If triangle ABC is reflected across the line y = x, are the pre-image and image congruent? Why, or why not?

OYes, distance and angle measure are preserved

OYes, angle measure is preserved and distance is not

O No, distance is preserved but angle measure is not

O No, neither distance nor angle measure are preserved

Answers

Answer 1

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Related Questions

Please answer as fast as you can.
what is 30 + 5(2x -1) + 20

Answers

Answer:

10x + 55

Hope this helps :)

the answer is 40 brainliest plz

help as soon as possible pleaseee

Answers

Answer:

(3x + 2)(x-4)

Step-by-step explanation:

3x² - 10x - 8 = 0

(splitting the middle term)

3x² -12x + 2x -8 = 0

3x(x-4) + 2(x-4) = 0

(3x + 2)(x-4) = 0

(3x + 2)(x-4) is the correct answer (option a)

Factor by grouping so your answer you be #1 (3x +2)(x-4)

I need to find the answers to 5-9 sorry for bad quality

Answers

Answer: 5: y=7/8x+1

              6: y=-10x

              7: y=2.5x-7

              8: y=1.2x

              9: y=-5x-8

Step-by-step explanation:

There you go. You are welcome.

Find the value of X
40°

(12x-8)



please help I have 10 mins left on my test

Answers

Answer:

B.4  12x-8 would be 12x_-8=40   this is because 12x-8 is congruent to the 40 degree angle. so what -8 is 40?  48   12x_=48   x=4   12x4=48  48-8 is 40

plz let me know if i am wrong mark brainliest if right

Step-by-step explanation:

Ron has 198 feet Of fencing to make a rectangular garden in his backyard. He wants the length to be 19 feet more than the width. Find the width?

Answers

Answer:

68.5

Step-by-step explanation:

u do 198 divided by 4 then add 19 to the awnser that u got

Answer:

width = 40 feet

Step-by-step explanation:

If w = width, then l = 19 + w

l = 19 + w

2l + 2w = 198

"Substitute 19 + w as l in the second equation"

2(19 + w) + 2w = 198,

38 + 2w + 2w = 198,

38 + 4w = 198,

4w = 198 - 38 = 160,

w = 160/4 = 40 feet

=> Solution: width = 40 feet

25% of a spring basket is peeps.
The total number of items in the
basket is 20. How many of the
items are peeps?

Answers

Answer:

5

Step-by-step explanation:

25% of 20=5

Answer:

5 items are peeps

Step-by-step explanation:

25% is 1/4 of 100%, so divide 20 (your total # of items) by 4, and you get 5, which is 25% of your 20 spring basket items.

El primer término en una secuencia es 5 y el quinto término es 17. ¿Cuál es la diferencia común

Answers

The common difference of this Sequence is 12.

In mathematics, a sequence refers to an ordered list of numbers. When working with sequences, there are various concepts and formulas that are used to calculate different aspects of the sequence. One such concept is the common difference. Let's explore what the common difference is and how to calculate it.
What is the common difference?
The common difference in a sequence refers to the difference between any two consecutive terms in the sequence. For example, in the sequence 2, 4, 6, 8, 10, the common difference is 2. We get this value by subtracting the second term (4) from the first term (2) and so on.
How to find the common difference of a sequence?
To find the common difference of a sequence, you need to know at least two terms of the sequence. You can then subtract one term from the other to calculate the common difference.
Let's apply this to the given sequence, which has a first term of 5 and a fifth term of 17. To find the common difference, we can subtract the first term from the fifth term as follows:
17 - 5 = 12
Therefore, the common difference of this sequence is 12.

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Last year’s computer models are discounted 20%. What was the original price to the nearest dollar of a computer that now costs $1,480?

$1,184

$1,500

$1,510

$1,850

Answers

Answer:

x=$1850

Step-by-step explanation:

Let the original price of the computer model is x.

Last years discount is 20%

We need to find the original price if the computer now costs $1480.

ATQ,

[tex]x-20\%\ \text{of x}=1480\\\\x-\dfrac{20x}{100}=1480\\\\x-\dfrac{x}{5}=1480\\\\\dfrac{4x}{5}=1480\\\\x=\dfrac{1480\times5}{4}\\\\x=\$1850[/tex]

So, the original cost of the computer model is $1850.

Classify the four angles of the quadrilateral

Answers

Answer:

<A= right

<B= obtuse

<C= acute

<D= obtuse

Step-by-step explanation:

2x²-2x=12
quadratic equation​

Answers

x=3,-2 you solve by using the quadratic formula

You can solve with many ways but I'll do this one instead. Move 12 to the left side and change from positive to negative.

[tex]2x^2-2x-12=0\\[/tex]

Then divide by 2 whole equation.

[tex]\frac{2x^2-2x-12}{2}=\frac{0}{2}[/tex]

Simplify, as we get  [tex]x^2-x-6=0[/tex]

We can either use Quadratic Formula or Factoring the Polynomials. It depends but since the polynomial aren't that hard to factor because it doesn't have that many numbers in value. So using factoring will be faster.

From [tex]x^2-x-6=0[/tex] we can factor as -

[tex](x-3)(x+2)=0\\x-3 =0, x+2=0\\x=3, x=-2\\(x=3,-2)#[/tex]

Thus, the value of x is 3 or -2. So x = 3, -2 is the answer.

Note that we can also use Quadratic Formula to solve the equation, however that will take longer than factoring then solve the equation.

Do I have the right anwer if not what is it

Answers

Answer:

yes

Step-by-step explanation:

its rightsss

Answer:

Yes

Step-by-step explanation:

11.07 pt = mL can i have help

Answers

Answer:

6290.652

Step-by-step explanation:

Volume

11.07   Pint

=   6290.652  Milliliter

Formula

for an approximate result, multiply the volume value by 568

i wish this is the ans ur looking for.......

If there are 640 football stickers needed to fill my book and I have 80% of the stickers
I need. How many more stickers do I need to collect?

Answers

Answer:

160 more stickers

Step-by-step explanation:

640 divided by 4 is 160

160 times 5 is 800

800 minus 640 is 160

you need 160 more stickers

160 more stickers the person above is Correct.

Given sin(30 degrees) =1/2 and cos (30 degrees) = square root of 3/2 use trigonometry identities to find the value of cot(30 degrees)

1/2
Square root of 3/3
Square root of 3/2
Square root of 3

Answers

Answer: D)[tex]\sqrt{3}[/tex]

Step-by-step explanation:

cot(θ) = cos(θ) ÷ sin(θ)

cot(30) = [tex]\frac{\sqrt{3} }{2}[/tex] ÷  [tex]\frac{1}{2}[/tex]

cot(30) = [tex]\sqrt{3}[/tex]

The value of cot30 is √3 if sin30 = 1/2 and cos30 = √3/2 option (D) is correct.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

sin30 = 1/2

cos30 = √3/2

As we know,

cotA = cosA/sinA

A = 30 degrees

cot30 = cos30/sin30

cot30 = (√3/2)/(1/2)

cot30 = √3

Thus, the value of cot30 is √3 if sin30 = 1/2 and cos30 = √3/2 option (D) is correct.

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3x² + 2x + 2 + 4x² + 5​

Answers

Answer:

7x^2 + 2x + 7

Hope this helps :)

Answer:

7x²+2x+7

Step-by-step explanation:

Hope this helps. Plz give brainliest.

-2(k+12)=2k + 16


Show work

Answers

Answer:

k=-10

Step-by-step explanation:

[tex] - 2k - 24 = 2k + 16[/tex]

[tex] - 2k - 2k = 16 + 24[/tex]

[tex] - 4k = 40[/tex]

[tex]k = 40 \div - 4 = - 10[/tex]

i think this is the answer

Pls help xdcdcdcdcdcd

Answers

Answer:

A

Step-by-step explanation:

YESYESYESYESYESx85

Plzzzzzzzz help right answer gets brainly

Answers

Answer:

20

Step-by-step explanation:

5k = 100

To figure out k, divide both sides by 5. Cancel out 5 from 5k, and you’re left with k=100/5
Simplify, and you’re left with k=20

Mrs.Manning is making cookies for the bake sale. She jas 3/4 cup of flour and needs 1/3 cup of flour for her chocolate chip cookies. What fraction of the flour Mrs.Manning has will be used for her chocolate chip cookies?

Answers

Answer:

The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9

Step-by-step explanation:

Fraction of Portion

Suppose we have a number n and another number m such as m>n. The portion or fraction of size n of m is given by the quotient n/m.

For example, 3 pieces of cake out of a total of 6 make them a fraction of 3/6 = 1/2 of the whole cake, i.e. half of the total available.

Mrs. Manning needs 1/3 cup of flour to make cookies for the bake sale. She actually has 3/4 cups of flour. Calculate the fraction of needed against the available flour:

[tex]\displaystyle \frac{\frac{1}{3}}{\frac{3}{4}}[/tex]

The division can be easier performed by multiplying by the reciprocal of the denominator:

[tex]\displaystyle \frac{1}{3}\cdot \frac{4}{3}=\frac{1*4}{3*3}[/tex]

[tex]\displaystyle =\frac{4}{9}[/tex]

The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9

Find and simplify as much as possible. Let f(x)=x^2+2 be for f(x+h)-f(x)/h

Answers

Answer:

In picture

Step-by-step explanation:

Use the given functions to set up and simplify

3x-2y=2
i always get mixed up in the final answer y=1 -3/2x 0r y= 1 +-3/2x ?

Answers

Answer:

Both answers are correct

Step-by-step explanation:

both y = 1 - 3/2x and y = 1 + -3/2x are correct answers, it is just that y= 1 - 3/2x is the simpler version. Adding a negative number is the same as subtracting a positive.

Answer:

y=3/2x-1

Reasoning:

-3x was negative initially, but dividing by -2 made it positive

1.6 Write the following numbers in order of size. Start with the smallest number.
0.5, 0.14, 0.092, 0.33​

Answers

0.092, 0.14, 0.33, 0.5

PLEASE HELP ME ANSWER THIS
What is cos 60?

Answers

Answer:

The angle with measure 60° is one of those angles that has a well-known cosine value: cos(60°) its C= 1/2.

Step-by-step explanation:

cos(60°) =[0; 2] and cos^2=[0; 4] so cos 60°=1/2

How long is 10:36 to 11:23​

Answers

Answer:

47 minutes

Step-by-step explanation:

Answer:

47 mins hope this helps

Step-by-step explanation:

simplify the following

-(3z)2

Answers

Answer:

-9x²

Step-by-step explanation:

-(3x)²

In PEMDAS, we solve the exponent first then multiply.

-(3x)²

-(9x²)

-9x²

Best of Luck!

Uisng the PEMDAS method of simplifying arithmetic expressions, the expression would be 9z²

Given the expression :

-(3z)²

This can be written as :

-3z × - 3z

Negative values will cancel out,

= 9z²

Therefore, the simplified form of the expression would be 9z²

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ASAP HELP PLEASE WILL GIVE BRAINLIEST

The perimeter of a rectangle
is 40 centimeters. The length of the rectangle can be represented by (2x + 1), and its width can be represented by (x - 5). What is the
length of this rectangle in centimeters?

Answers

Answer:

17cm

Step-by-step explanation:

equation:

[tex]2(2x + 1) + 2(x - 5) = 40 \\ x = 8 \\ [/tex]

substitute 8 into

[tex](2x + 1)[/tex]

[tex]2(8) + 1 = 17[/tex]

[tex]lenghth = 17cm[/tex]

Help!!!Geometry chapter three

Answers

Answer: 50

Step-by-step explanation:

3(50)-14=136

Solve. Enter your answer as an inequality.
4x + 5 < 5x + 3
w

Answers

Step-by-step explanation:

4x+5<5x+3

4x=-5<5x=-3

x=-5/4<x=-3/5

1.25<0.6

what is the number in scientific notation? ​0.000000000093 enter your answer in the box.​

Answers

Answer:

9.3 × 10^-11

Step-by-step explanation:

Which of the following sets represents the domain of the function shown?
{(2, 7}, (15, 13), (21,-4), (24, 18). {-4, 2, 7, 13, 15, 18, 21, 24}
{(7, 2), (13, 15), (-4, 21), (18, 24)}
{2, 15, 21, 24}
{-4, 7, 13, 18}

Answers

Answer:

(2, 15, 21, 24)

Step-by-step explanation:

Domain the x values

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Its goal is to rapidly prototype new discoveries, pas nonpla that might otherwise be dormant deep within the organization mber 2019, Labs launched Request for Application 3 (RFA 3), its third pitch competition, where more than 20,000 associates across the globe were i research, development, and genencs divisions of High-noon were asked to propose their innovative ideas for reimagining medicine To wcale and r with Plenbox, the top-ranked innovation management platform external link provider The Goal praten can be challenging for large organizations with groups spread across different locations, each with its own prorties and otinctives gho together associates from across the company via Planbox's platform, harness their knowledge and creativity, nurture co-creation, and ensure the best ideas could According to Aimee Reynolds, Genesis Labs Project Liaison, High-noon "We had nearly 4,000 people who checked out ideas on Planes and am 1.500 Panbox, we encouraged peychological safety with our colleagues who were willing to put themselves out there and propose what sometimes might som the pla The Results at Then w COVID During the two-month ideation phase, associates submitted ideas, commented on others, and shared them with people in the networks who might have 19 pand threw a sparver in the works, and the Genesis Labs team had to adapt the contest to accommodate changing cecumstances so the live pachowy hral v event Despite setbacks, the RFA 3 contest came to a successful conclusion with the selection of a handful of groundbreaking ideas for further devpent through Late 100 ideas received from colleagues in 11 countries comment-alt 467 Comments received MEGAPHONE - 1570 Associates who logged on and engaged with RFA 3 gem Define the Advantages of development of even-handed environment at High-noon? How would you relate the components of ETOIL in the given scenario? Which external event triggered innovation and proved advantageous results? hich external event triggered innovation and proved advantageous results?