The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of the original equilateral is decreased by 20%, resulting in triangle DEF, how much greater is the area of triangle ABC than the area of triangle DEF?

Answers

Answer 1

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]

[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]

[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]

Now, comparing areas:

[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]

[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.


Related Questions

For what value of the variable is each of the following fractions equal to zero: 2y +3/10

Answers

I think its 3/10=0.3

2×(-0.15)= -0.3

and -0.3+0.3=so variable value is -0.15

Answer:

2×-1,5+3

Step-by-step explanation:

Hope this helped have an amazing day!

PLEASE HELP!!!
Use linear equation to calculate intercepts.
x - 1/2y=-4
complete the table with values for a and b.
a=
b=

Answers

Answer: a=8 b=-4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Nathan usually drinks 38 ounces of water per day. He read that he should drink 66 ounces of water per day. If he starts drinking 66 ounces, what is the percent increase? Round to the nearest percent.

Answers

Answer:

73.6%

Explanation: 38 is the old value and 66 is the new value. In this case we have a positive change of 73.68... percent because the new value is greater than the old value.

Southlake Cable charges $50 per month for basic cable and $5 for each premium movie channel. Lakeview Cable charges $41 per month for the same cable package and $6.50 for each premium movie channel. The graph of the equations representing the costs for each company is shown in the graph.

Answers

Answer:

Six movie channels, because 5(6) + 50 = 6.5(6) + 41

Step-by-step explanation:

1. For a soccer party, Juan collects $90 for pizza. He must buy more than 5 pizzas to
feed the team. Pizzas are $7.25 for a small pizza and $10.50 for a large pizza. Let:
S = number of small pizzas he can buy & L = number of large pizzas he can buy.
Select the system of inequalities that represents this situation.

Answers

Answer:

7.25S + 10.50L ≤ 90

The system of inequalities that represents a given situation are  S+L>5 and 7.25S+10.50L≤90.

Given that, For a soccer party, Juan collects $90 for pizza. He must buy more than 5 pizzas to feed the team. Pizzas are $7.25 for a small pizza and $10.50 for a large pizza.

What are inequalities?

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let S = the number of small pizzas he can buy and L = the number of large pizzas he can buy.

Juan must buy more than 5 pizzas to feed the team.

That is, S+L>5

Pizzas are $7.25 for a small pizza and $10.50 for a large pizza=7.25S+10.50L

Juan collects $90 for pizza. So, 7.25S+10.50L≤90

Therefore, the system of inequalities that represents a given situation are  S+L>5 and 7.25S+10.50L≤90.

To learn more about the system of inequalities visit:

https://brainly.com/question/16339562.

#SPJ2

180=16x -5+5x +4 +9O

Answers

Answer:

The answer is in the pic below

Step-by-step explanation:

Answer:

x = 4.3 (repeating 3) in Decimal Form

x = 13/3 in Exact Form

x = 4 1/3 in Mixed Number Form

Step-by-step explanation:

180=16x - 5 + 5x +4 + 90

180 = 21x -5 + 4 + 90 (combine like terms)

180 = 21x + 89

180 = 21x + 89 (subtract 89 on both sides)

-89           - 89

91 = 21x (divide 21 by both sides)

91/21 = 21x/21

4.3 (repeating 3) = x

City A has an elevation of 45 feet above sea level. City B is below sea level, with an elevation of -15 feet. What is the difference in elevation between City A and City B?

Answers

Answer:

60 hope this helps!

Step-by-step explanation:

45-(-15) = 60

Answer:

Well person, it's 60 feet.

Step-by-step explanation:

Because it is simple math. You just add 45 and 15 then BOOM! ANSWER

Sharon makes bracelets and necklaces to sell at the school fair. She makes a total of 40 bracelets and necklaces. She makes 3 times as many bracelets as necklaces. Which system of equations can be used to determine how many bracelets, x, and how many necklaces, y, she m

Answers

Answer:

So, the system of equations are

x+y=40

x= 3 y

Step-by-step explanation:

Let's make system of equations for the given information.

Let x number of bracelets and y number of necklaces made.

So, for the information

She makes a total of 40 bracelets and necklaces, we can set up equation as

x+y=40

Now, for she makes 3 times as many bracelets as necklaces, we can set up equation as

x=3 y

Determine if this is a function or not based on the graph
O yes
O no

Answers

Answer:

yes

Step-by-step explanation:

brainiest plz

The zoo has 12 Emperor penguins, which makes up 24% of all penguins at the zoo. How many penguins live at the zoo?​

Answers

Answer:

[tex]50[/tex] penguins

Step-by-step explanation:

Let [tex]p[/tex] = number of penguins at the zoo

[tex]24\%p=12[/tex] (Is given that 12 Emperor penguins at the zoo make up 24% of total penguins)

[tex]0.24p=12[/tex]

[tex]p=12\div0.24[/tex]

[tex]p=50[/tex]

∴ There are [tex]50[/tex] penguins at the zoo

Hope this helps :)

What is 2x + 2 when x = 0? A 0 B 2 C 20 D 22

Answers

Answer:

B. 2

Step-by-step explanation:

Step 1:

2x + 2          Equation

Step 2:

2 ( 0 ) + 2        Input x value

Step 3:

0 + 2        Multiply

Answer:

B. 2

Hope This Helps :)

Answer:

B

Step-by-step explanation:

What is the value of 2(5b - 7) in terms of y if b = 3y ?

Answers

2(5b-7), you can input b as 3y
2(5(3y)-7) —> 2(15y-7) —> 30y -14
—> 30y = 14 —> y = 14/30 —> y = 4.6667
It’s just 2(5(3y)-7) or 2(15y-7), which is 30y-14.

What is the domain of the square root function graphed below?
8
6
4
2
-6 -4
6
8
х
-6
X>1
O x21
OOOO
x>3
x23
Mark this and return
Save and Exit
Next
Submit

Answers

Answer:

x ≥ 3

Step-by-step explanation:

the domain of a graph consists of all the input values shown on the x -axis

The domain of the square root function graphed below would be x ≥ 3

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable , functions are indispensable for formulating physical relationships.

The domain is all  real numbers for x>3 and the range of the square root function graphed is equal to the interval------> [1,∞)

so, the range is all real numbers for x>3

Hence, the domain of a graph consists of all the input values of the x -axis.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ7

20 points!

24, and 25 has to be in simplest form.

JUST NEED HELP ON 24 AND 25!

Answers

Answer:

I think they would be 7 4/6 & 5 2/8

Step-by-step explanation:

srry if im late!

Drag the correct word into the space provided in order to complete the sentence.
If an outlier is included in a data set the....... is least affected

mean , median, range or standard deviation

Answers

Answer:

mean for the the second median for the 1st one

Step-by-step explanation:

Select the values that makes the inequality -w≥ 7 true. Then write an equivalent inequality, in terms of w

Answers

The values of [tex]w[/tex] that make the inequality [tex]-w\ge7[/tex] true are

[tex]\{... ,-11,-10,-9,-8,-7\}[/tex]. An equivalent inequality, in terms of [tex]w[/tex], is [tex]w\le-7[/tex]

To get the values that make the inequality true, we have to solve the inequality for [tex]w[/tex]. This will also give an equivalent inequality in terms of [tex]w[/tex]

[tex]-w\ge7\\\\\implies \dfrac{-w}{-1}\le\dfrac{7}{-1}\\\\w\le-7[/tex]

the solution set is the set of values [tex]\{... ,-11,-10,-9,-8,-7\}[/tex]. In other words, [tex]w[/tex] can take up values less or equal to [tex]-7[/tex] to make the inequality  [tex]-w\ge7[/tex] true

Also, the inequality equivalent to [tex]-w\ge7[/tex] is [tex]w\le-7[/tex]

Learn more about solving inequalities here https://brainly.com/question/12306534

5.) On Wednesday, a restaurant serves coffee to 75 of 150 of its customers.
What percent of the customers ordered coffee?

Answers

Answer:

50%

Step-by-step explanation:

Long division

Answer:

50%

Step-by-step explanation:

To find the percent, divide 75 by 150 and multiply by 100:

75/150

= 0.5

0.5(100)

= 50

So, 50% of the customers ordered coffee

−(5x−0.4)=−7(−0.4−x) need to be exact or rounded to the nearest hundredth.

Answers

Answer:

-0.2

Step-by-step explanation:

it's that exact answer , I did not rounded

Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!

Answers

Answer:

11,60,62

Hope this helps

what isn’t your the first time in the year you have a baby shower

calculate the quotient 9/4 divided by 3/8

Answers

Answer:

6

....................................

6 ordhejfhrjdjdjrjdiehe

Help me with this answer I know there is no solution I just wanna know why

Answers

Answer:

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. ... This is because there is truly no solution—there are no values for x that will make the equation true

Answer:

No solution

Step-by-step explanation:

The solution x = 0 means that the value 0. “No solution” means that there is no values

QUESTION 15!1!!11!JAKQKQKAKAKS

Answers

Answer:

2 groups of 3 boys = 6

Step-by-step explanation:

evaluate : 7^4×7^5×7^-9
pls solve to get brainiest ​

Answers

Answer:

1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] and [tex]a^{0}[/tex] = 1

Given

[tex]7^{4}[/tex] × [tex]7^{5}[/tex] × [tex]7^{-9}[/tex]

= [tex]7^{(4+5-9)}[/tex]

= [tex]7^{0}[/tex]

= 1

Dan runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?

Answers

Answer:

I think it would be 4 not sure

A puppy weight increases by 15% each week for the first 6 months. The puppy currently weight 3.7 pounds. which expression will not calvulate how much the puppy will weigh in 1 week? A) 3.7(0.15) B) 3.7(1.15) C) 3.7 + 3.7(0.15) D) 3.7 + 0.555​

Answers

Answer:

B) 3.7(1.15)

Step-by-step explanation:

DOG has coordinates D(3,2), O( 2,-4), G(-1,-1) .A translation maps point D to D (2,4). Find the coordinates of O and G under the translation.

Answers

Answer:

If you're on edge and it's the multiple choice one it would be a

3(23−2v)+3v=48
what is v?

Answers

Answer:

v=7

Step-by-step explanation:

my previous answer was incorrect, my bad

Answer: v=-7

Step-by-step explanation:

3(23−2v)+3v=48

Distribute:

69-6v+3v=48

Combine like terms:

-6v+3v=-3v

69-3v=48

Subtract 69 on both sides:

69-69-3v=48-69

-3v=-21

Divide 3 on both sides:

-3v/3=-21/3

v=-7

Calculate the slope of a line that passes through the points (9, 3) and (19, -17). 10 2 -2 7/5

Answers

Answer:

slope = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 3) and (x₂, y₂ ) = (19, - 17)

m = [tex]\frac{-17-3}{19-9}[/tex] = [tex]\frac{-20}{10}[/tex] = - 2

What is the compliment of a 45 degree angle

Answers

The complement of 45° is the angle that when added to 45° forms a right angle (90° ).

A man has 20.24$. He bought a thing for 4.49$. He also bought another thing for 3.99$. Will the money be enough to buy another item that costs 9.99$. If yes, how much money will remain?

Answers

Answer:

Yes: $1.77

Step-by-step explanation:

20.24 - 4.49 = 15.75

15.75 - 3.99 = 11.76

Yes, there will be enough for the 9.99 thing

11.76 - 9.99 = 1.77

The man will have 1.77 at the end.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Other Questions
please help me 56 points RJ Corporation has provided the following information about one of its inventory items: Date Transaction 1/1 Beginning Inventory 6/6 Purchase 9/10 Purchase 11/15 Purchase During the year, RJ sold 3,000 units. Number of Units 400 800 800 1,200 800 Cost per Unit $3,200 $3,600 $4,000 $4,200 What was ending inventory using the LIFO cost flow assumption under a periodic inventory system? a. $880,000. b. $640,000 c. $770,000. d. $840,000 Jill runs a factory that makes lie detectors in Little Rock,Arkansas.This month,Jill's 34 workers produced 690 machines.Suppose Jill adds one more worker and,as a result,her factory's output increases to 700.Jill's marginal product of labor from the last worker hired equals ________.A) 10B) 20C) 690D) 700E) None of the above answers is correct. Please select the correct conjugation of the verb llevar ("to take,wear") to go in the blank.Vosotraslas nias a la ciudad.llevamosllevanllevaisllevaisFill in da blank Which value is equivalent to the expression 45? Glucose is what type of molecule A: Multi- complex B: Protein C: Sugar D: Lipid 1. What was the main argument the British used to justify taxing the thirteen colonies after the French and Indian War?A. The written constitution provided Parliament with the power to tax coloniesB. Taxes were uniform throughout the British coloniesC. Tax money was being used to protect the mining interests of the British EmpireD. Colonies should contribute to the expenses involved in providing for their defense2. In writing the Declaration of Independence, Thomas Jefferson was influenced most by John Lockes idea ofA. the rights of the accusedB. natural rightsC. the right to privacyD. due process of law3. Which important reason for the American victory in the Revolutionary War is missing from the chart?A. aid from foreign nationsB. control of railroads and canalsC. naval superiority of the thirteen coloniesD. greater number of Indian allies4. The main criticism of the Articles of Confederation was that they failed toA. provide adequate powers for the central governmentB. prevent the development of military ruleC. allow for the admission of new statesD. limit the powers of the president5. In the 1780s, the national government under the Articles of Confederation established its authority in the Northwest Territory byA. settling the border dispute with MexicoB. rejecting Native American Indian claims of sovereigntyC. extending the nations border to the Rocky MountainsD. providing a system for the formation of new states6. A principal reason for calling the Constitutional Convention of 1787 was toA. strengthen the central governmentB. increase the power of the statesC. weaken the system of checks and balancesD. settle land disputes with Canada7. The United States Constitution corrected a weakness of the Articles of Confederation byA. giving greater power to state governmentsB. providing a clear definition of states rightsC. granting the right to vote to all white malesD. creating three branches of government8. This quotation from the Preamble illustrates the constitutional principle that peopleA. are the true source of political powerB. are guaranteed an adequate standard of livingC. have the right to assembleD. have a right to a trial by jury9. A republican form of government is described as one in whichA. there is a two-party systemB. elected officials have limited termsC. government power is limited by checks and balancesD. representatives are elected by the people10. New Congress to Have Two Houses | Slaves to Count as Three-Fifths of a Person | President to be Chosen by Electoral Vote. Which conclusion about the Constitutional Convention is best supported by these headlines?A. States with large populations controlled the outcome of the convention.B. States that were small in area would lose power in the new Constitution.C. The president and Congress would have equal power under the new constitution.D. The framers of the Constitution were able to compromise on important issues. A national bank was established in the U.S. to:A) promote trade and economic growth B) pay for political campaigns C) create new taxesD) count the votes in the presidential election What does the first amendment say about freedom of speech The difference between PCR and real-time PCR is thatA. real-time PCR can measure the amount of DNA amplified as the reaction proceeds, while standard PCR cannot.B. real-time PCR can amplify DNA a billion-fold within just a few hours, while standard PCR cannot.C. real-time PCR can determine the DNA sequence, while standard PCR cannot.D. real-time PCR uses DNA polymerase, while standard PCR does not. The height of a parallelogram is 5 feet more than its base. If the area of the parallelogram is 204 feet, find its base and height how do you give a brainllest or what ever its calledill give one to whoever tells me first ( ones i figure it out ) Science: Look at the image and answer the question correctly. If f(x)=2(x-3)x4, what is f(-2)? PLEASE HELP ILL GIVE BRAINLIEST The amount of change that goes up Use the diagram below to help you to choose ALLL the CORRECT answers for the question: What are the differences between Meiosis i and Meiosis II?(MULTIPLE CHOICE)A In Metaphase I and Metaphase II the chromosomes line up differently because there are a different number of copiesB Telophase and cytokinesis do NOT happen in Meiosis IIC After Meiosis II the 4 daughter cells undergo cell specialization to become eggs or sperm, which does not happen after Meiosis ID In Prophase I the chromosomes crossover, in Prophase II they do not crossover Please help due soon! When you are posting your rsum online, be sure to adjust it so it is _____.one page in lengthboldcolorfulcyber-safe A ball of mass 4kg moving with a velocity of 20m/s collides with another ball of mass 15kg moving with a velocity of 15m/s in the same direction. Calculate the velocity of the 5kg ball if the collision is perfectly inelastic. The midpoint of EF is M(1. 1). One endpoint is E ( 3,2). Find the coordinates of endpoint F