6. Triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form

Triangle

ABC: Which transformation can be used to map each point (.y) on Triangle ABC

to its corresponding point on Triangle A B C?

A

G.y) - (y + 3, x)

B

6. y) - (x+3)

(x, y) - (y+3.x)

D. (.y)-( y. x+3)

C

Answers

Answer 1

Given:

Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.

To find:

The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.

Solution:

If a figure rotated 90 degrees counterclockwise, then

[tex](x,y)\to (-y,x)[/tex]

[tex]P(x,y)\to P_1(-y,x)[/tex]

If a figure translated 3 units up, then

[tex](x,y)\to (x,y+3)[/tex]

[tex]P_1(-y,x)\to P'(-y,x+3)[/tex]

If  triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is

[tex](x,y)\to (-y,x+3)[/tex]

Therefore, the required rule of transformation is [tex](x,y)\to (-y,x+3)[/tex].

Note: Option are not in proper form.

Answer 2

All the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.

How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?

Let the point be having coordinates (x,y).

Case 1: If the point is in first quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (x, -y)

Subcase: Counterclockwise rotation:

Then (x,y) → (-x, y)

Case 2: If the point is in second quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (-x, y)

Subcase: Counterclockwise rotation:

Then (x,y) → (x, -y)

Case 3: If the point is in third quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (x, -y)

Subcase: Counterclockwise rotation:

Then (x,y) → (-x, y)

Case 4: If the point is in fourth quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (-x, y)

Subcase: Counterclockwise rotation:

Then (x,y) → (x, -y)

Case 5: For points on axes

You can take that point in any of the two surrounding quadrants. Example, if the point is on positive  x axis, then it can taken as of first quadrant or fourth quadrant.

Case 6: On origin

No effect as we assumed rotation is being with respect to origin.

Since no quadrant is specified, we assume triangle is fully in first quadrant. That means all points (x,y) will turn (-x,y) after counter clockwise rotation.

Now translation of 3 units up means all y coordinates will be increased by 3, thus, all (x,y) points of triangle first become (-x,y) then (-x, y+3).

Thus, all the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.

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Related Questions

Parker owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $7. Yesterday Parker made a total of $552 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.

Answers

Answer:

let t= the number of tacos sold

let b= the number of burritos sold

3.25t+7b=552

b=2t

Step-by-step explanation:

Since there were twice as many burrito sold as tacos sold, there were more burritos sold, so if we multiply by 2 the number of tacos sold, we will get the number of burritos sold, meaning b=2t.

The system of equation should be considered as the  3.25t+7b=552 and the value of b should be equivalent to 2t.

Calculation of the equation:

here we assume that

t= the number of tacos sold

And, b= the number of burritos sold

As per the situation, the equation be like

3.25t+7b=552

b=2t

So,

put b value in the first equation

3.25t + 14t = 552

t = 3.01

And, b = 1.51

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In (2x-3) +In (3x+4)

Answers

Answer: x=7

Step-by-step explanation: is that what you're looking for?

help please
25 + 2v = 47, v = ?

Answers

Answer:

11

Step-by-step explanation:

2v = 47-25

2v = 22

v = 11

A total of 2000 people attended a benefit concert was held to raise money for a children foundation. Student ticket cost $2 and an adult ticket cost $3. If the organizer raises a total of $5050, how many students attended the concert?

Answers

Answer:

257 kids

Step-by-step explanation:

PLEASE HELP
Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.

140 ft2
160 ft2
180 ft2
200 ft2

Answers

Answer:

D.) 200ft²

Step-by-step explanation:

The formula for the area of a trapezoid:

[tex]A=\frac{1}{2} (b_{1}+b_{2})h[/tex]

where:

[tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the basesh is the height

Insert the given values:

[tex]A=\frac{1}{2}(16+24)*10[/tex]

Simplify the equation using PEMDAS. Simplify parentheses:

[tex]A=\frac{1}{2}*40*10[/tex]

Simplify multiplication:

[tex]A=\frac{1}{2}* 400[/tex]

Simplify multiplication. Use the rule [tex]\frac{a}{b}*c=\frac{ac}{b}[/tex] :

[tex]A=\frac{1*400}{2}\\\\A=\frac{400}{2}[/tex]

Simplify division:

[tex]A=200[/tex]

The area is 200ft²

:Done

The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?

Answers

Answer:

France's GDP is 50 000 times larger than Tuvalu's GDP.

Step-by-step explanation:

Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]

            Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]

To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.

[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]

           = [tex]\frac{200000}{4}[/tex]

           = 50000

Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.

A hiker climbed up from the bottom of a mountain. His elevation increased at a rate of 40 feet each hour. Which equation models the change in his elevation at 3 hours.
O A.3(-40)=120
O B.(-3)(-40)=120
O C. 3•40=120
O D.3(-40)=120

Answers

Answer:

I believe it is C

Step-by-step explanation:

Answer:

Its C

Step-by-step explanation:

A-P-E-X

Please look at number 10. from the slope and write the equation for me

Answers

Answer:

y = 8x + 38

Step-by-step explanation:

To find the slope we set up y = mx + b and plug m (our slope) in and then plug in the point into x and y to find b (our y-intercept)

   y = mx + b

   y = 8x + b

   6 = 8(-4) + b

   6 = -32 + b

+32   +32

 38 = b

So using our slope and our intercept we have our slope intercept

y = mx + b

y = 8x + 38

Hope this helps :)

Answer:

y - y1 = m(x - x1)

y - 6 = 8(x - (-4))

y - 6 = 8(x + 4)

y - 6 = 8x + 32

y = 8x + 32 + 6

y = 8x + 38

Step-by-step explanation:

First you input the given values ( m = 8 and (-4, 6)) into the point-slope equation.

After that, you multiply the 8 by the two terms inside the parentheses, giving you 8x and 32.

Then you add 6 to both sides of the equation to isolate the y.

The slope-intercept equation ends up looking like this: y = 8x + 38

Hope this helps :)

which expression is equivalent to 8c+6-3c-2

Answers

Answer:5c+4

Step-by-step explanation:

Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side. adjacent included longest shortest

Answers

Answer:

longest

Step-by-step explanation:

was Answer Expert Verified on a different question :)

Answer:

Longest

Step-by-step explanation:

Edgen 2021

i can’t figure this one out

Answers

Answer:

H.

Step-by-step explanation:

the number of premiums sold in week 3 was 50

the number of premiums sold in week 2 was 25

25 times 2 is 50

1. The price of a ring is directly proportional to its weight. If 10grams ring worth is
$3000, what is the weight of a ring worth $9000?​

Answers

30g

your welcomeeeeeeeeeeeee

HAIIIIIII PLS HELPPPPPP
dis is confusing -_-
Miguel has $30. He spends $8.00 on a movie ticket, $3.85 for snacks and $1.00 for bus fare each way.

How much money does Miguel have left?
Miguel has_____dollars left

Answers

Answer:

$16.5

Step-by-step explanation:

$30-$8-$3.85-$1-$1 = $16.5

which equation repersent functions?

2x+3y=10
4x=16
2x-3=14
3y=18
14.6=2x​

Answers

Answer:

y= (-2/3)x+10/3  is a function

3y=18 is a function

Step-by-step explanations

in both cases for each input x there is exactly one output y

PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help

Answers

Answer:

22 units.

Step-by-step explanation:

We want to find the perimeter of the polygon with vertices at: (-3, 1); (5, 1); (-3, 4); and (5, 4).

Let’s first plot the points and see what polygon we acquire. Please refer to the graph below.

As we can see, when plotting the points and connecting them, we get a rectangle.

So, we can use the perimeter formula for a rectangle, given by:

[tex]P=2(\ell+w)[/tex]

Where [tex]\ell[/tex] Is the length and [tex]w[/tex] is width.

Remember that the perimeter is simply the distance around the figure.

So, let’s find the length. We can do so by counting or by subtracting.

By counting, we can see that the length (longer side) is 8 units.

And by subtracting, we get the same length of |5-(-3)| or 8 units.

We use absolute value because distance is always positive.

Using the same process, we find the width to be 3 units.

Using subtract, we can see that this is indeed true as |1-4|=3.

So, we can now substitute the values into our formula:

[tex]P=2(8+3)[/tex]

Evaluate:

[tex]P=2(8+3)=2(11)=22\text{ units}[/tex]

So, the perimeter of the polygon is 22 units.

Explain in your own words why you would use division to change a smaller unit to a bigger one . What would happen if you multiplied instead ? TOPIC IS MEASUREMENT

Answers

Answer:

you would use division to change bigger units into smaller ones as a form of cancellation

how do i solve -3=-2x+1 by graphing?

Answers

Answer:

x = 2

Step-by-step explanation:

-3 = -2x + 1

minus 1 to the both sides

-3 -1 = -2x

-4 = -2x

divide both sides by -2

x = 2

9/4 ÷ 3/8

HELP ME PLS​

Answers

Answer:

the answer is 6 u welcome


3. The product of two rational numbers is 15. If one of the numbers is - 10, find the other.​

Answers

Answer: -1.5

because one of the numbers is - 10 => the other is 15/-10 = -1.5

Step-by-step explanation:

In RST, RS=15, RT=12, and ST=17. Which angle of RST has the smallest measure?

Answers

Answer:A

Step-by-step explanation: I took the test

Letf(x)=(x+2)2. Letg(x)=3(x+2)2. Which statement describes the graph of g(x) with respect to the graph of f(x)?

Answers

Answer:

I say two.

Step-by-step explanation:

I need to find the slope for the question: 6y-14x=2

Answers

Answer:

Step-by-step explanation:


Two triangles have the same height. The base of one
triangle is twice that of the other. Find the difference in
their areas.​

Answers

[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}[/tex]

They both have same height,

let the height of both triangles be = x

let the base one triangle = y

then the base of another trainlgle = 2y

Area of triangle = 1/2 X B X H

Area of Triangle 1

[tex] \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} [/tex]

Area of Triangle 2

[tex] \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy[/tex]

Difference in the area =

[tex]xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} [/tex]

Hence Area of Triangle 1 is half the area of Triangle 2

Difference of 1/2 area.

Answer:

[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}∣ANSWER∣

They both have same height,

let the height of both triangles be = x

let the base one triangle = y

then the base of another trainlgle = 2y

Area of triangle = 1/2 X B X H

Area of Triangle 1

\begin{gathered} \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} \end{gathered}21×y×x=>2xy

Area of Triangle 2

\begin{gathered} \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy\end{gathered}21×2y×x=>22xy=>xy

Difference in the area =

\begin{gathered}xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} \end{gathered}xy−2xy=>22xy−xy=>2xy

Hence Area of Triangle 1 is half the area of Triangle 2

Difference of 1/2 area.

[/tex]

Step-by-step explanation:

side it

siso,;-):-(

plss show the work

6 − 4v = 3 − v

Answers

Answer: = 1

Step-by-step explanation: 6−4v=3−v

Step 1: Simplify both sides of the equation.

6−4v=3−v

6+−4v=3+−v

−4v+6=−v+3

Step 2: Add v to both sides.

−4v+6+v=−v+3+v

−3v+6=3

Step 3: Subtract 6 from both sides.

−3v+6−6=3−6

−3v=−3

Step 4: Divide both sides by -3.

−3v

−3

=

−3

−3

v=1

Answer:

v=1

Answer:

V=1

Step-by-step explanation:

6 - 4v = 3 - v

move the varible

6 - 4v + v = 3

collect like terms

-3v = 3 - 6

divide both sides by -3

V = 1

y-2 = -3(x + 6), write the equation of the line in slope intercept form.

Answers

Answer:

y = -3x - 16

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Given: y - 2 = -3(x + 6)

Slope-intercept form: y = mx + b

To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).

To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:

y = mx + b

2 = -3(-6) + b

2 = 18 + b

Subtract 18 from both sides of the equation to isolate b:

2 - 18 = 18 - 18 + b

-16 = b

The y-intercept is -16.

Now that we know the slope and the y-intercept, we can write the equation:

y = -3x - 16

A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000​

Answers

Answer:

C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above

A person in the 44 and under age group is more likely to have an annual income of at least $50,000​ is a correct statement.

We have given that,

A sociologist polled a random sample of people and asked them their age and annual income.

What is the annual income?

annual income is the amount of money you receive during the year into your bank account, before any deductions.

The two-way frequency table below shows the results.

Annual income vs. age group Less than $50,000 At least $50,000

Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132

Total 186 162 348

A person with an annual income of at least

[tex]=\$50000\\=$50,000dollar[/tex]

Therefore statement b is true.

A person in the 44 and under age group is more likely to have an annual income of at least $50,000​.

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Alice needs twice as many yards of ribbon as Quincy. how many rolls of ribbon does Alice need? explain your answer i like your cut g

Answers

Twice the length of 322 yards is 644. If I divide by 15 I get 42 r14. Alice needs to buy 43 rolls of ribbon .

Answer: Twice the length of 322 yards is 644. If I divide by 15 I get 42 r14. Alice needs to buy 43 rolls of ribbon. I like your cut G !

Step-by-step explanation:

A store advertises a 20% markdown on a dishwasher that normally sells for $952. a. Find the price on sale. b. The markdown is the greatest possible without the store losing money. What does this tell you about the store’s cost?

Answers

Answer:

a. $761.60

b. The store bought the dishwasher for the price they are currently selling it at. They are receiving no profit when it is on sale.

Step-by-step explanation:

give brainliest pls

If 20% is the greatest possible markdown the store can give without losing money, then the price of the dishwasher is $761.60

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that the Sales price = $952

Markdown % = 20%

The Sales price = (100 - 20)% x $952

The Sales price = 80% x $952

The Sales price = $761.60

If 20% is the greatest possible markdown the store can give without losing money, then the price of the dishwasher is $761.60

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Decrease £40 by 70%

plz answer and ill brainlist u!

Answers

Answer:

12

Step-by-step explanation:

Answer:

£12

Step-by-step explanation:

It's asking us to find the 30% of the 40 and to do this we multiply 40 by 30 then divide it by 100

40 × 30 ÷ 100 = 12

Is X +3 a factor of 2X squared minus 2X -12

Answers

Answer: No, x+3 is not a factor of 2x^2-2x-12

========================================================

Explanation:

Let p(x) = 2x^2 - 2x - 12

If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).

Compare x+3 = x-(-3) to x-k to find that k = -3.

Plug x = -3 into the function

p(x) = 2x^2 - 2x - 12

p(-3) = 2(-3)^2 - 2(-3) - 12

p(-3) = 12

We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12

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

Let's see what happens when we factor p(x)

2x^2 - 2x - 12

2(x^2 - x - 6)

2(x - 3)(x + 2)

The factors here are 2, x-3 and x+2

Other Questions
Explain how the Missouri Compromise worked. (Your answer must be at least 4sentences long.) * Give two possible themes in the movie jaws. Express each theme in one sentence. Felicia Fellini is applying for a receptionist position. She wrote the following letter to the Hiring Manger. However, there are several errors in subject-verb agreement. Help Felicia correct the letter before she turns it in to the manager.Dear Hiring Manager:I feels that I am the ideal candidate for the receptionist position at your company. I has three years of experience as a receptionist in a company that is similar to yours. My phone skills and written communication is excellent. These skills helps me understand that every person in a company helps make the business a success. At my current job, the team say that I am very helpful. Everyone appreciate when I go the extra mile to get the job done right. My current employer and coworkers feels that I am an asset to the team. I is efficient and organized. Are there any other details about me that you would like to know? If so, please contact me. Here are my rsum. You can reach me by e-mail or phone. I looks forward to speaking with you in person. Thanks, Felicia Fellini [tex]( \frac{3}{5} ) - 2[/tex]simplify What element has 4 energy levels and 8 valence electrons? Why has there been a decline in horses being used for a working field and pulling carriages what is 50 times 2 hahahahah Help!Which is not a characteristic of romanticismA) power of reasonB) focus on the individualC) power of the ImaginationD) nature brings wisdom and inspiration More than 300 rivers drain into Siberia's Lake Baikal, which holds 20% of the world's fresh water, more than all the North American Great Lakes combined. A. More than 300 rivers drain into Siberia's Lake Baikal, which holds 20% of the world's fresh water, more than all the North American Great Lakes combined. B. With 20% of the world's fresh water, that is more than all the North American Great Lakes combined, Siberia's Lake Baikal has more than 300 rivers that drain into it. C. Siberia's Lake Baikal, with more than 300 rivers draining into it, it holds more of the world's fresh water than all that of the North American Great Lakes combined, 20%.D. While more than 300 rivers drain into it, Siberia's Lake Baikal holds 20% of the world's fresh water, which is more than all the North American Great Lakes combined. E. More than all the North American Great Lakes combined, Siberia's Lake Baikal, with more than 300 rivers draining into it, holds 20% of the world's fresh water. Worth 15 points. Brainliest will also be given to the first correct answer.In the movie Titanic, the blue, diamond heart-shaped necklace that was given to Rose was called _______________.a) The Heart of the Atlanticb) The Diamond Heartc) The Heart of the Oceand) The Royal Diamond Help I will give brainliest Write a division problem that has a quotient of 12.At least one of the numbers you give must be a proper fraction. The other can be a proper fraction, whole number, orimproper fraction. Neither the dividend nor the divisor can be 12. what is an example of natural material for fabric? What is the next term in the following sequence?-3.4, 11, 18, ...2725712 HELP!!!!!!! PLEASE THIS IS MY LAST QUESTION ON A TEST DUE TODAY!!!!!!!!!!!!By analyzing an authors use of epigraphs, we can determine his or her ____A. conclusionB. VernacularC. MoodD. Purpose Throe would like to hire a guitarist for his charity concert. Guitarists A and B are offering their services toThroe but each guitarist charges different initial fees and hourly rates. How can Throe check to see whenthey will charge the same amount of money? Name three ways to perform this task. There are 20 boys and 16 girls. what is the largest number of groups that you can form such that boys and girls are distributed equally among the groups? Please answer C and D please ! I would love you forever !!!! Which situation could be represented by the equation 32.4 = 8.1x?A. An athlete swam 32.4 miles. It took the athlete 8.1 minutes to swim each mile. What is x, the total number of minutes the athlete swam?B. An athlete swam 32.4 miles on Friday. The athlete swam 8.1 miles on Saturday. What is x, the total amount of miles the athlete swam on Friday and Saturday?C. An athlete swam 32.4 miles. On Monday, the athlete swam 8.1 miles and the rest on Tuesday. What is x, the number of miles the athlete swam on Tuesday?D. An athlete swam a total of 32.4 miles. The athlete swam 8.1 miles every day. What is x, the number of days the athlete swam? The Elkmont Corporation needs to raise $52.5 million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. If the offer price is $21 per share and the company's underwriters charge a spread of 7.5 percent, how many shares need to be sold?