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

Camila started reading a 500 page book. She read of the book in hour. What is the maximum number of pages can she read in hour if she reads at the same rate?
A.
10 pages
B.
15 pages
C.
40 pages
D.
20 pages

Answers

Answer:

Need more information

Step-by-step explanation:

I need to know what percentage/fraction of the book she read in 1 hour or any other information about the rate she is reading

-0.2 + 7/10 Enter the answer as an exact decimal or simplified fraction.

Answers

Answer:

.5 or 1/2

Step-by-step explanation:

an equation of the line with a slope of 2 and y-intercept of 9

Answers

Answer:

y = 2x + 9

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Slope m = 2

y-intercept b = 9

Step 2: Write linear equation

Slope-Intercept Form:   y = 2x + 9

Which statement would be included in the proof of why Measure of angle C + measure of angle G + measure of angle H = 180 degrees.?
A. Angles F and H are congruent.
B. Angles A and G are congruent.
C. Angles A and H are congruent.
D. Angles E and C are congruent.

Answers

I think c

Step-by-step explanation:

I did it a min ago

Answer:

ur answer would be C. Angles A and H are congruent.

Step-by-step explanation:

right on edge 2021 for math

what is the greatest common factor of 10 & 12,17 & 51,78 & 48,11 & 55,88 & 66,95 & 38,6 & 27,56 & 49,60 & 45,42 & 63,38 & 40,81 & 54,40 & 80,46 & 69

Answers

yeah baby girl it will be best for you to look that up on Google

ms kim borrowed 1350 to buy to used a automobile if she repays 75 a month how many months will it take ro pay back the loan

Answers

Answer:

18 months

Step-by-step explanation:

since 1350/75 is 18

C. Solve for each quotient:
8÷5/8
I Mark brainlies ​

Answers

The exact form is: 64/5

The decimal from is: 12.8

And the Mixed number form is: 12 4/5

Answer:

12.8

Step-by-step explanation:

8÷5/8 is also the same as:

8 x 1/5 x 8

Proof:

Plz Help...
Find x in the given triangle.

Answers

Answer:

[tex]\huge\boxed{x=2\sqrt{286}}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have:

[tex]leg=x\\leg=15\\hypotenuse=37[/tex]

Substitute and solve for x:

[tex]x^2+15^2=37^2\\\\x^2+225=1269\qquad|\text{subtract 225 from both sides}\\\\x^2+225-225=1269-225\\\\x^2=1144\to x=\sqrt{1144}\\\\x=\sqrt{4\cdot286}\\\\x=\sqrt4\cdot\sqrt{286}\\\\x=2\sqrt{286}[/tex]

Find the equation of the line. Use the exact numbers.

Equation: y = _____ x _____

Answers

Y= 3x+3 is the correct answer:)


Michael is building a fence around his garden to keep the rabbits out. The perimeter of his garden is 42 feet. If the length of the garden is 5 more than the width, what are the dimensions of the fence? Hint: draw a rectangle, and label all 4 sides for the length and width, given what you know this is the last question on my test please help me

Answers

Answer: 8ft by 13ft

Here are the steps

im lost on this one​

Answers

oki so the missing angle is also 2x + 15 since that’s equal so add all three of those together and equal it to 180 and solve
2x+15 Because There Equal Sides

A town population of 14000 and grows 3.5% every year. What will be the population after 14 years to the nearest whole number

Answers

Answer:

22662

Step-by-step explanation:

Since the growth is exponential, your equation will be y = a • b^x. a being the beginning amount, b the percentage it increases by, and x is the time taken.

y = 14000 • 1.035^14

  = 22661.72

Round your answer since people can only be integers and your answer is a population of 22662  

F (x) = x^2 + 4x; Find f (−7)

Answers

Answer:

f(-7) = 21

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

f(x) = x² + 4x

f(-7) is x = -7

Step 2: Solve

Substitute:                    f(-7) = (-7)² + 4(-7)Evaluate:                       f(-7) = 49 + 4(-7)Multiply:                        f(-7) = 49 - 28Subtract:                       f(-7) = 21

Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?

Answers

9514 1404 393

Answer:

  it is application of the multiplication property of equality

Step-by-step explanation:

You can use "cross products" to solve any proportion. What looks like a "cross product" is just application of the multiplication property of equality. That property says the variable value is unchanged if both sides of the equation are multiplied by the same value.

For your fraction, the "cross product" is what you get when you multiply both sides of the equation by 500.

  [tex]\dfrac{18}{5}=\dfrac{x}{100}\qquad\text{given}\\\\\dfrac{18\cdot5\cdot100}{5}=\dfrac{x\cdot5\cdot100}{100}\qquad\text{multiply by $5\cdot100$}\\\\18\cdot100=5\cdot x\qquad\text{cancel common factors; looks like cross product}[/tex]

__

Note that the next step here is to divide by the x-coefficient, the 5 that was in the left-side denominator.

  [tex]\dfrac{18\cdot100}{5}=x\qquad\text{divide by 5}[/tex]

Please also note that this is exactly the same result you would get by multiplying the original equation by the original denominator of x.

I have never really watched anime but I have been thinking to start watching it soooo does anyone have suggestions?

Answers

Answer:

yeah watch my hero academy One punch man n Naruto also Dragon Ball Z

Answer:

It’s not really an amine but avatar the last airbender

Step-by-step explanation:

Attack on titan

One punch man

the devils a part-timer

HELP ASAP. ABC is an isosceles triangle.

Answers

Answer:

please make it more clear

Step-by-step explanation:

what you are asking

Please ask your question full not sure what you mean by this

HELP ASAP! Relations and Functions!!! Giving brainliest!!!

Answers

Answer:

I think the answer is relation only.

Step-by-step explanation:

sorry if I'm wrong

Answer:

D

Step-by-step explanation:

What is y+3=7(x-2) written in standard form?

Answers

Answer:

7x-y=17

Step-by-step explanation:

Answer:

7x-y=17

Step-by-step explanation:

Solve for x

3x−8≤23 AND −4x+26≥6

Answers

Answer:

Step-by-step explanation:

Ok so the first one is X<31/3

And the second one is X>-5

HELPPPPP its geo and I need help​

Answers

Answer:

61

Step-by-step explanation:

first we set <B and <E equal to each other to find x (they are equal because it is a given in the phrase below the pics)

5x + 8 = 7x - 12

5x + 20 = 7x

20 = 2x

10 = x

now we know x is 10, so substitute it into an equation to find the measure of the vertex of the triangles

5(10) + 8 = 58

subtract 58 from 180 to find what the base angles are combined

180 - 58 = 122

since there are two congruent base angles (the base angles of isosceles triangles are always congruent), we have to divide 122 by 2 to find the measure of a base angle

122 ÷ 2 = 61

<F is a base angle, so <F is 61

can someone please help .. will mark brainliest !

Answers

Answer:

B and B

Step-by-step explanation:

The first one is B because all of the slopes are negative except B. And so I think that's the correct answer

The second one I know is B for sure, I remember learning it in 8th grade 2 years ago.

It's really just the first one I am second guessing myself on but B and B make sense to me :)

With a coupon, you get a pair of shoes that normally cost $80.00 for 30% off. How much is the discount?

Answers

Answer: The discount is 24$ so the 80$ shoes are now 56$.

if f(x)=10x+3 whar is the value when f(x)=19

Answers

Answer:

x = 1.6

Step-by-step explanation:

Given f(x) = 10x + 3 and f(x) = 19, then equate right sides, that is

10x + 3 = 19 ( subtract 3 from both sides )

10x = 16 ( divide both sides by 10 )

x = 1.6

Answer:

x = 1.6

Step-by-step explanation:

Given

f(x)=10x+3

and

f(x) = 19 ⇒ x = ?

Solution

10x + 3 = 1910x = 16x = 16/10x = 1.6

Two students used different methods to measure the length of their model bridge

project. One student measured the bridge length in feet using 11n−2.9. The second

student measured the bridge length in feet using 5n + 6.4 What is the value of n if

the two measurements are equal?

Answers

Answer:

Two students used different methods to measure the length of their model bridge

project. One student measured the bridge length in feet using 11n−2.9. The second

student measured the bridge length in feet using 5n + 6.4 What is the value of n if

the two measurements are equal?

Step-by-step explanation:

Two students used different methods to measure the length of their model bridge

project. One student measured the bridge length in feet using 11n−2.9. The second

student measured the bridge length in feet using 5n + 6.4 What is the value of n if

the two measurements are equal?

To add or subtract fractions, what must you have?

Answers

Answer:

You need a common denominator.

Step-by-step explanation:

3/4+2/3

9/12+8/12

Answer:

Equal denominators/common denominators

Step-by-step explanation:

You need to have equal denominators. If you do not, then you have to multiply the denominators against each other as well as multiplying the same number to the numerator. If a number is a factor of one of the numbers then multiply the number by its other factor so as to get the same number.

Ex. 1

First one explained:

2/3 + 4/5

1/3 * 5/5 = 5/15

2/5 * 3/3 = 6/15

5/15 + 6/15 = 11/15

Common denominator = 15

Ex. 2

Second one explained:

2/8 + 1/4

2/8 + 1/4*2/2 = 2/8 + 2/8

= 4/8

Common Denominator = 8

Hope this helped,

Kavitha Banarjee

?????Help please?????? I’ll cashapp u

Answers

Answer:

x int = (-2,0) (2,0)

y int = (0,12)

Step-by-step explanation:

my work is in the picture attached

anything in color is what I did in that certain step

Item 18
Write the word sentence as an equation. Then solve.

10 more than a number c is 3.

Equation:

Solution: c=

Answers

Answer:

I would say c is .3 . The equation is 3÷10

Step-by-step explanation:

because its saying c times 10 is 3 and the reverse of multiplication is division. So you divide 3 by 10 to find c Hope This helps!! C is 0.3

b. Selena has a coupon for 15% off ice cream. If she pays $2.68 with the coupon, what was the original price of the ice cream?

Answers

$3.15 , if you took off 15% then that would be $0.47

bologna is hot dog pancakes! ;)​

Answers

Answer:

cool

Step-by-step explanation:

I have no idea what this means but good on u:)

Answer: haha is it weird that i want bologna now lol

Step-by-step explanation: have a nice night :)

An earthworm times 2 cm into the ground each day the earth worm tunnels at about the same place every day how many days will it take the earthworm to tunnel 14 cm

Answers

Answer:

7 days

Step-by-step explanation:

Given that:

Distance tunneled into the ground each day = 2cm

The rate is the same everyday ;

Hence, to. Tunnel 14cm into the ground , it will take the earthworm;

1 day = 2cm

x days = 14cm

Cross multiply :

2x = 14

x = 14 /2

x = 7

Hence, it will take 7 days for the earthworm to tunnel 14cm

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