triangle ABC undergoes a series of transformations to result in Triangle DF is triangle DEF congruent to triangle ABC
Answers
Since, translation and rotation both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.
Thus, here ΔABC is congruent to ΔDEF.
Triangle ABC is reflected over x axis ,and then translated 6 units down to form triangle DEF.Since, translation and reflection both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.
Thus, here ΔABC is congruent to ΔDEF.
Triangle ABC is rotated 180°, and then dilated by a scale factor of 3 to form triangle DEF.Here rotation is a rigid transformation which maps only congruent images but dilation is not a rigid transformation because it produces similar images for scale factor other than 1 (with scale factor 1 it also produce congruent images) .
Thus, here ΔABC is not congruent to ΔDEF.
The determination of congruency between Triangle DEF and Triangle ABC depends on the nature of the transformations applied to Triangle ABC. If these transformations are rigid motions, then Triangle DEF will be congruent to Triangle ABC.
Explanation:The question concerns whether Triangle DEF is congruent to Triangle ABC after undergoing a series of transformations. Congruent triangles are those that are identical in terms of size and shape, meaning their corresponding sides and angles are equal.
According to the given information, to determine congruency, we must consider the properties of the transformations involved. If the transformations applied to Triangle ABC are rigid motions (such as rotation, reflection, or translation), which do not alter the shape or size of figures, then Triangle DEF will be congruent to Triangle ABC. If however, the transformations include dilation or other non-rigid transformations that change the size but not the shape, Triangle DEF would not be congruent, although it could be similar to Triangle ABC.
Since the question provided involves linear transformations that transform lines into lines and take parallel lines to parallel lines, it is likely referring to rigid motions. Therefore, it suggests that Triangle DEF should be congruent to Triangle ABC, assuming that the series of transformations includes only those that preserve lengths and angles.
Related Questions
PLEASE HELP QUICK
Which question can best be answered by finding the volume of a figure?
A)How much gas is needed to fill a gas tank?
B)How much wrapping paper is needed to cover a prism?
C)How much wood is needed to frame a window?
D)How much material is needed to line a garden with a sheet of weed-blocking material?
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Hope this helps
~ Jordan ~
Harry's Health club costs $20 per month plus a $75 membership fee. Fiona's fitness costs $35 per month. What is the dollar amount at the break even point?
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First, we need to set up an equation for each plan.
Harry's Health Club can be y = 20x + 75 because it starts at 75 and increase 20 per month.
Fiona's Fitness can be just y = 35x because it is just 35 per month.
Set the equation equal to each other and solve.
20x + 75 = 35x
75 = 15x
5 = x
What is the value of x^2 + 4 for x = 5?
Answers
A probability experiment is conducted wich of these can not be considered a probability of an outcome: a) 0.222 b) 8.2% c) 0.0234 d) 122.96% e) 5/3 f) 0.45%
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122.96% and 5/3 cannot be considered probabilities of outcomes in a probability experiment because they are greater than 1. Correct option is d and e.
In probability, the probability of an outcome must be a value between 0 and 1, inclusive. Therefore, any value less than 0 or greater than 1 cannot be considered a probability of an outcome.
Let's check each option:
a) 0.222 - This is a valid probability since it is between 0 and 1.
b) 8.2% - This can be converted to a decimal as 0.082, which is a valid probability since it is between 0 and 1.
c) 0.0234 - This is a valid probability since it is between 0 and 1.
d) 122.96% - This can be converted to a decimal as 1.2296, which is not a valid probability since it is greater than 1.
e) 5/3 - This can be simplified to approximately 1.6667, which is not a valid probability since it is greater than 1.
f) 0.45% - This can be converted to a decimal as 0.0045, which is a valid probability since it is between 0 and 1.
Therefore, options (d) 122.96% and (e) 5/3 cannot be considered probabilities of outcomes in a probability experiment because they are greater than 1. The other options are valid probabilities as they fall within the range of 0 to 1, inclusive.
To know more about probability:
https://brainly.com/question/29262621
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Natalie worked during the summer for 12 weeks at an amusement park. She earned a salary and put 30% of her earnings into savings. At the end of the summer, her savings were a total of $486. How much was she paid every month (4 weeks)? Help please
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162/3=54
54x10=540
$540 every 4 weeks
Five years ago the population of Australia was 23.13 million. It has grown by 870 000. What is the population of Australia now?
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The current population of Australia is 24 million.
It is given to us that the initial population was 23.13 million and the population 5 year later has grown by 870000 or 0.87 million. Thus to find the current population we simply need to add the initial population and the growth that has happened in 5 years. This gives us:
[tex]Current\ population = 23.13\ million + 0.87\ million = 24\ million[/tex]
Thus, the current population of Australia is 24 million.
Must a decimal divisor and a decimal dividend have the same number of decimal places in order to have a whole number quotient? write a division equation using two decimal numbers to support your answer.
Answers
https://brainly.com/question/9153852
What is the solution to the system of equations?
3x - 4y= 16
2x + 3y=5
A. (-4,1)
B. (4,-1)
C.(-4,-1)
D.(4,1)
Answers
Hope this helps!
Answer:
B: (4, –1)
Step-by-step explanation:
Which relationship between x and y in the equation shows a proportional relationship y=12x y=12/x y=2x+6 y=x/2+3
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_____
y = 12/x is an inverse relationship
y = 2x+6
y = x/2 +3 are both linear relationships, but not proportional relationships.
Madeline sold $167 worth of items at a garage sale and then received her $232 paycheck. Estimate how much money she now has by rounding to the nearest ten first and then adding the rounded numbers.
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Madeline has approximately $400 after rounding her garage sale earnings and paycheck to the nearest ten and adding them together.
The question involves estimating the total amount of money Madeline has after selling items at a garage sale and receiving her paycheck. To estimate the total amount, we need to round each amount to the nearest ten and then add the rounded numbers together.
First, round $167 to the nearest ten, which is $170.
Next, round $232 to the nearest ten, which is $230.
Finally, add the rounded numbers: $170 + $230 = $400.
PLZ HELP!!!!!! (WILL GIVE BRAINLIEST!!!!)
Answers
Alison is currently three times as old as Mike. 5 years ago, Alison was eight times as old as Mike. How old is Alison now?
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Joel is looking at costs for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per month plus $4 per visit. How many visits would he have to make each month to make the $50 per month unlimited use option the cheapest one?
Answers
[tex]y = 4x + 12[/tex]
Joel would have to go at least 10 times per month to make the 50 dollars per month the cheapest one.
Answer:
First choice is cheaper.
Step-by-step explanation:
Joel could pay $50 per month for unlimited use or he could pay $12 per month plus $4 per visit.
Let the monthly visits be x
We can define this as :
[tex]12+4x> 50[/tex]
[tex]4x >50-12[/tex]
[tex]4x >38[/tex]
[tex]x> 9.5[/tex]
So, x can be greater than 9.5 means 10.
[tex]4(10)+12>50[/tex]
[tex]52 > 50[/tex]
Comparing both we can say that the first choice is cheaper.
all books in a store are being discounted by 30 percent
part a: let x represent the regular price of any book in the store.write an equation that can be used to find the sale price of any book in the store.
Jerome bought a book on sale at the store. the sale price of the book was $ 8.96.
part b: solve the equation to find the regular price of the book to the nearest cent.
Answers
The regular price of $8.96 should be 11.65.
I need to know the area of the shape base 1 (27ft) base 2(34ft) Height (12ft)
Answers
.. A = (1/2)*(b₁ +b₂)h
Use it.
.. A = (1/2)*(27 ft +34 ft)*(12 ft)
.. = (1/2)*(61 ft)*(12 ft)
.. = (30.5 ft)*(12 ft)
.. = 366 ft²
find the separate equations form the lins represented by 3x^2 + 10xy + 8y^2 + 14x + 22y + 15
Answers
3x^2 is factorable only as 3x and x.
15 can be 15 * 1 or 3 * 5.
As a first guess, I place 5 and 3 in that order.
The coefficients of y are unknown so far.
= (3x + Ay + 5)(x + By + 3)
= 3x^2 + 3Bxy + 9x + Axy + ABy^2 + 3Ay + 5x + 5By + 15
(3B + A)xy = 10xy
(3A + 5B)y = 22y
A + 3B = 10
3A + 5B = 22
-3A - 9B = -30
3A + 5B = 22
4B = 8
B = 2
A + 3B = 10
A + 6 = 10
A = 4
3x^2 + 10xy + 8y^2 + 14x + 22y + 15 = (3x + 4y + 5)(x + 2y + 3)
The product of (3x + 4y + 5)(x + 2y + 3) is indeed
3x^2 + 10xy + 8y^2 + 14x + 22y + 15
The lines are
3x + 4y + 5 = 0
x + 2y + 3 = 0
sorry.. I didn't know where else to send dis...(+_+)
Helppp!!!! I’m not sure what this is...
Answers
.. Atrapezoid = (1/2)(b1 +b2)h
.. = (1/2)(12 in + 8 in)*(8 in)
.. = 80 in^2
The remaining faces unroll into a rectangle 8 in wide and (12 +8 +8+9) in long. The area of a rectangle is the product of its length and width.
.. Arectangle = length*width
.. = (37 in)*(8 in) = 296 in^2
The total surface area is the sum of the rectangle area and the two trapezoidal faces.
.. Atotal = Arectangle + 2*Atrapezoid
.. = 296 in^2 +2*80 in^2
.. = 456 in^2
The 1st selection is appropriate.
write the rule for the pattern 1,5,9,13,17
Answers
Someone please help
Answers
9-6 = 3
answer would be 4k^3
i really need help. thanks
Answers
S = √3*73.5 /4.5=7 (Khufu’s pyramid)
The volume of Khafre’s pyramid is about 9/10 the volume of Khufu’s pyramid. If Kristina wants to make the second model pyramid so its volume is 9/10 the volume of the first model pyramid, what volume should she make the second model pyramid?
This goes with the other questions! if you need information i can get that for you!
Also, could you work it out!
Answers
3/6 should b you answer answer
Final answer:
The volume will be of 6.3 for the second model.
Explanation:
The student is asked to calculate the volume of the second model pyramid, Khafre's pyramid, which is 9/10 the volume of the first model, Khufu's pyramid. The student has already calculated that, for Khufu's pyramid, S = √3*73.5/4.5=7. To find the volume Kristina should make the second model, we simply multiply the volume of the first model by 9/10.
Although the question does not provide the exact volume of the first model, we will assume the value of S given is the volume of Khufu's pyramid model. Therefore, the volume of Khafre's pyramid model should be 7 * (9/10) = 6.3.
This result is based on the proportion given between the two pyramids' volumes and is a straightforward calculation of this proportion.
The sum of Emil’s and Rosa’s ages is 27 years. Nine years ago Emil was twice as old
as Rosa was then. How old is each person?
Answers
e - 9 = 2 x ( r - 9 );
So, e = 27 - r;
Then, 27 -r - 9 = 2r - 18;
18 - r = 2r - 18;
18 + 18 = 2r + r;
36 = 3r
Finally, r = 12 years (Rosa);
e = 27 - 12;
e = 15 years (Emil);
A recipe calls for 1/4 teaspoon of shortening for every 2/3 cup of milk. What is the unit rate of cups per teaspoon? Explain
Answers
To find the rate for a whole teaspoon, multiply 2/3 by 4 to get 8/3, or 2 2/3.
So, the rate is 2 2/3 cups of shortening per teaspoon.
Hope this helps!
His train has been running for 2 1/2 Days straight at a constant speed of 4.8 mph. How far has he traveled?
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Please help me 4and 5
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A square pyramid and a cube have the same volume if the length of each side of the base of the square pyramid is 2 cm in the height of the cube is 4 cm what is the height of the pyramid
a 8cm
b 16cm
c 24cm
d 48 cm
Answers
Vol cube = s^3
since height of cube is 4, that height = s
V = (4)^3 = 64 cubic cm
now since their Vs are the same,
1/3×s^2×h = 64
they said length of side in square pyramid
was 2, then:
1/3×(2)^2×h = 64
1/3×4×h = 64
4/3 h = 64
h = 64×3/4 = 16×3 = 48 cm
D) is the correct answer
a circular rug is 6 feet in diameter. binding for the edge costs $1.50 per yard. what will it cost to bind the rug? justify your answer
Answers
d = diameter length
C = πd
How many yards in 6 feet?
1 yard = 3 feet
So, 2 yards = 6 feet
C = π(2 yards)
C = 2π yards
Each yard is $1.50.
So, what do you think we do next?
Can you finish?
Find the area of the trapezoid.
A) 38.75 in2
B) 77.5 in2
C) 155 in2
D) 198 in2
Answers
To solve this add the two lengths. . .
22 + 9 = 31
Multiply the height and the total. . .
31 x 5 = 155
Divide 155 and 2 . . .
155 divided by 2 = 77.5 <------
The correct answer to your question is option B.
Hope this helps you.
Have a great day!
Answer: The answer is b) 77.5
Step-by-step explanation:
hope i helped
Roger served 5/8 pound of cracker wich was 2/3 of the entire box what was the weight of the crackers originally in the box
Answers
original weight of the box = 15 / 16 pounds
Explanation:
Assume that the original amount in the box is x.
We are given that:
5/8 pounds represent 2/3 of the total amount (x).
This can be translated into the following equation:
(2/3) x = 5 / 8
Now, we will solve for x as follows:
(2/3) x = 5 / 8
Multiply both sides by 24 to get rid of the denominators as follows:
(2/3) x * 24 = (5 / 8) * 24
16 x = 15
Divide both sides by 16 to isolate the x as follows:
x = 15 / 16 pounds
Hope this helps :)
The original weight of the crackers in the box is 15/16 pound.
The question asks us to determine the original weight of a box of crackers, given that 5/8 pound of crackers was served, which was 2/3 of the entire box.
We can set up the proportion by stating that 5/8 pound represents 2/3 of the whole, so let's represent the total weight of the crackers with the variable 'w'. The equation to represent this situation is (5/8) pound = (2/3) * w.
To solve for 'w', we'll multiply both sides of the equation by the reciprocal of 2/3, which is 3/2:
(5/8) * (3/2) = w
Simplifying this equation gives us the total weight:
(5 * 3) / (8 * 2) = w
15 / 16 = w
w = 15/16 pound, which is the original weight of the crackers in the box.
if g(x) equals 4x + 5, which statement is true? Select the correct answer.
Answers
Hey l need summ more info just email me and we can get this done