Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, instead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin.




Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis?

Answers

Answer 1

Answer:

We rotate the point counterclockwise by an angle θ = tan⁻¹ (y/x)

Step-by-step explanation:

If we have the point (x, y), its reflection along the x-axis (x,-y). The reflection of the point (x, -y) along the y - axis is (-x, -y). So, the angle between the initial point (x, y) and the final point (-x, -y) is θ = tan⁻¹ [(-y - y)/(- x -x)] = tan⁻¹ [(-2y/(-2x)] =  tan⁻¹(y/x).

So, the point (x, y) is rotated counterclockwise by an angle of  θ = tan⁻¹ (y/x) to perform both reflections.


Related Questions

This is my sister's work, please help. will give brainliest. DON'T GIVE STUPID ANSWERS, I WILL REPORT

Answers

blue is 2 6 9 12 hope this helps

FREE BRAINLY! What is the equation of the line perpendicular to the line y = -3 and passing through the point (2, -1)?

Answers

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

We want the equation of the line perpendicular to y=-3.

Notice that y=-3 is a horizontal line.

Therefore, in order to be perpendicular, our new equation must be vertical.

We know that it must pass through the point (2, -1).

Since it must be vertical, it must pass through the x-coordinate.

Therefore, our line must be:

[tex]x=2[/tex]

It passes through (2, -1) and is a vertical line, so it’s perpendicular to y=-3.

Answer:

x=2

Step-by-step explanation:

A chef locates a pre-made tuna salad that is nearly identical to the one she makes from scratch in her sandwich shop. To make it from scratch, an $8.25/hour employee needs 20 minutes to prepare the tuna salad. The ingredients cost $12.18 and yield 10 four-ounce servings. The chef can purchase the pre-made tuna salad at $26.99 for a 5# tub. Calculate the cost per portion for the scratch-made and the premade versions. If cost were the only factor, should the chef make or buy this product?

Answers

Correct question

A chef locates a pre-made tuna salad that is nearly identical to the one she makes from scratch in her sandwich shop. To make it from scratch, an $8.25/hour employee needs 20 minutes to prepare the tuna salad. The ingredients cost $12.18 and yield 10 four-ounce servings. The chef can purchase the pre-made tuna salad at $26.99 for a 5 pound tub. Calculate the cost per portion for the scratch-made and the premade versions. If cost were the only factor, should the chef make or buy this product?

Answer:

If cost were the only factor, the chef should not make version of the tuna salad from scratch because it is expensive that the premade version

Step-by-step explanation:

For tuna: Made from scratch

The ingredients cost $12.18 and yield 10 four-ounce servings.

10 servings = $12.18

1 serving = x

10 × x = 1 × $12.18

x = $12.18/10

x = $1.218

Hence, 1 four ounce serving cost $1.218

The chef can purchase the pre-made tuna salad at $26.99 for a 5# tub.

5 pound tub salad = $26.99

1 pound tub of tuna salad = x

5 × x = 1 × $26.99

x = $26.99/5

x = $5.398 per pound

Converting to ounces

0.0625 pound = 1 ounce

5 pound = x

x = 5/0.0625

x = 80 ounces

80 ounces of tuna salad = $5.398

4 ounces of tuna salad = x

80 × x = 4 × $5.398

x = 4 x 5.398/80

x = $0.2699

Hence, 1 4 ounce pre made tuna salad cost = $0.2699

Hence, the cost per portion for the scratch-made is $1.218 per 4 ounces servings and the premade versions is $0.2698 per 4 ounce servings

If cost were the only factor, the chef should not make version of the tuna salad from scratch because it is expensive that the premade version

Determine whether each triangle with sides of 28 yd, 195 yd, and 197 yd is a right triangle

Answers

Answer:

yes it is

Step-by-step explanation:

to have a right traingle two sides cannot be equal and the first added and squared cannot be more than the last side squared

HELP PLEASE IM FAILING!!!The Horizon Resort charges $150 per night for a single room, and a one-time
valet parking fee of $35. If a person stays 4 nights what is the total cost? Make an equation

Answers

The total cost is $635.

An equation to solve this would be 150x · 35 = 635 with x equaling 4, or 150(4) · 35 = 635. Glad I could help. PLEASE GIVE BRAINLIEST. I NEED 5 OF THEM TO LEVEL UP.

Rachel has $1,800 to spend on renting a venue for a party. The available locations to rent for the party cost between $660 and $2,500. This cost includes a base cost, plus a set-up fee that is one-fifteenth of the base cost. The total cost can be modeled by the function shown below, where c represents the base cost of renting a venue.

f(c)=c+1/5c
State the domain of values that represents the base cost for the venues Rachel can afford.

Answers

Answer:

618.75 to 1687.50

Step-by-step explanation:

Daisy filled a bucket with 7/6 gallon of rain.water.
later she poured out 1/6 of gallon of of the water. how much water is left in the bucket?​


I'll mark you brilliantest

Answers

A gallon or 6/6 gallon

Will give brainliest if correct.

Answers

Your answer should come to:

y = -2/3x + 3

can you help me with this I need it done by tomorrow thank you

Answers

Answer:

x = 17deg

Step-by-step explanation:

angle DCE = angle ACB (vertically opposite angles)

therefore,

x + 100 = 4x + 49

3x = 51

x = 17deg

Answer:

X=

Step-by-step explanation:

First you have to divide the shape into to triangles. Triangle CED and triangle ACB.

Second you have to find what angle C is in the triangle ACB. For this you'll have to:

Find out which of the sides are which. For triangle ACB, side CB is the hypotenuse, CA and AB are adjacent.

The formula we use is [tex]a^{2} +b^{2} =c^{2}[/tex].  a and b are adjacent and c is hypotenuse.

When you found what angle C is, you can go on and to the second triangle same theorem applies to the second triangle [tex]a^{2} +b^{2} =c^{2}[/tex]. At this stage you will already know two angles, 100 and c, so finding E using this formula will be easy

Kim decides to give her old toys to her younger cousins. She gives her cousin Sarah 2/3. Then, she gives her cousin Ryan 2/5 of the remaining toys. She has 6 toys left. How many toys did Kim have to begin

Answers

Answer:

30

Step-by-step explanation:

Work backwards:

6 is 3/5 of a number, and that number is 1010 is 1/3 of a number, and that number is 30

Check your work:

2/3 of 30=20 toy to Sarah30-20=10 toys left2/5 of 10=4 toys to Ryan10-4=6 toys left

Nathan drinks 25 cups of coffee over 5 weeks. How many cups of coffee will Nathan drink in 3 weeks?​

Answers

Answer: 15

Step-by-step explanation: 5, 10, 15, 20, 25

Answer:

15 cups of coffee in 3 weeks

Step-by-step explanation:

every week Nathan drinks 5 coffees because if we were to do 25 divided by 5 we get 5, and 5 x 5 is 25, so if we did 5 x 3 we would get 15. the 3 represents the amount of weeks.

PLEASE HELP
PART A

Diego deposited $10,000 for 4 years at a rate 6% simple interest. find the amount of interest Diego earned after 4 years.

PART B

If Diego closes his account after the 4 years, how much money will he have total?

Total Amount=

Answers

Answer:

Part A=2,400  Part B=12,400

Step-by-step explanation:

The amount of interest Diego earned after 4 years is 2400 and the money Diego have after 4 years is 12400.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Diego deposited $10,000 for 4 years at a rate 6% simple interest

We need to find the interest earned by Diego after 4 years.

Let us find what is 6% of 10000

Convert 6% to decimal value by dividing with 100.

6/100=0.06

Now multiply zero point zero six with 10000

0.06×10000

600

Noe for four years she earned

4×600

2400

2400 is the amount of interest Diego earned after 4 years.

Now let us find the money Diego have after 4 years.

Which is 10000+2400

12400

Hence the amount of interest Diego earned after 4 years is 2400 and the money Diego have after 4 years is 12400.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ2

A school set a goal to collect at least $360 from a book sale. They have already collected $180. The school receives $3 for each book sold. Write an inequality to show the number of books the school needs to sell to meet their goal.

Answers

I attached the inequality!
Goal-$360
Already have- $180
They receive $3 for each book bought
$180 x $3 = 540

Which of the following is equivalent to 8^(1/3)?
Option 1
Option 2
Option 3
Option 4
(look at photo for answers)

Answers

the answer is option 2....

Answer:

Option 2

Step-by-step explanation:

when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1

Esteban stands on a dock 1.25 yd above the water. A fish swims below Esteban at -4.61 yd from the surface of the water. How many yards apart are Esteban and the fish?

Answers

Answer:

3.36 yards

Step-by-step explanation:

✓From the question, Esteban stands on a dock 1.25 yd above the water which means the distance of Esteban above the water is 1.25 yd

✓A fish swims below Esteban at -4.61 yd from the surface of the water which means the distance of the fish away from the surface is 4.61 yd in opposite direction of Esteban

NOTE: The negative sign only signify direction of the fish which is opposite of Esteban

✓then the distance in yards apart of Esteban and the fish is

=4.61-1.25

=3.36 yards

can I have topics for STEAM (Science, Technology, Engineering, Art, Math) It must be a real-life problem and I have to figure out a solution and the solution must include Science, Technology, Engineering, Art, Math in it. If you have any ideas please help thank you.

Answers

Answer:

See below.

Step-by-step explanation:

I find autonomous robotics and fuzzy-related topics interesting. But it must include all the topics? I mean, Art as well? In the field of robotics, some interesting approaches involve building robots capable of moving in cluttered environments, places with humans efficiently. In this context the study of mapping algorithms and computer vision is interesting.

3. You have saved $140 for a new pair of skis. They have a regular price of $189. They have been reduced by 30%. There is a 13% tax as well. a. What is the discount? b. What is the new price? c. What is the tax? d. What was the total price of the shoes, after the discount and tax? e. Do you have enough money?

Answers

Answer:

$56.70

$132.30

$17.199

$149.499

No

Step-by-step explanation:

Given that:

Regular price of skis = $189

Discount % = 30%

Amount saved = $140

After sales tax = 13%

a. What is the discount?

Discount amount = Regular price * discount %

Discount amount = $189 * 0.30

Discount amount = $56.70

b. What is the new price?

Regular price - Discount amount

$189 - $56.70

= $132.30

c. What is the tax?

Sales tax = new price * tax %

Sales tax = $132.30 * 0.13

Sales tax = $17.199

d. What was the total price of the shoes, after the discount and tax?

New price + sales tax

= $132.30 + $17.199

= $149.499

e. Do you have enough money?

No

$149.499 > $140


The function g(x) is a transfomation of the function f(x). If g(x) = 2(x – 3) 2
f(x) = 2(x + 4) then what translation describes the change from f (x) to g(x)?
2
1

Answers

Answer:

881 (-6x)

Step-by-step explanation:

881 (-6x) i think that the answer

find the total cost or sale price to the nearest cent and write your answer with a dollar sign

$2,500 jet ski; 6.5% tax

Answers

Answer:

$2662.5 is the answer in my opinion

please need this asap!! will give brainliest and a thanks to fast answers :)

Answers

Answer:

15 days

Step-by-step explanation:

Answer:

27 days

Step-by-step explanation:

Juan rented a chainsaw from Steve's Tools. It cost $19 plus $6 per hour. If Juan paid
$49, then he rented the chainsaw for how many hours?

Answers

Answer:

2 hours

Step-by-step explanation:

if you do 19x2 then that is 38 and then you have to add 6 dollars per hour so that would be 2 hours


Asher reads 2 books a week. Kyla reads 7 books a month. Sawyer reads 90 book a year. Who
reads more books?

Answers

Answer:

Asher

Step-by-step explanation:

Answer:

Asher reads more books

Step-by-step explanation:

Asher reads 2 books a week wich is about 102 books a year (because there about 52 weeks in a year)

kyla reads 7 books a month wich is 84 books a years

Sawyer reads 90 books a year

If $800 is deposited into a new savings account with a simple interest rate of 1.8%, what will be the total amount in the account after 15 years?

Answers

Answer:

Step-by-step explanation:

I = prt

I = 800 × 1.8% x 15

I = $216

Remember the percent sign for the rate or write it as a decimal (multiplier)! In this case the multiplier would be 0.018!

Hope this helps, please mark as brainliest! :)

2(-6m - 3) =6(5m - 1) please show work what is m ?

Answers

Answer: m=0

Step-by-step explanation: simplify each individual expression first. The left side of the equation is equal to -12m-6, and the right side is equal to 30m-6. Then together, it equals to -12m-6=30m-6. The -6 cancel each other out. M=0

Solve: -2+x=4 Please please answer quickly

Answers

Answer:

x = 6

Step-by-step explanation:

-2 + x = 4

x = 4 + 2

x = 6

Thank you :-)

La Srta. Vázquez tiene 17 una clase de estudiantes. Ella puede gastar 24 dólares por estudiante para comprar material de matemáticas para el año escolar. Ella compra primero calculadoras para todos sus estudiantes, con un costo total de 134,81 dólares . Después de comprar las calculadoras, ¿cuánto dinero le queda para gastar por estudiante? Lis ayúdenme debo entregar hasta el viernes

Answers

Answer:

A la Srta. Vázquez le quedan $18,39 para gastar por estudiante.

Step-by-step explanation:

Primero, tienes que dividir el costo total de las calculadoras que compró la Srta. Vázquez entre el número de estudiantes para saber cuánto gastó por estudiante:

134,81/24=5,61

Ahora que sabes cuánto gastó por estudiante, debes restar esto de la cantidad que puede gastar por estudiante para saber cuánto le queda:

24-5,61=18,39

De acuerdo a esto, la respuesta es que a la Srta. Vázquez le quedan $18,39 para gastar por estudiante.

The bike cost $120. The sales-tax rate was 8%. What is
the total cost of the bike including sales tax?

Answers

Answer:

$129.6

Step-by-step explanation:

just use ur calculator i think

Answer:

$129.60

Step-by-step explanation:

8 percent of 120 is 9.6

9.6+120=129.6

PLS HURRY!!!
A parabola has a vertex at (0,0). The equation for the
directrix of the parabola is x = -4. In which direction does the parabola open?

Answers

Answer:

Right.

Step-by-step explanation:

The answer is right on edge2020 I just took the test.

The direction in which the parabola will open is; To the right

What is the equation of a parabola?

We are given;

The vertex of the parabola is at (0, 0)

Directrix of the parabola is x = -4

We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;

y² = 4ax

Thus, we can conclude that the parabola opens towards the right.

Read more about Parabola at; https://brainly.com/question/17987697

Evaluate the expression shown below and write your answer as a fraction in simplest form.
3
4
+
1
6
4
3

+
6
1

plss help

Answers

Answer:

Step-by-step explanation:

the answer would be 11/12

PLZ HELP ME IF YOU ARE A MR.BEAST FAN. The sum of 7 and 5 times a number is 48. What are the two numbers? What is the equation and the solution of the question.

Answers

Answer:

I´m not a Mr. Beast fan but the answer is 4. 4*12 (which is the sum of 7 and 5) = 48

The equation is (7+5)x=48

Answer:

i am a big fan here is the answer  (7+5)x=48

Step-by-step explanation:

Other Questions
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