ΔABC is similar to ΔDEF. The ratio of the length of AB to the length of DE is 2:1. Which ratio is also equal to 2:1?
Answers
Answer:
4)
Step-by-step explanation:
When triangles are similar, their corresponding angles are congruent. So, it is not 1) and 2).
Areas ratio is squared to ratio of their sides, so it is not 3).
Perimeter is sum of the sides. All corresponding sides in similar triangles have the same ratio. So, answer is 4).
The ratio \(\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}\) is also equal to 2:1
What are similar triangles?"Two triangles are similar when their corresponding sides are in proportion to each other and corresponding angles are equal."
What is ratio?"It is the comparison of two quantities of the same kind."
For given question,
ΔABC is similar to ΔDEF.
⇒ \(\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}\)
And ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
We know, if two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
⇒ \(\frac{area~of~\Delta {ABC}}{area~of~\Delta DE F} =(\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{AC}{DF})^2\)
We know, the perimeters of the similar triangles are in the same ratio as the sides.
\(\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}\)
The ratio of the length of AB to the length of DE is 2:1
\(\Rightarrow \frac{AB}{DE} = \frac{2}{1}\)
\(\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{2}{1}\)
Therefore, the ratio \(\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}\) is also equal to 2:1
Learn more about similar triangles here:
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Related Questions
Find each probability.
Answers
Answer:
5,9
Step-by-step explanation:
I think row A would be 5 and B would be 9 im sorry if im wrong
5 on top 9 on bottom
If you connect points W and X, What would be the distance between the two points?
*Hint draw the legs
Answers
Answer:
\(\displaystyle d = 12\sqrt{2}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a Cartesian graphCoordinates (x, y)Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²Algebra II
Distance Formula: \(\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Step-by-step explanation:
*Note: The Distance Formula is derived from the Pythagorean Theorem
Step 1: Define
Point W(-6, 4)
Point X(6, -8)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [DF]: \(\displaystyle d = \sqrt{(6--6)^2+(-8-4)^2}\)(Parenthesis) Simplify: \(\displaystyle d = \sqrt{(6+6)^2+(-8-4)^2}\)(Parenthesis) Add/Subtract: \(\displaystyle d = \sqrt{(12)^2+(-12)^2}\)[√Radical] Exponents: \(\displaystyle d = \sqrt{144 + 144}\)[√Radical] Add: \(\displaystyle d = \sqrt{288}\)[√Radical] Simplify: \(\displaystyle d = 12\sqrt{2}\)Select all the expressions that are equivalent to 16x + 36.
a 16(x + 20)
b. x(16+36)
C. 4(4x + 9)
d. 2(8x + 18)
e. 2(8x + 36)
Answers
Answer:
2(8x + 18) and 4(4x + 9)
Step-by-step explanation:
16 and 36 are both evenly divisible by 2 and 4. Thus, possible equivalents of 16x + 36 are 2(8x + 18) and 4(4x + 9).
Expressions equivalent to 16x + 36 are 4(4x+9) and 2(8x + 18).
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
Given expression
16x + 36
= 4.4x + 4.9
16x + 36 = 4(4x+9)
= 2.2(4x + 9)
16x + 36 = 2(8x + 18)
Hence, 4(4x+9) and 2(8x + 18) are equivalent to 16x + 36.
Learn more about expression here:
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TRY beating an answer expert! If 20 articles cost ? 90, then the cost of 9 articles is ?
? 45
? 4.50
? 40.50
? 42
Answers
Answer:
C) $40.50
Step-by-step explanation:
It is given to you that 20 articles cost $90. Find the unit cost of the articles. Divide the total cost of the articles with the amount of articles there are:
$90/(20 articles) = $4.50/article.
Each article costs $4.50 each.
Next, find the cost of 9 articles. Multiply the total amount of articles with the unit cost:
4.50 x 9 = 40.50
C) $40.50 is your answer.
~
C
Darcy likes to eat peanut butter and raisins on apple slices. On each apple slice, she puts 1/16 cup of peanut butter and 8 raisins. Darcy has 2/5 cups of peanut butter and 80 raisins. She eats a whole number of apple slices until the peanut butter is all gone. What fraction of the 80 raisins did she eat? Enter the fraction in the response box.
Answers
Good morning and night. Can anyone help me on this question?
I'm stuck on this question for khan that I need to master.
Answers
Answer:
X = Y x 3
Step-by-step explanation:
In the table, we can look at 5 and 15 as well as 11 and 33 and easilly tell that it has a correlation of tripling the number. To check our answer, all we must do is 8 1/3 x 3 and end up with 25
Answer:
→ y = 3x because 15 divided by 5 equals 3, 25 divided by 8 1/3 equals 3 and 33 divided by 11 equal 33 ( I hope you have a good day or night! and I also hope you get you homework correct as well:))))).
Two circles are drawn below. The diameter of the smaller circle is the radius of the larger circle. What is the ratio of the smaller circle's circumference to the larger circle's circumference?
Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers.
Answers
1:2????
so basically the smaller circle is 50% of the larger circle being 1/2 of it??
(might be incorrect)
please help WILL GIVE BRAINLIEST!
Answers
Answer:
13 ish
Step-by-step explanation:
x is botem
y is top
Naomi surveyed some students to determine their favorite subject. The experimental probability of a student choosing math as their favorite subject is . If 16 of the students chose math as their favorite subject, what is most likely the number of students surveyed?
A. 112
B. 28
C. 21
D. 64
Answers
George solved the equation -103 = -2(-7x + 7) + 8x as follows:
-103 = -2(-7x + 7) + 8x
Step 1: -103 = 14x + 7 + 8x
Step 2: -103 = 22x + 7
Step 3: -110 = 22x
Step 4: -5 = x
At which step did he make an error?
Explain the error:
Answers
-103 = -2(-7x + 7) + 8x
-103 = 14x - 14 + 8x
-103 = 22x - 14
-89 = 22x
x = -4
Step 2: -103 = 22x - 14
Step 3: -117 = 22x
Step 4: -5.31818182 = x
A fruit juice recipe calls for 2 parts orange juice and 8 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 18 L of pineapple juice?
2 over 8 equals j over 18
8 over 2 equals j over 18
8 over j equals 2 over 18
16 over 18 equals j over 100
Answers
The correct proportion to use to find the amount of orange juice, j, needed to add to 18 L of pineapple juice is:
2/8 = j/18
This proportion relates the ratio of orange juice to pineapple juice in the recipe (2:8) to the amount of orange juice needed to add to 18 L of pineapple juice. By cross-multiplying, we can solve for j as follows:
2/8 = j/18
218 = 8j
36 = 8*j
j = 36/8
j = 4.5
Therefore, you would need to add 4.5 L of orange juice to 18 L of pineapple juice to create the fruit juice recipe that calls for a ratio of 2 parts orange juice to 8 parts pineapple juice.
Answer:
2 over 8 equals j over 18Step-by-step explanation
2 over 8 equals j over 18
This proportion represents the ratio of orange juice to pineapple juice in the recipe. By setting up the proportion, we can solve for the value of 'j,' which represents the amount of orange juice needed.
So, the correct proportion is:
2 over 8 equals j over 18
Pls help, will choose brainliest!
Answers
Answer:
$11
Step-by-step explanation:
February 14th is the 4th day after February 10th, so t=4 on the 14th. The price of pizza that day is ...
C(4) = 7 +4 = 11
The price of pizza on Valentine's Day is $11.
Now we look and use the second function because it has parameters 3 < t <= 8 and 4 is greater than 3 and less than or equal to 8. So our function is 7 + t for our price.
We plug in the 4 for our t and get 11$ (7 + (4))!
Consider the standard form of an exponential function:
\(y=a(b)^x\)
How does changing the base number (inside the parentheses) change your graph?
Answers
Answer:
Step-by-step explanation:
Challenge 1
We have exponential decline if 0 b 1. As you move from left to right, the curve will get less steep.
If b is greater than 1, exponential growth is present, and the curve slopes upward from left to right.
Examples include exponential decline (y = 2(0.5)x) and exponential growth (y = 2(1.2)x).
Remember that b cannot be negative.
===========================================
Challenge 2
In the general template provided, enter x = 0.
y = a(b)^x
y = a(b)^0
y = a(1) (1)
y = a
When x = 0 is plugged in, the result is y = a.
The curve is therefore on the point (0,a). The y intercept appears here. It is the point when the curve veers off the y axis. The y intercept is altered if the value of "a" is altered.
Examples:
Mackey invested some money in an account paying 6% interest for one year. She invested $1000 more than this amount in an account paying 8.5%. How much did she invest in total if the total interest earned in the year was $737.50?
Answers
Step-by-step explanation:
Let's assume the amount Mackey initially invested in the 6% account is x dollars.
According to the given information, Mackey invested $1000 more than x in the 8.5% account, which means she invested (x + $1000) dollars in that account.
The total interest earned from the 6% account would be 0.06x dollars, and the total interest earned from the 8.5% account would be 0.085(x + $1000) dollars.
The total interest earned in the year is given as $737.50, so we can set up the equation:
0.06x + 0.085(x + $1000) = $737.50
Simplifying the equation:
0.06x + 0.085x + 0.085($1000) = $737.50
Combining like terms:
0.145x + $85 = $737.50
Subtracting $85 from both sides:
0.145x = $737.50 - $85
0.145x = $652.50
Dividing both sides by 0.145:
x = $652.50 / 0.145
x ≈ $4500
Therefore, Mackey initially invested approximately $4500 in the 6% account, and she invested $1000 more, which means she invested a total of $5500.
$4500
$4500
$4500
$4500
A stainless steel patio heater is a square pyramid. The length of one side of the base is 25.4 in. The slant height of the pyramid is 88.1 in. What is the height of the pyramid?
Answers
Answer:
Approximately 84.35
Step-by-step explanation:
Since we know that base^2+height^2=hypetenuse*2, then hypetenues^2-base^2=height^2
Answer:
The answer is 84.35
Scientist Asterix uses 19 base number system. Which
one is his largest symbol?
A. I
B. J
C. 9
D. P
Answers
Answer:
A. I
Step-by-step explanation:
first 10 symbols are digits from 0 to 9
then next 9 symbols are alphabets from A to I
so the largest symbol is I
19 base number system has 19 symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I
The largest symbol is I
Answer:
A. Iplace holder for the question
Answers
Answer:
The area of the trapozoid would be 192 inches.
Step-by-step explanation:
Here are the steps on how to find the area of a trapozoid.
Add the two bases together. 14 + 18 = 32Divide that by 2. 32/2 = 16Then lastly multiply that by the height. 16 x 12 = 192.I hope I helped
brainliest would be appreciated.
help and thank you :DDDDDDDDD
Answers
Answer:
0.72
Step-by-step explanation:
I just looked it up. The 10 with the little three on it is how many time you multiply that number. So, 10 x 10 x 10 is equal to 1000, so it's 720 divided by 1000. That equals 0.72 or .72!
Hope that helps!
Paddy has a circular fishpond in the middle of his square backyard. The fishpond has a circular stone border. The radius of the fishpond is one foot less than the radius from the center of the pond to the outer edge of the stone border. The width of Paddy's yard is 6 feet more than the diameter of the fishpond and border. Let x be the radius in feet of the fishpond. Write an expression for the area of the yard that is not taken up by the fishpond and border.
A. (4−π)x^2+(24+2π)x+(36−π)
B. (4x^2+32x+64)−π(x^2+2x+1)
C. 4x^2−πx^2+32x−2πx+64−π
D. both B and C
Answers
PLEASE HELP if you can
they might be mixed up but portland, missippi, then questions
(file below)
Answers
Answer:c
Step-by-step explanation:
The cost of
3
bags of grapes is normally
$
9.36
, but they are on sale for
$
7.59
. What is the savings for each bag?
Answers
Answer:
The answer will be one dollar and 77 cents ($1.77)
Step-by-step explanation:
$9.36
-$7.59
—————
$1.77
9.36-7.59
=$1.77
Please help me answer.
Answers
Answer: First blank is 15 then 28 then 25 in the last blank.
Step-by-step explanation:
On the left side column it is going up by 5 and the right column is going up by 7.
And second column is 7,14,21,28,35
Sid has a baseball cap collection. 65% of his caps have sports team symbols. If 26 of the caps have the team symbols, how many total caps does Sid have?
39
40
73
91
Answers
B. 40
As we know Sid has 26 Caps
we also know that 26 is 65% of total
so let total caps = x
to calculate x
we know that percent = (Values*100)/total Values.......... i
and here Value = 26 caps
percentage = 65
So we have
65 = (26*100)/x---------------- (As we know that per = fraction*100)..... from i
65x= 2600x = 2600/65x=40 capsHence Answer is 40
Learn more about percentages: https://brainly.com/question/24877689
what is melody MUSIC TERMS. ill mark brainliest
Answers
Lane read a book 15 of the 30 days in April. What percentage is equivalent to the number of days Lane read a book in April?
Answers
Answer:
1/2
Step-by-step explanation:
PLEASE HELP :'( 20 points! +brainly!
Type the number to the left of the rational number in the box to the point it represents on the number line.
1/2
1/5
9/10
-0.5
0.6
-4/5
Answers
Answer:
-4/5, -0.5, 1/5, 1/2, 0.6, 0.9
Step-by-step explanation:
Answer:
-4/5, -0.5, 1/5, 1/2, 0.6, 0.9
Step-by-step explanation:
please helppppp meeeeee
Answers
Answer: The slope is 3 and the y-intercept is (0, -2)
Step-by-step explanation:
So y=mx+b right? and the m is the slope and b is the y intercept.
Answer:
slope = 3
y intercept = 0, -2
Please need help ASAP.
Answers
Answer: in this order angle d, e, f line de, ef, fd
Step-by-step explanation:
what is 0.000377 in scientific form
Answers
Answer:
3.77 × 10^-4
Step-by-step explanation:
Answer:
Step-by-step explanation:
Each decimal move left or right is x 10
For scientific notation the decimal needs to be after the first number (in this case 3).
The main rule for scientifc notation is the decimal can only be placed after a 1 or less than 10
if a decimal is to the left (such as this number) keep moving it until it
is behind the 3; now because you moved it to the right the exponant will be negative. so 0.000377 in scientifc notation is 3.77 x 10⁻⁴
A positive example is 23,000,000 000 = 2.3 x 10¹⁰ because you moved the decimal after the first number (2) to the right.
whats the surface area?
Answers
Answer:
1108 in²
Step-by-step explanation:
You want the total surface area of the pentagonal prism shown.
Base areaThe area of each of the two pentagonal bases is the sum of the area of the yellow rectangle and the area of the triangle above it. That sum is ...
A = LW +1/2bh
A = 5(12) +1/2(12)(9) = 12(5 +9/2) = 114 . . . . square inches
Lateral areaThe lateral area of the prism is the sum of the areas of the 5 rectangles. That sum will be the product of the perimeter of the pentagonal base and the distance between bases.
LA = (12 +5 +11 +11 +5)(20) = (44)(20) = 880 . . . . square inches
Total areaThe total surface area of the figure is the sum of the two base areas and the lateral area:
SA = 2(114 in²) +880 in² = 1108 in²
The surface area of the composite figure is 1108 in².
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