Is there a similarity transformation that maps Triangle ABC to Triangle DEF? If so, identify the similarity transformation and write a similarity statement. Explain your answer.
Answers
Answer:
Yes, there is a similarity transformation that maps triangle ABC to Triangle DEF.
Step-by-step explanation:
Similarity transformation;
Triangle DEF has been transformed(dilated) by a factor of 2.
Since each dimension is twice that of the triangle ABC.
Two triangles are similar if their corresponding sides are congruent and corresponding angles are congruent.
Similarity statement:
ΔABC [tex]\sim[/tex] ΔDEF
these two triangles are similar because;
[tex]\frac{AB}{DE}= \frac{4}{8} = \frac{1}{2}[/tex]
[tex]\frac{AC}{DF}= \frac{4}{8} = \frac{1}{2}[/tex]
[tex]\frac{BC}{EF}= \frac{3}{6} = \frac{1}{2}[/tex]
⇒ [tex]\frac{AB}{DE}=\frac{AC}{DF} =\frac{BC}{EF}[/tex]
Yes, there is a similarity transformation that maps Triangle ABC to Triangle DEF.
To determine if two triangles are similar, one must check if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.
Let's denote the angles of Triangle ABC [tex]\(A\), \(B\), and \(C\),[/tex] and the angles of Triangle DEF as [tex]\(D\), \(E\), and \(F\),[/tex] respectively. Similarly, let's denote the sides opposite these angles as [tex]\(a\), \(b\), and \(c\)[/tex] for Triangle ABC, and [tex]\(d\), \(e\), and \(f\)[/tex] Triangle DEF.
For Triangle ABC and Triangle DEF to be similar, the following conditions must be met:
1. [tex]\(A = D\), \(B = E\), and \(C = F\)[/tex] (AA postulate for similarity).
2. [tex]\(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\)[/tex] (corresponding sides are in proportion).
If these conditions are satisfied, then there exists a similarity transformation that maps one triangle to the other. This transformation can be broken down into the following steps:
1. Dilation: To make the sides of Triangle ABC proportional to the sides of Triangle DEF, we perform a dilation. The scale factor k can be determined by the ratio of any pair of corresponding sides. For example, [tex]\(k = \frac{d}{a} = \frac{e}{b} = \frac{f}{c}\)[/tex]. This single scale factor should work for all three sides if the triangles are similar.
2. Rotation/Reflection (optional): If Triangle DEF is not oriented in the same direction as Triangle ABC, we may need to rotate or reflect Triangle ABC to align it with Triangle DEF. This does not affect the similarity.
3. Translation (optional): Finally, if Triangle DEF is not in the same position as Triangle ABC (but has the same orientation and size after the dilation), we perform a translation to move Triangle ABC to the position of Triangle DEF.
Since the angles are preserved under dilation, rotation, and translation, and the sides are made proportional by the dilation, the similarity transformation is complete.
If the corresponding angles are equal and the corresponding sides are in proportion, then the two triangles are similar, and a similarity transformation exists that maps one to the other. The similarity statement captures this relationship, indicating that the triangles are similar to the AA postulate and the sides are in proportion.
Related Questions
Which of the following options best describes an algebraic fraction?
Select all that apply.
common denominators
a variable in the numerator
a variable in the denominator
a variable with an exponent
Answers
Answer:
Common denominators
A variable in the numerator
A variable in the denominator
Step-by-step explanation:
Note: An an algebraic fraction is the fraction that has some algebraic expression in numerator and some algebraic expression in denominator.
So, if fractions would have common denominators, a variable in the numerator or a variable in the denominator would be an algebraic fraction.
Therefore, following options best describes an algebraic fraction:
common denominatorsa variable in the numeratora variable in the denominatorsolve the inequality. graph your solution |x|>5
Answers
[tex]|x|>5\iff x>5\ \vee\ x<-5[/tex]
Factor the expression. d2 − 4d + 4
Answers
Rewrite it in the form a^2 - 2ab + b^2, where a = d and b = 2
d^2 - 2(d)(2) + 2^2
Use the Square of Difference: (a - b)^2 = a^2 - 2ab + b^2
(d - 2)^2
Answer:
(d - 2)²
Step-by-step explanation:
d² - 4d + 4 ← is a perfect square of the form
(x ± a )² = x² ± 2ax + a²
compare coefficients of like terms
- 2a = - 4 ⇒ a = 2 and a² = 4, hence
d² - 4d + 4 = (d - 2)²
The value of the digit 4 in 24, 601 is how many times greater then the value digit 4 in 437
Answers
Answer:
The Answer is 10 times as much.
Step-by-step explanation:
We know that the 4 in 24,601 is 4000. We also know that the 4 in 437 is 400. If we do 4000/400, we get 10 times as much!
I hope this helps.
What is the proportion of 19/12 = f/9
Answers
Answer:
Alright well solve for f by cross multiplying
Exact form: f = 57/4
Decimal form: f = 14.25 Hope this helps have a nice day :)
Step-by-step explanation:
Which explains whether or not the values in the table represent a direct variation? x 4 6 10 20 y 1 1.5 2.5 5 The table represents a direct variation because the values are proportional. The table represents a direct variation because the values are nonproportional. The table does not represent a direct variation because the values are proportional. The table does not represent a direct variation because the values are nonproportional.
Answers
Answer:
Option A is correct.
The table represents a direct variation because the values are proportional.
Step-by-step explanation:
The direct variation says that:
[tex]y \propto x[/tex]
then; the equation is of the form : [tex]y =kx[/tex] where k is the Constant of Variation.
Consider any values of x and y from the table, to solve for k;
Let x = 10 and y = 2.5
then;
[tex]2.5 = 10k[/tex]
Divide both sides by 10 we have;
[tex]k = \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4}[/tex]
Then the equation becomes:
[tex]y =\frac{1}{4}x[/tex]
Therefore, the table represents a direct variation because the values are proportional.
Answer: A The table represents a direct variation because the values are proportional.
Step-by-step explanation:
Can anyone help me plz ?? Lakita has 66 water bottles for the 5K race participants. In addition, she is planning to buy boxes of water bottles that have 12 water bottles each. All of the boxes cost the same. Lakita can buy up to 5 boxes of water bottles given the amount of money she has.Write a function to describe how many water bottles will Lakita buy.Find a reasonable domain and range for the function.
Answers
Answer:
65,81,97,113,129
Step-by-step explanation:
she has 65 water bottles and she is buying boxes of water bottles (x) that hold 16 water bottles each. She can only buy up to 5 water bottles.
f(x) = 16x + 65...where f(x) = total water bottles and x = number of boxes
x < = 5 here is ur restriction
the range is ur f(x) values which represent the total number of water bottles...keep in mind, she can only buy 5. Therefore, the numbers that can be subbing in for x are 0 thru 5.
So when subbing in 0 thru 5 for x, the results for f(x) are :
{ 65,81,97,113,129 }
What is the simplified form of (−7x3 + 5x2 − x + 6) − (−8x3 + x2 + 3)?
A. −x3 + 4x2 − x + 3
B. x3 + 4x2 − x + 3
C. x3 − 4x2 − x − 3
D. −15x3 + 6x2 − x + 9
Answers
Answer:
B. x3 + 4x2 − x + 3
Step-by-step explanation:
(−7x^3 + 5x^2 − x + 6) − (−8x^3 + x^2 + 3)
Distribute the negative sign
(−7x^3 + 5x^2 − x + 6) + (8x^3 - x^2 - 3)
I like to line them up vertically.
−7x^3 + 5x^2 − x + 6
8x^3 - x^2 - 3
----------------------------------
x^3 +4x^2 -x +3
The simplified form of the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3) is x³ + 4x² – x + 3, corresponding to option B.
To simplify the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3), we need to remove the parentheses and then combine like terms.
First, distribute the negative sign through the second set of parentheses: –7x³ + 5x² – x + 6 + 8x³ – x² – 3.
Next, combine like terms: (–7x³ + 8x³) + (5x² – x²) – x + (6 – 3).
This simplifies to x³ + 4x² – x + 3.
So, the correct simplified form of the expression is option B. x³ + 4x² – x + 3.
Rewrite the following expression using the associative property
(4x+9x)+12x
Answers
Answer is 4x+(9x+12x)
There is a café at the park.
It is 13 metres long and 8 metres wide. What is the area of the café?
Answers
Answer:
42 meters
Step-by-step explanation:
because 13 + 13 + 8 + 8 = 42. and that's your answer
Final answer:
The area of the café is calculated by multiplying the length (13 meters) by the width (8 meters), resulting in an area of 104 square meters (104 m²).
Explanation:
The area of the café at the park can be calculated using the formula for the area of a rectangle, which is the product of its length and width. Given that the café is 13 meters long and 8 meters wide, we multiply these two dimensions to find the area.
Step-by-Step Calculation
Identify the length (13 meters) and the width (8 meters) of the rectangle.
Multiply the length by the width: Area = length × width.
Calculate: 13 meters × 8 meters = 104 square meters (104 m²).
Therefore, the area of the café is 104 m².
In Maria's store, the customer count this week is 3000. Maria is planning a promotion and expects a 5% increase in customers next week. How many additional customers is Maria expecting?
Answers
Answer:
150
Step-by-step explanation:
3000 * 0.05 = 150
What percent is equivalent to 18/40 ?
18%
22%
40%
45%
Answers
Answer:
45%
Step-by-step explanation:
You do 18 divided by 40
Which is .45
At a farm, Justin picks 3 bushels of fruit. The bushels weigh 8 1/4 pounds, 6 1/2 pounds and 6 5/8 pounds. What is the average weight per bushel .
Answers
Answer:
The average weight is 7 1/8 pounds
Step-by-step explanation:
To find the average, we add them up and then divide by how many
average = (b1+b2+b3)/3
= (8 1/4 + 6 1/2+ 6 5/8) /3
Let look at the sum
(8 1/4 + 6 1/2+ 6 5/8)
We need to get a common denominator of 8
8 1/4 *2/2 + 6 1/2 *4/4 + 6 5/8
8 2/8 + 6 4/8 + 6 5/8
20 11/8
20 + 1 3/8
21 3/8
average = (21 3/8) /3
Now we divide by 3
We need to change the mixed number to an improper fraction
21 3/8 = (8*21+3) /8 = 171/8
average = (171/8) /3
We can use copy dot flip
171/8 * 1/3
171/24
We need to change it back to a mixed number
24 goes into 171 7 times with 3 left over
7 3/8
7 1/8
The scoop Shop sells many types of nuts. Lily asks for this mix:
1/2 pound peanuts
1/6 pound hazelnuts
1/3 pound almonds
3/4 pound cashews
1/4 pound pecans
What fraction of the mix does each nut represent
What fraction of the mix does each type of nut represent?
How to do?
Answers
Answer:
1/12 = 24/12 = 2
pea: 12/24
haz: 4/24
alm: 8/24
cash: 18/24
pec: 6/24
how to do it: find a common denominator, or write it how and scan it with photo math and it will show you how to work it out!
hope this helped or was right, thanks <3
-7n+4(-6+3n) what is the answer
Answers
Answer:
5n - 24
Step-by-step explanation:
distribute the parenthesis by 4
= - 7n - 24 + 12n ← collect like terms
= (- 7n + 12n) - 24 = 5n - 24
Answer:
5n-24
Step-by-step explanation:
-7n+4(-6+3n)
Distribute:-7n-24+12n
Simplify: 5n-24
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answers
Answer:
The helicopter still needs to fly up sec 17.0886 at maximum speed.
Step-by-step explanation:
To find out how far the helicopter went down do 100(seconds) * 10.5 and get 1050
Then how much he traveled back up same thing 150 (seconds) * 5.2 and get 780
Next find the difference 780-1050 and get -270 ft it is negative because it is still BELOW GROUND ( That's how you know if it need to fly up or down)
Last to find how many seconds you need you work backwards so instead of multiplying you do the opposite witch is dividing so you take your feet (270) and divide by the maximum speed (15.8). 270/15.8 is 17.08
Chris need a graphing calculator for math class c find a $60 model on sale for 15% off if you decide to buy this calculator how much will the sale price be
A)9
B)12
C)51
D)69
Answers
Answer:
C) $51
Step-by-step explanation:
Step 1. Calculate the discount
The discount is 15 % of $60
Discount = 60 × 0.15
Discount = $9
===============
Step 2. Calculate the sale price
Sale price = original price - discount
Sale price = 60 - 9
Sale price = $51
The sale price will be $51.
Eliot made a line plot to record the number of birds he saw at his bird feeder .How many more sparrows than blue jays did he see?If you help me answer the question correctly I will give you 48 points and mark u BRAINLIEST
Answers
Answer:
He saw 4 more
Step-by-step explanation:
There were 5 sparrows and 1 blue jay 5 - 1 = 4
we found that out by this equation: 5-1=4
hope i helped :)
i dont know can you help?
Answers
Answer:
84
Step-by-step explanation:
42x2=84
multiply 2 with 42 which comes out as 84
Elizabeth received a car loan for $12,000. She was charged 8% for the bank fees. What is the total amount that she will need to pay the bank back for the loan?
A.
$860
B.
$960
C.
$11,040
D.
$12,960
Answers
Answer:
B
Step-by-step explanation:
If you do 12,000 - 92% it gives you 960 and the 92% is = 11,040
Solve the equation -18=p/2?
Answers
Answer:
p=-36
Step-by-step explanation:
-18=p/2
______________________
Multiply both sides by 2
-18(2)= p/2 (2)
______________________
-36 = p
switch the sides of the equation
______________________
p=-36
in the equation
[tex] - 18 = p \div 2[/tex]
you want to make 'p' alone so,
move 2 by the opposite of division,
Multiplcation
[tex] - 18 \times 2 = - 36[/tex]
so
[tex]p = - 36[/tex]
I hope I was able to help you
what scale factor was used in dilation
Answers
Answer: (c) [tex]\bold{\dfrac{3}{4}}[/tex]
Step-by-step explanation:
Chooe any point I am choosing point W.
The W' is closer to C than W so the dilation is less than 1
The only answer choice that is less than 1 is option c.
Why is this the answer? because the side lengths are proportional
[tex]\dfrac{CW'}{CW} = \dfrac{WX'}{WX}= \dfrac{3}{4}[/tex]
The perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm. Find the length of the other diagonal and area of the rhombus
Answers
Hi there! :)
Answer:
Length of the second diagonal: 54 cm
Area of the rhombus: 1,944 cm²
Step-by-step explanation:
1) To find the value of the second diagonal, you first need to know some important properties of rhombuses:
Since the perimeter is 180, and by definition a rhombus has four congruent sides (of equal length), each side length of the rhombus is equal to 45.
The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to half the lengths of the diagonals. In this case one hypotenuse would be equal to 45 and one leg would be equal to 36 (72 ÷ 2 = 36).
We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:
c² = a² + b² → Where "c" is the hypotenus & "a" and "b" are the two other sides.
45² = 36² + b² → Where "b" is the half of the unknown diagonal.
We can now solve this equation for "b":
45² = 36² + b²
45² = 2,025
36² = 1,296
2,025 = 1,296 + b²
Subtract "1,296" from each side of the equation → 2,025 - 1,296 = 729
729 = b²
Square root on each side of the equation → √729 = 27
27 = b
Since "b" represents half of the unknown diagonal, we need to multiply by 2 to find the full length of the diagonal:
27 × 2 = 54 ⇒ Length of the other diagonal.
2) To find the area of the rhombus, you need to multiply the length of the 2 diagonals and divide the answer by 2:
(72 × 54) ÷ 2 = A
Multiply "72" & "54" together → 72 × 54 = 3,888
3,888 ÷ 2 = A
1,944 = A
There you go! I really hope this helped, if there's anything just let me know! :)
What's the lateral area of a right cylinder if the radius of the base is 12mm and the altitude of the cylinder is 5 times the base radius? Use the π key to calculate and round your answer to the nearest whole number.
Answers
Answer:
1440π squared mm.
Step-by-step explanation:
Given is the radius of base of cylinder, r = 12mm.
The altitude is five times the base radius, h = 5 times 12mm = 60mm.
The lateral area of the cylinder is the curved surface area of the cylinder.
The formula for curved surface area of cylinder is as follows:-
Curved Surface Area = Circumference of base x altitude of cylinder.
SA = 2πrh = 2π•12•60 = 1440π sq. mm.
Hence, Lateral area of cylinder is 1440π squared mm.
Answer:
1440π
Step-by-step explanation:
We are given the radius of the base of a right cylinder to be 12 mm and its altitude or height to be 5 times the base radius which is equal to (12 x 5) = 60 mm.
We know the formula for the lateral area of a right cylinder:
[tex]A = 2\pi rh[/tex]
So putting in the given values with [tex]\pi[/tex] as it is to get:
[tex]A=2\pi *12*60[/tex]
[tex]A=2(720)\pi[/tex]
[tex]A=1440\pi[/tex]
Therefore, the lateral area of this right cylinder is 1440π.
Ben made a model that was 5 3/4 inches tall. Laquisha made a model that was 70 11/12 inches tall. How many times as tall was Laquisha’s model?
Answers
To determine how many times taller Laquisha's model is compared to Ben's model, convert their heights to improper fractions and divide, simplifying the result to find the ratio.
Explanation:To find out how many times taller Laquisha's model is compared to Ben's model, we divide their heights. Laquisha's model height is
70 11/12 inches, and Ben's model height is 5 3/4 inches. First, convert the mixed numbers to improper fractions. Ben's height as an improper fraction is 23/4 inches. Laquisha's height as an improper fraction is 851/12 inches. Next, divide Laquisha's model by Ben's: (851/12)
÷ (23/4). To divide fractions, we multiply by the reciprocal of the second fraction: (851/12)
× (4/23). Simplify to find the ratio, which represents how many times taller Laquisha's model is.
A particular computer takes 13-minutes to download a 52-minute TV show. How long will it take the computer to download a 1.5-hour movie?
Answers
The particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
Explanation:In this particular problem, we need to figure out how long a computer will take to download a movie. The computer in question takes 13 minutes to download a 52 minute TV-show, establishing a rate of downloading. We can therefore calculate how long the computer takes to download a minute of TV-show by dividing the download time by the length of the show: 13/52 = 0.25 minutes per minute of show. Next, we convert 1.5 hours (the length of the movie) into minutes, because our rate is in terms of minutes: 1.5*60 = 90 minutes. We then multiply this by our download rate (0.25) to get our answer: 90*0.25 = 22.5 minutes. Thus, this particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
Learn more about Calculating Download Time here:https://brainly.com/question/33722206
#SPJ2
PLEASE HELP ASAP
Approximately how many times greater is 5 x 10 to the eighth power than 8 x 10 to the fifth power?
Answers
Answer:
about 11920.92896
Step-by-step explanation:
There are 38 cube houses with 1000 unit cubes that are 1 meter by 1 meter by 1 meter discribe the dimensions of a cube house using unit cubes
Answers
Which phrase should be inserted on the line to make a true statement
Answers
Answer:
[tex]\frac{8}{12}[/tex] equal to [tex]\frac{8}{12}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ------------------------- [tex]\frac{8}{12}[/tex]
Lets compare both the fractions
To compare both the fractions the denominators should be same
Lets make the denominators same
WE try to get 12 in the denominator of first fraction, so we multiply top and bottom by 4
[tex]\frac{2*4}{3*4}=\frac{8}{12}[/tex]
[tex]\frac{8}{12}[/tex] ------------------------- [tex]\frac{8}{12}[/tex]
Both fractions are equal
So [tex]\frac{8}{12}[/tex] equal to [tex]\frac{8}{12}[/tex]
Tim answered all the questions on his math test but got 10 answers wrong . He revived 4 points for every correct answer , and there was no penalty for wrong answers . His score was 76 points .
Write an equation to determine the total number of question (q) on Tim’s math test .
Answers
76 points/ 4 points per questions means he answered 19 questions correctly
plus the 10 he answered incorrectly
76/4+10=x
19+10=x
29=x