Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.

Find The Lengths Of UV And ST And Determine Whether They Are Congruent.Hint: Congruent Line Segments

Answers

Answer 1

The length of both UV and ST is [tex]3\sqrt{2}[/tex] and hence they both are congruent.

Here, we are given two lines- UV and ST.

We can find the length of the lines using distance formula. According to distance formula, distance between two points- (x1, y1) and (x2, y2) is given as-

[tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2} }[/tex]

Here, for UV,

the two endpoints are- (1,0) and (4,3)

thus, the length of UV will be-

[tex]\sqrt{(4-1)^{2} + (3 - 0)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (3 )^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

Similarly, the two endpoints of ST are- (-2,-1) and (1,-4)

thus, the length of UV will be-

[tex]\sqrt{(1+2)^{2} + (-4 +1)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (-3)^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

So we can see that UV = ST = [tex]3\sqrt{2}[/tex], which means that both of them are congruent. Hence, option 1 is the correct answer.

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Find The Lengths Of UV And ST And Determine Whether They Are Congruent.Hint: Congruent Line Segments

Related Questions

A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain
number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?

Answers

Answer:

It traveled south for 22 kilometers.

Step-by-step explanation:

Think of it as a rectangle. Two sides are 50 kilometers (east and west), and the other two sides are 22 kilometers (north and south).

Which mixed number is equivalent to the improper fraction?
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Answer:

what is the question?

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The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
Prove: ABCD is a rhombus
Statements
1. ABCD is a parallelogram and
AD= AB.
AB a DC, AD a BC
2.
3.
AB a CD a AD a BC
4. ABCD is a rhombus.
Reasons
1. Given
PREVIOUS
2. ?
3. Transitive property
4. By definition, if all four sides of a
parallelogram are congruent, then
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O A. Consecutive sides of a parallelogram are parallel.
B. Opposite sides of a parallelogram are parallel.
C. Opposite sides of a parallelogram are congruent.
O D. Consecutive sides of a parallelogram are congruent.

Answers

From the two column proof below to prove that ABCD is a rhombus, the missing reason is reason 6; C. Opposite sides of a parallelogram are congruent.

How to carry out a two column proof?

Given: ABCD is a parallelogram.

The two column proof that ABCD is a rhombus is;

Statement 1;  ABCD is a parallelogram. AD = AB and AC bisects ∠BCD and ∠BAD

Reason 1; Given

Statement 2; ∠BCA ≅ ∠DCA

Reason 2; Definition of an angle bisector

Statement 3; AC ≅ AC

Reason 3; Reflexive property of congruence

Statement 4; ΔABC ≅ ΔADC

Reason 4; Angle Side Angle Congruence Postulate

Statement 5; AB ≅ AD, BC ≅ DC

Reason 5; Corresponding parts of congruent triangles are equal.

Statement 6; AB ≅ CD, BC ≅ AD

Reason 6; Opposite sides of the parallelogram are congruent

Statement 7; AB ≅ AD, BC ≅ CD

Reason 7; Transitive Property of Congruence

Statement 8;  ABCD is a rhombus

Reason 8: Definition of rhombus

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Read the following description of a relationship:
Each crate of ceramic tiles has 17 more hexagonal tiles than square tiles.
Let s represent the number of square tiles in a crate and h represent the number
of hexagonal tiles in the same crate.
Complete the table using the equation h = s + 17.
S
5
6
7
8
h
24
Submit
I don't know

Answers

It’s c
I got it right

Find the equation of the line that passes through the points
3) and (-1, 11)
Enter your answer in slope-intercept form, y=mx+b

Answers

Answer: y=-4x+7

Step-by-step explanation:

(1, 3) and (-1, 11)

m=(y2-y1)/(x2-x1) ==> Slope formula

m=(11-3)/(-1-1)

m=8/(-2)

m=-4

y=mx+b

3=-4(1)+b

3=-4+b

b=7

y=-4x+7

Kitchen
Living
Room
Bathroom
Laundry
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Bedroom #1
Scale: 2 units = 3 feet

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to much long and I want brainliest

What is the answer to this question?

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Not sure if I'm right, but is
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Jean's bedroom is 12 feet by 10 feet. She has chosen a carpet which costs $30.95 per square yard.
This includes installation.

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Answer: i think its 1238 dollars

Step-by-step explanation:

What is the difference between Earth's highest mountain and its deepest ocean canyon? What is the difference between Mars' highest mountain and its deepest canyon? Which difference is greater? How much greater is it?​

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earth's difference= 65,233 ft

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1/2 ( 2p + 9 ) = p + 5 solve equation

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that is impossible to solve because both sides do not equal eachother

How do division properties help you evaluate expressions?

Drag a word or number to the box to correctly complete the statement.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the Response area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the

Answers

The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

How to explain the information?

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:

When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Step-by-step explanation:

I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

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just give an clearly answers

How can I solve this?

Answers

Step-by-step explanation:

by using formula a²-b²=a+b

a²b=a²-b² like this

Mel and 5 friends went to the go-kart track. Four people rented helmets for $3 each. The total cost to
rent the helmet and to ride the karts was $75. What was the cost to ride the karts for each person?

Answers

The cost of a ride for an individual person will be $10.5

It is given that Mel and 5 friends went to ride which makes the Total number of people for the Ride will be 6. Also, Four of them rented Helmets for the rides each helmet cost $3. It is also given that the total cost of helmets and rides is $75. From this we get :

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Taking the cost of a ride as 'x' we get the equation representing this statement:  

              => 4*3 + 6x = 75  =>  6x = 63

              =>  x = 10.5

We get value of x = $75.

Hence, we get the cost of an individual ride $75.

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Students were asked how they travel to
school. 37% of the students said they
travel by train.
Of these, 24% live more than seven miles
from their school. What percentage of the
students travel over seven miles to school
by train? Give your answer to 2 d.p.

Answers

the percentage of the students travel over seven miles to school by train is 9 %.

Let the total number of students be represented by variable x

now, 37 % of them travel by train.

So, we get that:

By train = 37 % of x

By train = 37 / 100 (x)

By train = 0.37 x

Now, 24 % of them lives 7 miles away from the school.

So, 7 miles away = 24 % of 0.37 x

= 24 / 100 ( 0.37 x )

= 0.24 ( 0.37 x)

= 0.09 x

In percentage:

= 9 %

Therefore, we get that, the percentage of the students travel over seven miles to school by train is 9 %.

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A salesperson sold a pick-up for $18,760. They were paid a 4.5% commission. How much money were they paid?

Answers

the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

We are given that the selling price of a pick up item is given as:

Selling price = $ 18,760

Now, it is also given that, on every sale, the salesperson gain a commission of 4.5 % as their pay.

The money they get paid for one pick up that they sell will be calculated by finding the percentage. So, we get that:

Money = 4.5 % of $ 18,760

Money = 4.5 / 100 × $ 18,760

Money = 0.045 × $ 18,760

Money =  $ 844.2

Therefore, we get that, the salesperson will be paid $ 844.2 for the one pickup they sell for $ 18,760 as 4.5 % commission is theirs.

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Find f '(a).
f(x) = [tex]\frac{1}{\sqrt{x} +5}[/tex]

Answers

Answer:

[tex]f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

Step-by-step explanation:

[tex]f'(x)=\frac{\frac{d}{dx} (\sqrt{x}+5)(1)-(\sqrt{x}+5)\frac{d}{dx}(1)}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{(\sqrt{x}+5)^2} \\ \\ =\frac{\frac{1}{2\sqrt{x}}}{x+10\sqrt{x}+25} \\ \\ =\frac{1}{2x^{3/2}+20x+50\sqrt{x}} \\ \\ \therefore f'(a)=\frac{1}{2a^{3/2}+20a+50\sqrt{a}}[/tex]

What time does the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday? United Airlines has a 3 hour 45 minutes flight.

Answers

At 17:30 the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday.

                   

The time difference of two zone is -7-(-6) = -1

The shipment departs at 14:45 pm

flight took time = 3:45 min

adding the time = 14:45 + 3:45

                           = 18:30

So it arrived at Dallas at 18:30 according to Edmonton (GMT -7)

It arrived in Dallas according to Dallas (GMT -6) = 18:30 - 1 hour

                                                                                = 17:30

What is time zone?                    

A time zone is a region where everyone adheres to the same standard time for social, business, and legal activities. Because it is simpler for regions that communicate often to maintain the same time, time zones frequently follow national borders and their subdivisions rather than strictly following longitude.

Coordinated Universal Time (UTC), which ranges from UTC12:00 to UTC+14:00, is used to determine all time zones. Most zones have full hour offsets, but some, like those in India, South Australia, and Nepal, have additional offsets of 30 or 45 minutes.

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Order these decimals from least to greatest.
A) 12.205
B) 12.2
C) 12.25
PLEASEEE BE ACCURATE! FIRST PERSON WHO RESPONDS CORRECTLY GETS BRAINLIST!!

Answers

The correct order would be the following:
B) 12.2
A) 12.205
C) 12.25

B would be the least of these numbers because A is just 0.005 more than it. C would be the greatest of these numbers because it is 0.05 greater than B putting it also ahead of letter A.

2 1/2 = 1 2/3 divided by y; what does y equal

Answers

Step-by-step explanation:

21/2=12/3

y=10.5*4

Sana nakatulong:)

Another job is advertising leaflets printed on sheets of A4 paper
The sheets are the fold into thirds as shown
What are the measurements in millimetres of each fold leaflet?

Answers

The measurement of the fold leaflet shorter dimension stays same but the longer side becomes 99 mm.

What are referred as dimension?

In mathematics, dimensions are the measurements of the size or distance between an object, region, or space in one direction. In layman's terms, it refers to the measurement of something's length, width, and height.

Dimensions are commonly expressed as follows:

LengthBreadthWidthHeight or Depth

A leaflet is mainly folded into thirds just on long side, so the short side remains unchanged while the long dimension has become 1/3, or  297/3 = 99 mm.

The final dimensions are

210 mm × 99 mm

Therefore, the measurement of the sorter side of the fold leaflet remains same but longer side becomes 99 mm.

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The complete question is-

Another job is advertising leaflets printed on sheets of A4 paper (210 x 297 mm).

The sheets are then folded into thirds as shown.

What are the measurements in millimetres of each folded leaflet?

Determine by composition whether f(x) = 3x + 18 and g(x)=x-6 are inverses of each other.
O No, f(g(x)) + X
O No, f(g(x)) = x
O Yes, f(g(x)) = g(f(x)) = x
O Yes, f(g(x)) = g(f(x)) * x

Answers

Thus, (x) = 3x + 18 and g(x)=x-6 are not inverses of each other.

Two function are inverse if they do undo or cancel each other, which means

f and g are inverse if

f(g(x)) = x and g(f(x)) = x

Here, f(x) = 3x + 18 and g(x)=x-6

Lets check by substituting the values in the formula

⇒ f(g(x))

⇒ f(x-6)

⇒ (3x + 18) - 6

⇒ 3x - 12

⇒ x = 4

g(f(x))

⇒ g(3x + 18)

⇒ 3(x-6) + 18

⇒ 3x - 18 + 18

⇒ 3x

⇒ x = 1/3

What is composition maths?

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

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Stop light A changes color every 45 seconds and Stop light B changes color every 80 seconds. Both Stop lights just changed. After how many seconds will the stoplights change color at the same time?

Answers

The stoplights will change color after 720 seconds. at the same time again.

Given: Stoplights A and B alternate between changing colors every 45 and 80 seconds, respectively.

One copy of each of the unique components and the common factor make up the Least Common Multiple (LCM).

The least common multiple of 45 and 80 is the amount of seconds before they change color simultaneously once more.

Since 80 = 5 x 2 x 2 x 2 and 45 = 5 x 3 x 3 respectively

A least common multiple of 45 and 80 is equal to 2x2x2x2x3x3x5 = 720.

Hence, the color of the spotlight will change after 720 seconds. at the same time again.

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COULD YALL PLEASE HELP ME !!!!!!

Answers

Answer:

Adjacent Angles

Step-by-step explanation:

Angles ∠1 and ∠2 are next to each other so adjacent

Shinji reads 25 pages of a book every night. 1. Write an equation that represents how many pages Shinji reads (ppp) in some number of nights (nnn).

Answers

The equation that represents how many pages Shinji reads is P(n) = 25n

How to write an equation that represents how many pages Shinji reads?

The given parameters are:

25 pages = 1 night

Multiply both sides by n

So, we have:

25 * n = 1 * n nights

Express as a function

25 * n = P(n)

Rewrite as

P(n) = 25n

Hence, the equation that represents how many pages Shinji reads is P(n) = 25n

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Answer:

Step-by-step explanation:

Riley is starting a running plan to train for a race. In the first week of her running
plan, Riley will run 15 miles. The plan calls for Riley to increase her weekly milage by
3 miles every week. If Riley sticks to the plan, how many miles would she be expected
to run during her 5th week of the training plan?

Answers

Week 1: 15 miles
Week 2: 18 miles
Week 3: 21 miles
Week 4: 24 miles
Week 5: 27 miles

Answer **please** ill give brainliest!

Answers

Answer:

w = -0.8

sum = 0

Step-by-step explanation:

An additive inverse is when two numbers add up to 0. 0.8+ (-0.8) = 0.

A company makes pencils. they sell each pencil for $10.
Their revenue is represented by R= 10x
The cost to make the pencils is $3 each with a one time start up cost of $5000.
Their cost is represented by C= 3X+5000

1.Find the profit, P, (P=R-C) when the company sells 1000 pens.
2. Find the number of pens they need to sell to break even ( when R=C)

Answers

We have the profit fomula:

P = R - C

= $10.x - ($3.x + 1000)

= $7.x - 1000

1. If the company sells 1000 pens:

P = $7 . 1000 - $1000

= $6000

2. If they want to break even:

P at least = 0

Assume P = 0

=> $7.x - $1000 = 0

=> x = 1000/7 ≈ 142,86

So if they want to break even, they have to sell at least 143 pens

Show work of how $7.40 for 5 pounds

Answers

Answer:

the answer is $35.40 sir there you go

Step-by-step explanation:

that's the answer which is located above

Answer:

1.48 each

Step-by-step explanation:

you have to divide 7.40/5

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