which statement explains why ABC is congruent to A’B’C’?

Which Statement Explains Why ABC Is Congruent To ABC?

Answers

Answer 1

The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.

What is congruent triangles?

When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.

Main Body:

First let us find the co-ordinates of both the triangles.

A= (3,5)

B = (-2, 3)

C= (-4,-1)

A' =(10,-5)

B'= (5, -3)

C' =(3,1)

Distance between two points =  d=√((x₂ – x₁)² + (y₂ – y₁)²).

In ΔABC

Distance of side AB =  √((3 –(-2) )² + (5 –3 )²)

                                 = √5² +2²

                                 = √29

Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)

                                 = √20

Distance of side CA = √((3-(-4) )² + (5-(-1) )²)

                                 = √7² + 6²

                                 = √85

Distance of side A'B' = √((10 -5)² + (-5-(-3))²

                                   = √(5² +2²)

                                   = √29

Distance of side B'C' = √ ((5-3)² + (-3 -1)² )

                                  = √ (2)² +4²

                                  = √20

Distance of side C'A' = √((10-3)² + ( -5-1)²)\

                                   = √(7)² + 6²

                                   = √85

This shows each side of ΔABC is equal to side of ΔA'B'C'.

hence the triangles are congruent.

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Related Questions

The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters

Answers

The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.

What is the length and width of the rectangle?

The perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let x represent the width be represented by variable x.

Width w = xLength l = x + 6Perimeter = 64

Plug the values into the equation above above.

P = 2( l + w )

64 = 2( (x + 6 ) + x )

64 = 2( 2x + 6 )

64 = 4x + 12

64 - 12 = 4x

52 = 4x

x = 52/4

x = 13

Hence, the dimensions of the rectangle are;

Width = x = 13m

Length = x + 6 = 13 + 6 = 19m

Therefore, the dimension of the rectangle are 13m by 19m.

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A model rocket is launched with an initial upward velocity of 235 feet the Rockets height H in feet after t seconds is given by the following

Answers

By assuming that the initial height of the rocket is the ground, we will get the height equation:

H(t) = -16*t^2 + 235*t

How to find the equation for the height?

The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:

H(t) = -16*t^2 + v*t + h

Where:

t represents the time in seconds.

the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.

v is the initial velocity, which in this case is 235 ft/s

h is the initial height, in this case we assume is zero (the rocket is launched from the ground)

Replacing all that in the height equation, we will get:

H(t) = -16*t^2 + 235*t

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Mara solved an exponential equation by using logarithms. This is her work.

Latex: 7 \cdot 3^x=189
7

3
x
=
189
7

3
x
=
189
Latex: 3^x=27
3
x
=
27
3
x
=
27
Latex: \log _3\!(3^x)= \log _3\!27
log
3
(
3
x
)
=
log
3
27
log
3
(
3
x
)
=
log
3
27
Latex: x \log _3\!3=9
x
log
3
3
=
9
x
log
3
3
=
9
Latex: x \cdot 1=9
x

1
=
9
x

1
=
9
Latex: x=9
x
=
9
x
=
9


Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.

b. Be sure to explain what she did and why it was correct or incorrect for Step 4.

c. Provide Mara with feedback on what the mistake was and how to fix it.

Answers

a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3

b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3

c) The mistake she made throughout is not applying the basic rule of logarithm.

How to solve Exponential Equations using logarithm?

She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;

Step 1. 7 x 3^x = 189

Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.

Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3

Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;

x log 3 = 3log 3

Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3

Step 6. x = 9; This is wrong because x = 3

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Complete question is;

Mara solved an exponential equation by using logarithms. This is her work.

1. 7 x 3^x = 189

2. 3^x = 27

3. log^3 (^3) = log^27

4. xlog^33=9

5. x * 1 = 9

6. x = 9

Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)

a. Be sure to explain what she did and why it was correct or incorrect for Step 3.

b. Be sure to explain what she did and why it was correct or incorrect for Step 4.

c. Provide Mara with feedback on what the mistake was and how to fix it.

I don't understand please help me...

Answers

The total fencing material required to fence the playground and both flower beds is

perimeter of a rectangle is 2( /  + w)perimeter of a square is 8a

How to find the material required for the fencing

Information from the question

The boundary of a park is shaped like a circle

The length of the rectangular playground is / and its width is w

The length of each side of the square flower beds is a

The problem is asking for the perimeter of a rectangle and 2 squares

perimeter of a rectangle is 2( /  + w)

perimeter of a square is 4a

If there was no over lap the expression will have no reduction and hence the quantity of material required for the fencing is equal to their respective perimeters

The flower beds are two so the perimeter will be multiplied by 2 to give 8a

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Solve the equation in the image below correct to 2 decimal places. in Logarithm Terms

Answers

The solution to the given equation is 5.630.

What is a logarithmic equation?

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Here, we have

2^(x+1) = 3^(2x-5)

Taking logarithms on both sides, we get

(x+1)log2 = (2x - 5)log3

xlog2 + log2 = 2xlog3 - 5log3

log2 + log3⁵ = 2xlog3 - xlog2

log 2* 243 = x(log6 - log2)

log486 = x(log6/2)

log486 = xlog3

x = log486/log3

x = 5.630

Hence, the solution to the given logarithmic equation is 5.630.

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A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent

Answers

Step-by-step explanation:

there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.

so, the tax is $1.50 for every $100 of the assessed value of the house.

how many $100 units are in that value ?

180,000 / 100 = 1,800 units.

that means the tax for that house is

1800 × 1.5 = $2,700

in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be

2700 / 12 = $225.00

Nolan went shopping for a new pair of sneakers because of a sale. The store was offering a 25% discount. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?

Answers

The number is 0.75.

From the question, we have

The store was offering a 25% discount.

number = 1-0.25

=0.75

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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1. A cone-shaped filter has a diameter of 10 inches and a height of 4 inches.
What is the volume of liquid the filter can hold? Round your answer to
the nearest hundredth.

Answers

The volume of liquid contained by cone is 105 inches cube.

What is volume?

It can be defined as the total content which can be held inside a container.

Main body:

the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex]  , where r = radius and h = height of cone

diameter = 10 , so radius = d/2 = 5 inches

V = [tex]\frac{1}{3}\pi 5*5*4[/tex]

V = 3.14 *5*5*4*1/3

v≈105 inches cube

Hence the volume is 105 inches cube.

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The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.

Answers

Answer:  $4x4x

Step-by-step explanation:

Emma wrote one hundred thousand as 1,000,000. Explain what she did wrong.Then write the number correctly

Answers

Answer:

she wrote 1 million. It's 100,000

Step-by-step explanation:

she wrote 1 million. It's 100,000

A school is arranging a field trip to the zoo. The school spends 654.84 dollars on passes for 32 students and 2 teachers. The school also spends 281.92 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?

Answers

The money was spent on a pass and lunch for each student is $28.07

How to calculate the amount?

It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.

Therefore the amount spent on pass will be:

= Total amount / Number of people

= 654.84 / 34

= 19.26

The amount spent on each student will be:

= 281.92 / 32

= 8.81

The amount spent in pass and lunch will be:

= 19.26 + 8.81

= $28.07

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Factor: 64x³ + 125y³

Answers

64x³+125y³

= (4x+5y)( 16x²-20xy+25y²)

a³ + b³ = ( a + b )( a² - ab + b² )

64x³ + 125y³

= ( 4x )³ + ( 5y )³

= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]

= (4x+5y)( 16x²-20xy+25y² )

if p is false,which row represents when p v(q^r) is true?
E
F
G
H​

Answers

Answer:

f and g 231

Step-by-step explanation:

how to interpret data from a frequency distribution

Answers

Answer:

The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.

The number written on the right of each category is its frequency

Step-by-step explanation:

A hexagon has exterior angle measures of (7n + 3), (10n-17)°,
(8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
Find the value of n.

Answers

Using the sum of exterior angle, the value of n is 11.

In the given question,

A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.

We have to find the value of n.

As we know that the sum of exterior angle of any polygon is equal to 360°.

As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.

So we can find the value of n by adding the all measures.

So the expression should be

(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°

Simplifying the bracket.

7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°

Solving the expression by solving the same term

(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°

33n-3 = 360°

Add 3 on both side

33n-3+3 = 360°+3

33n = 357°

Divide by 33 on both side

33/33 n= 363°/33

n = 11

Hence, the value of n is 11.

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Name the points. I give you brainiac or whatever.

Answers

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Help with this math problem

Answers

The value of the investment after 3.25 years is $434.93.

What is the interest rate?

The amount a lender charges a borrower, expressed as a percentage of the principle, is known as the interest rate.

Given that, the initial investment is P₀ = $400, the interest rate is n = 2.6%, and the time is x = 3.25 years.

The formula for the future value in continuous compounding is:

P(x) = P₀eⁿˣ

Substitute P₀ = 400, n = 2.6%, and x = 3.25 into the equation:

[tex]P(3.25) = (400)e^{2.6\%(3.25)}\\[/tex]

= 434.93

Hence, the value of the investment after 3.25 years is $434.93.

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the side length of a square is √8 find the area.
is the number rational or irrational?

Answers

The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.

Is the number behind the area of the square a rational number?

Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:

A = l²

Where l is the side length of the square.

First, substitute the side length of the square in the area formula:

A = (√8)²

Second, use algebraic properties to simplify the expression and find the corresponding result:

A = ([tex]8^{\frac{1}{2} }[/tex])²

A = 8

This number represents a rational number as 8 is equivalent to the rational number 8 / 1.

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{ ( - 4, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) } Write the set using set notation and in ascending order.

Answers

By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.

What is a listing method?

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.

For this exercise, the elements of the given data set would be listed in ascending order as follows:

Set = {-4, -3, -3, -1, 0, 1, 2, 2}

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Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and
a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?

Answers

Answer:

Strings packs cost $14 each

Step-by-step explanation:

Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?

Lenny: 2s

Lashae: 2s + b

when b = $16 then these equations are:

Lenny: 2s

Lashae: 2s + 16

together they spent $72 so:

lenny + Lashae = $72 or:

2s + 2s + 16 = 72

subtract 26 from both sides:

2s + 2s + 16 - 16 = 72 - 16

2s + 2s = 56

combine s terms:

4s = 56

divide both sides by 4:

4s/4 = 56/4

s = $14

At the toaster company, the weekly cost to run the factory is $1400 and the cost of producing each toaster is an additional $4 per toaster. Find a function rule representing the weekly cost in dollars, f(x), of producing x toasters. ​

Answers

Answer:

I believe... f(x)=1400+4x

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?

Answers

The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20

How to find the value of money?

When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.

If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.

In 20 years therefore, the value of $100 would be:

Value in 20 years = Value today x (1 - inflation rate) ^ number of years

= 100 x (1 - 4%) ²⁰

= $44.20

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What is 10,483,190 in word form?​

Answers

Answer:

Ten million, Four hundred eighty-three thousand, one hundred ninety

Step-by-step explanation:

Break it down! into the tens digit, hundreds digit, etc.

Ten million four hundred thousand one hundred ninety

5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)​

Answers

A is (2, -1)

The X axis will not change since A is not going left or right of (2,2). You would count down 3 spaces for the y-axis and that would land you at -1 or you could solve by subtraction.

2-3= -1

The radioactive substance cesium-137 has a half-life of 30 years. The amount At (in grams) of a sample of cesium-137 remaining after t years is given by the following exponential function.

=At26612t30
Find the initial amount in the sample and the amount remaining after 80 years.
Round your answers to the nearest gram as necessary.

Answers

The answer and steps is provided in the attachment below

Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola bars and a box of tissues.

If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?

A. $3.92
B. $24.71
C. $40.50
D. $116.91

Answers

If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.

How is the total amount determined?

Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.

We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.

Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.

The cost of gas per gallon = $2.91

The number of gallons of gas bought = 10

The total cost of gas = $29.10 ($2.91 x 10)

The total cost of granola bars and tissues = $11.40

The total amount spent = $40.50 ($29.10 + $11.40)

Thus, mathematically, Sebastian spent C. $40.50 at the gas station.

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Red- 5 skittles
Purple- 8 skittles
Yellow- 1 skittle
Orange- 2 skittles
Green- 4 skittles
Tomas reaches in a bowl and pulls out a green skittle. Without replacing the green skittle, what is the probability he picks a yellow skittle.

A. 1/100
B. 1/80
C. 1/95
D. 1/76

Answers

Answer:

I think its C. 1/95

Step-by-step explanation:

I am not sure this is the answer, i haven't done this math in ages so I'm a bit rusty so good luck on the test!

The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.

C = $3,173 + $31u

If the company wants to keep the cost of operation under $14,000 per month, what is the maximum number of units they can produce?
A. 3,490
B. 350
C. 3,491
D. 349

Answers

If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.

How to find the number of units?

Given function:

C = $3,173 + $31u

Hence,

Let u represent number of  units

Let c represent the operation cost

Where c = $14,000 per month

$14,000 = $3,173 + $31u

Combine like terms

$14,000 - $3,173 = $31u

$10,827 = $31u

Divide both side by $31u

u = $10,827 / 31

u = 349 units

Therefore the correct option is D.

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△MNP≅△QST.

What is m∠S?



Enter your answer in the box.

Answers

Answer:

78°

Step-by-step explanation:

∠M=∠Q

∠N=∠S

∠P=∠T

Answer:

m∠S =78°

---------------------

Given

Two congruent triangles △MNP≅△QST

We know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):

∠M ≅ ∠Q, ∠N ≅ ∠S, ∠P ≅ ∠T

Angle S corresponds to angle N, hence their values are equal:

m∠S = m∠N = 78°

In the following expression, n is a rational number: Which expression below is equivalent to this expression?

Answers

Answer:

none of them

Step-by-step explanation:

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Select all that apply.- Election Day could be eliminated in some states.- Election Day could occur at different times in different states.- Election Day could have different rules in different states. a eukaryotic cell has just started replicating its dna. what is a true statement about the cell? select all that apply. group of answer choices the cell is in the g2 stage of the cell cycle. near each origin of replication there are two replication forks. telomerase may be used to make sure that the lagging strand at the end of the chromosome is complete. ligase is being used to remove rna primers. the case describes approaches tek follows to minimize its international tax liability. based on your reading of the chapter, how would you advise tek management to reduce its taxes around the world further? Mrs. Wong is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Lakeside Florist charges $19 for each smaller arrangement, plus $50 for the large centerpiece. Spencer's Flowers, in contrast, charges $42 for the large centerpiece and $23 per arrangement for the rest. If Mrs. Wong orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be? What is the phase angle between the voltages of the inductor and capacitor in a rlc series circuit?. for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change? the study group you belong to is discussing class materials for the upcoming exam. based on research presented in your text about information sharing, which type of material would group members be most likely to focus on? in a cotransduction experiment the alleles a , b , and c were studied. the allele a alone was transduced into an auxotroph 1750 times, b alone 1700 times, and c alone 1725 times. alleles a and b were both found 11 times, b and c 117 times, and a and c 15 times. what can you definitely conclude? the monroe doctrine: group of answer choices stated that the united states would be neutral in all international conflicts. declared the americas off-limits for further european colonization. was the idea that all white men should have voting rights. secured florida from spain. what is the repricing gap if the planning period is 30 days? 3 months? 2 years? recall that cash is a non interest-earning asset. what is the impact over the next 30 days on net interest income if interest rates increase 50 basis points? decrease 75 basis points? the following one-year runoffs are expected: $10 million for two-year business loans and $20 million for eight-year mortgage loans. what is the one-year repricing gap? if runoffs are considered, what is the effect on net interest income at year-end if interest rates increase 50 basis points? decrease 75 basis points? What is the correct standard form for 400+3+0.07+0.001