 14 fewer than.." we simply subtract 14.

So we get 3x-14

Please help me I only have 3 days to get it done and if I don’t I won’t pass

Please help me I only have 3 days to get it done and if I dont I wont pass

Answers

K=(0,6)
L=(-8,0)
J=(10,4)

(x, 7) and (-7, 4); slope: 1

Answers

Answer: x= -4

Step-by-step explanation: slope = (y2-y1)/(x2-x1).

(4-7)/(-7-x)

-3/-7-x=1

Multiply both sides by -7-x

-3=-7-x

Add 7 to both sides

4=-x so x = -4

what is the maximum of the sinusoidal function? enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

B

The numbers of blue and green beads Emma uses to make five different pieces of jewelry are recorded below. Which of the following equations relate to the number of green beads, G, to the number of blue beads, b?

The numbers of blue and green beads Emma uses to make five different pieces of jewelry are recorded below.

Answers

Answer:

a

Step-by-step explanation:

follow the proportions

Answer:

A

Step-by-step explanation:

Starting with the graph of f (I) = 4", write the equation of the graph that results from a. shifting f(3 ) 1 units
upward. b. reflecting f(z) about the y-axis. y c. shifting f(x) 6 units left. y =

Answers

The graph of f(x) = 4x is a parabola that opens upwards. Shifting the graph 1 unit upwards, reflecting the graph about the y-axis, and shifting the graph 6 units left will all result in new graphs that are transformations of the original graph. Therefore:

a. Shifting f(x) 1 unit upward: y = 4x + 1

b. Reflecting f(x) about the y-axis: y = -4x

c. Shifting f(x) 6 units left: y = 4(x - 6)

The equations of the graphs that result from the given transformations:

a. Shifting f(x) 1 unit upward.

The graph of f(x) = 4x is a parabola that opens upwards. Shifting the graph 1 unit upwards means that all the points on the graph are moved 1 unit upwards. The new equation of the graph is:

y = 4x + 1

b. Reflecting f(x) about the y-axis.

Reflecting the graph of f(x) = 4x about the y-axis means that the x-coordinates of all the points on the graph are negated. The new equation of the graph is:

y = -4x

c. Shifting f(x) 6 units left.

Shifting the graph of f(x) = 4x 6 units left means that all the x-coordinates of all the points on the graph are decreased by 6. The new equation of the graph is:

y = 4(x - 6)

To know more about parabola refer here :    

https://brainly.com/question/11911877#

#SPJ11      

Month, Ticket
Sales, y
27
28
36
28
32
35
X
1
2
3
4
5
6
s
a. Use a graphing calculator to find an equation of line of best fit.
b. Identify the correlation coefficient.
c. Use a graphing calculator to find the standard deviation of the ticket sales
d. Plot the graph in a scatter plot.

Month, TicketSales, y272836283235X123456s a. Use a graphing calculator to find an equation of line of

Answers

a. The equation of line of best fit is ŷ = 1.26x + 26.6

b. The correlation coefficient is 0.60

c. undefined

d. The graph is attached

a. Find an equation of line of best fit.

From the question, we have the following parameters that can be used in our computation:

The table of values

From the graphing calculator, the summary of the above dataset is:

Sum of X = 21Sum of Y = 186Mean X = 3.5Mean Y = 31Sum of squares (SSX) = 17.5Sum of products (SP) = 22

The regression equation is represented as

ŷ = bx + a

Where

b = SP/SSX = 22/17.5 = 1.25714

a = MY - bMX = 31 - (1.26*3.5) = 26.6

So, we have

ŷ = 1.26x + 26.6

So, the linear regression model to represent the data set is ŷ = 1.26x + 26.6

b. Identify the correlation coefficient.

From the graphing tool, we have

r = 0.6032

This means that the correlation coefficient is 0.60

c. Use a graphing calculator to find the standard deviation of the ticket sales

This cannot be calculated

d. Plot the graph in a scatter plot.

See attachment

Read more about linear regression at

https://brainly.com/question/26755306

#SPJ1

Month, TicketSales, y272836283235X123456s a. Use a graphing calculator to find an equation of line of

What is the matching line that is parallel to the line y=3x+12 through the point (2,-5)?​

Answers

Answer:

y=3x-11

Step-by-step explanation:

-5 = 3(2) + b

-5 = 6 + b

b = -11

Find the point P such that v = PQ has the components (7,6,9) and 0 = (2, -4,3)

Answers

The point P is (9, 2, 12).

To find the point P, we need to add the vector v = PQ to the given point 0.

Given that v = PQ has the components (7, 6, 9) and the point 0 has the components (2, -4, 3), we can calculate the coordinates of point P as follows:

P = 0 + v = (2 + 7, -4 + 6, 3 + 9) = (9, 2, 12)

Know more about vector here;

https://brainly.com/question/24256726

#SPJ11

4+( ) Rewrite the expression 4-11 as the sum of two numbers

Answers

Answer:

4+(-11)

Step-by-step explanation:

you need to put the negative 11 in ()

A Question 9 (3 points) Retake question 4Listen ► When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when? advances are not given for sho

Answers

When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

To know more about advance fee, refer

https://brainly.com/question/32729770

#SPJ11

¿por qué no está definida la raíz de índice par de un número negativo?

Answers

Answer:

Porque se convierte en positivo cada vez que haces la raíz cuadrada.

Word problem:Sophia wants to buy a tablet so she can watch tv and play games as well as complete her school work. She is researching all her different options and the tablet she chose says the length is (-4x^2-2x-3)cm and the width is (4x+3)cm. Question: What is the area of Sophia’s tablet (the red outline)? You must show and explain all your work and do not forget units of measurement.

Word problem:Sophia wants to buy a tablet so she can watch tv and play games as well as complete her

Answers

Yonna, this is the solution to the problem:

Side 1 of the tablet = (4x + 3) cm

Side 2 of the tablet = (-4x² - 2x - 3) cm

Area of the tablet = Side 1 * Side 2

Area of the tablet = (4x + 3) * (-4x² - 2x - 3) cm²

Area of the tablet = (4x * -4x²) + (4x * -2x) + (4x * -3) + (3 * -4x²) + (3 * -2x) + (3 * -3)

Area of the tablet = -16x³ - 8x² - 12x - 12x² - 6x - 9 cm²

Area of the tablet = -16x³ - 20x² - 18x - 9 cm²

Please help on this!

Please help on this!

Answers

Answer:

18cm,21cm,27cm

Step-by-step explanation:

explanation in picture

Please help on this!

The oxygen atoms in the thermosphere absorb high-energy solar radiation and convert it into heat energy.
true
false

Answers

Step-by-step explanation:

Nitrogen and oxygen absorb solar radiation and release thermal energy, which causes temperatures in the thermosphere to be 1000 °C or higher. When most people think of an area that has high temperatures, they think of a place that is very hot. Although the thermosphere has very high temperatures, it does not feel hot. The answer is true

A survey of students showed that 32 students enjoyed country, 14 enjoy jazz, and 8 enjoy both, which of the following Venn diagram represents the result of the survey? (image)

A survey of students showed that 32 students enjoyed country, 14 enjoy jazz, and 8 enjoy both, which

Answers

The Venn diagram that represents the result of the survey is; Venn Diagram in Option A

What is a Venn Diagram?

Venn diagrams are used in sets in mathematics to group the union and intersection of subsets.

We are told that;

Number of students that enjoyed country = 32

Number of students that enjoyed jazz = 14

Number of students that enjoyed both country and jazz = 8

Now, the number of the students that enjoyed country and jazz should be the intersection of both circles in the venn diagram.

Secondly number of students that listened to only country = 32 - 8 = 24

Number that listened to only jazz = 14 - 8 = 6

Thus, the only correct option is Option A

Read more about Venn Diagrams at; https://brainly.com/question/2099071

a 6 ft board is cut into two pieces, on twice as long as the other. How long are the pieces?

Answers

Answer:One is 2 feet and one is 4 feet

Step-by-step explanation:

Divide using long division.

Divide using long division.

Answers

Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.

Explain Long Division?

Long division is a method of dividing two numbers using written arithmetic. It is a process of breaking down a division problem into a sequence of smaller and easier steps to obtain the quotient and remainder. Long division is typically used for dividing large numbers or when the division is not exact.

To perform long division, we follow the following steps:

Write the dividend (the number being divided) on the long division symbol, with the divisor (the number we are dividing by) outside the symbol.Determine how many times the divisor goes into the first digit of the dividend. Write this quotient above the first digit of the dividend.Multiply the divisor by the quotient and write the result below the first digit of the dividend.Subtract this result from the first digit of the dividend to obtain the remainder.Bring down the next digit of the dividend and write it next to the remainder.Repeat steps 2 to 5 until all digits of the dividend have been used.

The final result is the quotient and the last remainder obtained.

                                   __________________________

        x³ + 6x² - 3x - 5 | -3x⁵ - 22x⁴ - 13x³ + 39x² + 14x - 6

                                    -3x⁵ - 18x⁴ + 9x³ + 15x²

                                      ----------------------------

                                               -4x⁴ - 4x³ + 54x²

                                              -4x⁴ - 24x³ + 12x² + 20x

                                                          -------------------------

                                                           18x³ + 42x²

                                                           18x³ + 108x² - 54x - 90

                                                                        ------------------------

                                                                         150x + 84

                                                   

Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.

To know more about remainder visit:

https://brainly.com/question/22408054

#SPJ1

The town of Valley View conducted a census this year, which showed that it has a population
of 1,800 people. Based on the census data, it is estimated that the population of Valley View
will grow by 12% each decade.
Write an exponential equation in the form y = a(b) that can model the town population, y, x
decades after this census was taken.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answers

The exponential function to model the population of Valley View is \(y = 1800(1.012)^t\).

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

An exponential function is written in the form -

\(y=ab^t\)

Here, y is the function, a is the base value b is the rate and t is time period.

The number of people in Valley view is 1800. So, the base is a = 1800.

The function y depicts the towns population.

Each decade the population grows by 12%.

The growth rate per year is = 12 / 10

The growth rate is 1.2%

The value for b will be = 1 + r

b = 1 + 1.2/100

b = 1 + 0.012

b = 1.012

So, the exponential equation will be -

\(y = 1800(1.012)^t\)

Therefore, the exponential equation is \(y = 1800(1.012)^t\).

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

Complete the following statement. Write your answer as a decimal or whole number.
__% of $3,000,000 = $2,250,000
Submit

Answers

Answer: 75

Step-by-step explanation:

\(x\)% x 3000000 = 2250000

\(x\)/100 x 3000000 = 2250000

\(x\) x 30000 = 2250000

\(x\) = 2250000/30000

\(x\) = 75

A=1/2w(b+c) solve for c

Answers

9514 1404 393

Answer:

  c = 2A/w -b

Step-by-step explanation:

Multiply by the inverse of the coefficient of the parentheses.

  \(A=\dfrac{w}{2}(b+c)\\\\\dfrac{2A}{w}=b+c\\\\\boxed{c=\dfrac{2A}{w}-b} \qquad\text{subtract $b$}\)

Other Questions
Is this a valid argument ?Given:if an object is in the dhape of a sphere ,then it rolls. This ball is in the shape of a sphere . Conclusion:this ball rolls If a watch gains 5 seconds every hour.it was set right on monday at 11:48am. what time will it show following monday Find the 60th term of the following sequence.4, 8, 12, Reggie cuts 2 feet from a 9-foot length of rope. Then he cuts 14 inches from the rope. How many inches of rope are left? Question 1 (4 points)According to Romans, the person responsible for the construction of Rome was? A triangle has 3 interior angles and the sum of its interior angles is 180.If one of the three interior angles measures 80 and the two remaining angles has the same measure, what is the measure of the 3rd interior angle? grimm company has 2,400,000 shares of common stock outstanding on december 31, 2014. an additional 150,000 shares of common stock were issued on july 1, 2015, and 300,000 more on october 1, 2015. on april 1, 2015, grimm issued 6,000, $1,000 face value, 8% convertible bonds. each bond is convertible into 40 shares of common stock. no bonds were converted into common stock in 2015. what is the number of shares to be used in computing diluted earnings per share for the year ended december 31, 2015? * in a between subjects 2x2 factorial design with 30 participants randomly assigned to each factorial combination, how many total participants are required? Using the distributive law :43x15+43x5 5. Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X (1) f(x) Which of the following might be considered a conflict of interest?A. Studying a business in collegeB. Receiving free travelC. Attending a conference with a subject of the story as the keynote speakerD. Buying product from a company that the reporter is writing about The payroll of Pronghorn Company for September 2019 is as follows.Total payroll was $434,000, of which $108,000 is exempt from Social Security tax because it represented amounts paid in excess of $128,400 to certain employees. The amount paid to employees in excess of $7,000 (the maximum for both federal and state unemployment tax) was $423,000. Income taxes in the amount of $86,300 were withheld, as was $8,100 in union dues. The state unemployment tax is 3.5%, but Pronghorn Company is allowed a credit of 2.3% by the state for its unemployment experience. Also, assume that the current FICA tax is 7.65% on an employees wages to $128,400 and 1.45% in excess of $128,400. No employee for Pronghorn makes more than $135,000. The federal unemployment tax rate is 0.8% after state credit.Prepare the necessary journal entries if the wages and salaries paid and the employer payroll taxes are recorded separately. (Round answers to 0 decimal places, e.g. 5,275. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts .Credit account titles are automatically indented when amount is entered. Do not indent manually.) Select the correct answer from each drop-down menu.Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.The graph g(x) is the graph of f(x) translated units , and g(x) = . Describe the relative ability of iron to dissolve carbon in solution when in the form of austenite (the elevated temperature phase) and when in the form of ferrite at room temperature. Item 8Read the passage.EarthshipsWhat is an earthship?An earthship is a home designed to make use of recycled materials and increase energy conservation. Ideally, by living in an earthship, a person can have a home that is off the grid. People who live in earthships do not depend on outside sources for electricity, food, or water. Building an earthship may be an attractive choice for those who want to use fewer of our planets non-renewable resources.The FoundationFirst, the foundation is built by firmly packing dirt inside recycled tires. Then, the tires are placed in a pyramid-like stack going as high as needed. Next, cement is spread and smoothed between the tires to create a solid wall. When this is finished, the walls are sealed with a protective coating and painted. Some interior walls are built using recycled cans and cement, also sealed with a protective coating.Solar EnergySolar panels give enough stored energy in batteries to provide electricity for appliances, lighting, and electronics. However, solar-powered batteries hold about one-third the charge of energy used in a regular household wired for electricity. This means that people either buy more batteries or intend to use less electricity than a conventional household. Ideally, earthships are built in places where there is an abundance of sunshine year-round.Floor-to-ceiling windows on an earthships south wall also allow plenty of sunlight. It is important that no trees block the light on this side of the house. The sunlight shines directly onto a brick floor, which then absorbs the heat. This provides enough warmth to maintain a comfortable temperature in the house for the rest of the day. This method of heating the home is called passive solar. Most earthships also have either a wood stove or a heater that uses propane, a type of natural gas. These heat sources are useful on cloudy days. During the summer, the combination of the cool temperature of the earth beneath the floor plus the thick walls can keep the house comfortable without the use of air-conditioning.Recycled WaterGutters on the roof collect rainwater that then trickles down into large storage barrels. The water is used for taking showers, doing dishes, and flushing the toilet. It is also filtered for drinking. People sometimes build a greenhouse to grow their own food. Water that has been used for dishwashing or showers can be saved if the soaps are chemical-free. This recycled gray water can be used yet again to water the plants in the greenhouse.Potential ProblemsEarthships have been around since the 1970s. Now, long-term studies have revealed some problems. For one, without sufficient sunlight during the winter, large amounts of natural gas known as propane and/or wood are used to heat the home. Propane use can be costly, and unless one has planned far ahead, a wood supply can be quickly depleted.Another problem is that tires used in the foundation walls can, after a long period of time, begin to crack, releasing a toxic gas that has built up over time in the walls. The use of cement, which is a porous material with many small holes and spaces, allows the gases to leak into the air. The type of gas emitted is not detectable by smell but can make people sick. To address this problem, the walls of the home needs to be resealed every year.Cost can also be a significant challenge. Some earthship building companies claim that it is far cheaper to build an earthship because only recycled materials are used. Also, a contractors license or training is not needed to build one. This, though, is true if it is built 100% by the owner, which could take years to complete. Additionally, the cement, plumbing, and electrical components, as well as the cost of installing solar panels, can be expensive. Just as with the construction of a conventional home, proper permits are often needed to build an earthship.There are clear advantages and disadvantages to these unique homes. As technology improves and new solutions are discovered, earthships may continue to be a wise way to live sustainably using minimal resources._________________________________________________________________In the article "Earthships," how does the section "Recycled Water" contribute to the development of ideas in the passage?A). It describes different methods to filter water.B). It explains how to build a water collection system.C). It explains how earthships collect and use rainwater.D). It tells cost savings of using recycled water. if g(x)=f(1/3x), which statement is true?A the graph of function f is Stretched vertically by a scale factor of 3 to create the graph of function gB The graph of function F stretched horizontally by a scale factor of 3 to create the graph of function gC The graph of the function F is compressed horizontally by a scale factor of 1/3 to create the graph of function GD The graph of function F is compressed vertically by a scale Factor of 1/3 to create the graph function G Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial time reducible to R. Which of the following statements are true? A. R is NP complete B. R is NP Hard C. Q is NP complete D. Q is NP hard a. Draw two separate flow charts (one for lower temperaturesand another for increased temperatures). Show the homeostaticresponses that occur for each (including both physiological andbehavioral re Assume that you manage a risky portfolio with an expected rate of return of 17% and a variance of 27%. The T-note rate is 7%. What is the reward-to-volatility ratio of your risky portfolio what is the orbital period of a spacecraft in a low orbit near the surface of mars? assume the radius of the satellite's orbit is about the same as the radius of mars itself, rmars