On a coordinate plane, triangles P Q R and S T U are shown. Triangle P Q R has points (4, 4), (negative 2, 0), (negative 2, 4). Triangle S T U has points (2, negative 4), (negative 1, negative 2), (negative 1, negative 4). Complete the statements to verify that the triangles are similar. StartFraction Q R Over T U EndFraction = StartFraction P R Over S U EndFraction = StartFraction P Q Over S T EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction = Therefore, △PQR ~ △STU by the theorem.

Answers

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

The distance between two points on the coordinate plane is given as:

[tex]Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6[/tex]

In triangle STU:

[tex]|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2[/tex]

|QR| / |TU| = 4/2 = 2

|PR| / |SU| = 6/3 = 2

|PQ| / |ST| = 2√13 / √13 = 2

Hence:

|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|

Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.

Answer 2

Similar triangles may or may not be congruent

Triangles PQR and STU are similar by SSS theorem.

The vertices of triangle PQR are given as:

[tex]P= (4, 4)[/tex]

[tex]Q= (-2, 0)[/tex]

[tex]R = (-2, 4)[/tex]

The vertices of triangle STU are given as:

[tex]S = (2, -4)[/tex]

[tex]T = (-1, -2)[/tex]

[tex]U =(-1, -4)[/tex]

Start by calculating the side lengths of the two triangles, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

For triangle PQR, we have:

[tex]PQ = \sqrt{(4 --2)^2 + (4 -0)^2} = \sqrt{52}[/tex]

[tex]PR = \sqrt{(4 --2)^2 + (4 -4)^2} = 6[/tex]

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

For triangle STU, we have:

[tex]ST= \sqrt{(2 --1)^2 + (-4 --2)^2} = \sqrt{13}[/tex]

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

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

Check if the side lengths of both triangles are similar, by dividing corresponding sides

[tex]k = \frac{PQ}{ST} = \frac{\sqrt{52}}{\sqrt{13}} = 2[/tex]

[tex]k = \frac{PR}{SU} = \frac{6}{3} = 2[/tex]

[tex]k = \frac{QR}{TU} = \frac{4}{2} = 2[/tex]

Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.

Read more about similar triangles at:

https://brainly.com/question/8691470


Related Questions

Find the area. Simplify your answer.
3x
7

Answers

Answer:

21x?

Step-by-step explanation:

I think so

Maddie bought 3 2/3 yards of satin ribbon at the craft store. She wanted to make hair bows for the cheer squad. Each bow requires 2/3 of a yard of ribbon. How many complete bows can she make?

Answers

Answer:

4

Step-by-step explanation:

Given that:

Total yards of satin bought by Maddie = [tex]3\frac{2}{3}[/tex] yards

Number of yards required make one ribbon = [tex]\frac{2}{3}[/tex] yards

To find:

Number of complete bows that can be made ?

Solution:

First of all, let us learn about converting the mixed fraction to fractional form.

Formula:

[tex]a\dfrac{b}{c} = \dfrac{a\times c+b}{c}[/tex]

Therefore, total yards of satin bought by Maddie can be written in fractional form as:

[tex]3\dfrac{2}{3} = \dfrac{3\times 3+2}{3} = \dfrac{11}{3}[/tex]

One hair bow requires [tex]\frac{2}{3}[/tex] yards of ribbon.

Number of hair bows that can be made, can be found by dividing the total ribbon length by ribbon required for making one hair bow.

Answer is:

[tex]\dfrac{\frac{11}{3}}{\frac{2}{3}}\\\Rightarrow \dfrac{11\times 3}{2\times 3}\\\approx 4[/tex]

4 hair bows can be made.

EASY 7TH GRADE MATH QUESTION FIRST PERSON MARKED BRAINLIEST!

Answers

Answer:

30.

Step-by-step explanation:

What is the product of (4i) and (4+i)

Answers

Answer:

-4 + 16 i

Step-by-step explanation:

You are dealing with imaginary numbers so i dont remember y but i know that it is that answer

Answer:

- 4 + 16i.

Step-by-step explanation:

4i(4 + i)

= 16i + 4i^2       Now i^2 = -1 so we have:

16i - 4   (answer)

Every day, the Clinton Pet Store uses 3 bags of dog food to feed the dogs. How many days will 3/4 of a bag of dog food last?

Answers

This question is incomplete. There isn’t enough data to display an answer

3/4 of a bag of dog food will last for 2.25 days.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If 3 bags of dog food are used every day, then in one day, 1 bag of dog food will last:

1 day = 1/3 bag of dog food

To find how many days 3/4 of a bag of dog food will last, we can divide 3/4 by 1/3:

(3/4) ÷ (1/3)

= (3/4) × (3/1)

= 9/4

= 2.25

Therefore,

3/4 of a bag of dog food will last for 2.25 days.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Please help due in 15 min

Answers

It is 63 because 84 divided by 2 is 42 then half of that is 21 so that means 21 is 25% then 21 x 3 is 63

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6x – 15y = 135

Answers

Answer:

Step-by-step explanation:

Slope-intercept form means the equation of a line should be in this form:

[tex]y=mx+b[/tex]

So we re-write our equation into this form like this:

[tex]6x-15y=135\\-15y=-6x+135\\y=\frac{-6x+135}{-15} \\\\y=\frac{-6x}{-15}+\frac{135}{-15} \\\\y=\frac{2}{5}x-9 \\[/tex]

PLEASEEEEE HELPPPP!

Answers

Answer:

it is not 3.

l think correct answer is 2 .

Step-by-step explanation:

(y-b+a):m

If 8 boxes of crayons cost $20 , what would 6 boxes cost ?

Answers

Answer:

$15

Step-by-step explanation:

To figure thsi out, you do 20 divided by 8, which gives you 2.5 ($2.50.)

Next you do 2.50 x 6 which gives you 15 ($15.)

The answer is $15.

(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest. If my answer was wrong and you got marked wrong for it, I deeply apologize and hope you will forgive me, since everyone makes mistakes sometimes. If you need me to elaborate on my answer or give further explanation on it, please ask and I will do so. If you need to explain your reasoning on your work feel free to use my words- word for word- without crediting me, the answer was made for you anyways! Hope yall learn from my answer and it helps you in the future with assignments, quizzes, test’s, and more!

- •Trix•

( Yes I know my - •Trix• thingy is not my user but it’s what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)

Can somebody plz answer both these questions correctly thanks!! (Word problem)

WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDD

Answers

Answer:

a. 40%

b. 7.5%

Step-by-step explanation:

a. 60/ 150 x 100

b. 4.5/ 60 x 100

Select the correct locations on the graph

select the lines that represent functions

Answers

Step-by-step explanation:

Using the vertical line test, we can see which lines are functions, and which are not. If a vertical line were to hypothetically appear, would it touch more than one part of the line? If so, it is not a function.

The lines outlined in a black box are the correct answers.

Answer:the other person is right

Step-by-step explanation:

Jane buys a pack of 6 towels for 15.60 .
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.

Answers

Answer:

2.6

Step-by-step explanation:

Where is the circumcenter of this triangle located?
O at a vertex of the triangle
O outside the triangle
Thing
O on a side of the triangle
O inside the triangle

Answers

Answer:

I don't see a picture but the circumcenter is usually inside the triangle.

(a) 4x - 3y = 6,
7x + 3y = 27.
(d)
12x + 19y= 22,
18x + 23y = 44.
(g) 53x +41y = 147,
41x + 53y =135.
g​

Answers

a.4x=3y+6 we found the x that x=+3/4+3/2
Then we substitute x=+3/4+3/2 to the second equation (7x+3y=27)and we do the calculations to find y
7(3/4+3/2)+3y=27
21/4y+21/2+3y=27
21y+42+12y=108
33y=66
Y=2
We substitute y (2) to the first equation 4x-3y=6 to find x
4x -3(2)=6
4x=12
X=3

Can someone please solve number 9 and ten please

Answers

Answer:

In question number 9 I think is: 3. In question number 10 is: 3. If is not corect well...Im sorry I tried my best :) Hope it helps!

Step-by-step explanation:

what does x equal in 3.8x = -19

Answers

Answer:

x=5

Step-by-step explanation:

3.8x5=19 so 19 divided by 5 = 3.8

Find three consecutive even integers such that the sum of the second and third is 3 times the first integer.

Answers

Answer:

[tex]6[/tex], [tex]8[/tex] and [tex]10[/tex]

Step-by-step explanation:

Let [tex]x =[/tex] smallest consecutive even integer.

Since the second and third consecutive even integers can be expressed by our smallest even consecutive integer, we can express them as:

Second consecutive even integer = [tex]x+2[/tex]

Third consecutive even integer = [tex]x+4[/tex]

From "the sum of the second and third is 3 times the first integer", we can write:

[tex]x+2+x+4 = 3x[/tex]

[tex]2x+6 = 3x[/tex] (collect like-terms)

[tex]x=6[/tex]

∴ The first consecutive even integer is 6

Now, we can use substitution to find the values of the second and third consecutive even integers:

Second consecutive integer = [tex]x+2[/tex]

[tex]=6+2[/tex]

[tex]=8[/tex]

Third consecutive integer = [tex]x+4[/tex]

[tex]=6+4[/tex]

[tex]=10[/tex]

∴ The three consecutive even integers are [tex]6[/tex], [tex]8[/tex] and [tex]10[/tex].

Hope this helps :)

33% of what number Is 1.45?

Answers

ANSWER : Approximately 4.39

WHY? : You must round up the answer "x=4.3939". If thought of like .33X=1.45, then you divide 1.45 by .33

8.75x-2 i need help please

Answers

Answer:

-17.5

Step-by-step explanation:

there we go I can finally anwser here ya go have a good night keep working good :)

whats 1+1+8-3+5-8+4-8+3-5+8-7-7+5+4+3+9+8+2+14+78+

Answers

Answer:

115

Step-by-step explanation:

Hope this helps! Brainliest is appreciated!! Happy Holidays!!!

Answer:

The answer of this question is 123

which expression is equivalent to
2(3g-4)-(8g+3)?

-2g-1
-2g-5
-2g-7
-2g-11​

Answers

Answer:

-2g - 11

Step-by-step explanation:

Expand the brackets, multiply 2 over 3g and -4. One plus and one minus make a minus.

2(3g-4) - (8g+3) = 6g - 8 - 8g - 3

Evaluate like terms.

6g - 8 - 8g - 3 = -2g - 11

can someone tell ne the equation of this word problem.


will give brainliest

Answers

Answer:

Dude. The word problem is non-existent.

Answer:

????

Step-by-step explanation:

there ain't nothing 2 solve

its due today and please give a step by step answer

Answers

Answer:

x=3.333 or 10/3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x-(2*(-6*x+18)+14)=0

Pull out like factors :

  -6x + 18  =   -6 • (x - 3)

to make 3x -  (-12 • (x - 3) +  14)  = 0

Pull out like factors :

15x - 50  =   5 • (3x - 10)  to get

5 • (3x - 10)  = 0

Solve  :    3x-10 = 0

Add  10  to both sides of the equation :

                     3x = 10

Divide both sides of the equation by 3:

                    x = 10/3 = 3.333

Answer:

f

Step-by-step explanation:

substitue the y

3x=2(-6x+18)+14

distrubute

3x=-12x+36+14

combine like terms

3x=-12x+50

add -12x on both sides

15x=50

divide 15 on both sides

x=50/15

simplify

x=10/3

What information is needed to determine that the two triangles are congruent be ASA?

Answers

Answer:

ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

ASA requires two angles and the side that lies between them. The list below is a list of such. (The ends of the segments are the vertices of the angles.)

Minnie is making tea. She knows that her tea tastes best if she lets her tea bag sit in the hot water for exactly fifteen minutes. However, depending how hot the water is, she may have to leave her tea bag in the water for 2 minutes more or less than usual. Write and solve an absolute value equation to describe this situation

Answers

Answer:

|x - 2| = 15 ; |x + 2| = 15

Step-by-step explanation:

Given that:

Wait time = 15 minutes

Variation in wait time depending on level of hotness = 2 minutes

X ± 2 = 15

x + 2 = 15 or x - 2 = 15

x = 15 - 2 = 13 or x = 15 + 2 = 17

Hence, to express the above as an absolute value equation :

|x - variation| = mean time

|x - 2| = 15 ; |x + 2| = 15

Tom and his friend both purchased some CD’s from an online store. The CD’s were all the same price. Tom purchased 5 CD’s for $80.00 and his friend purchased 3 CD’s for $52.00. Let x represent the number of CDs purchased, and y represent the total cost of the CDs. Write the equation in slope intercept form (y=mx+b). Show your work? NEED ASAP!

Answers

9514 1404 393

Answer:

  y = 14x + 10

Step-by-step explanation:

We are given two points, (x, y) = {(5, 80), (3, 52)}. The 2-point form of the equation for a line can be used to find the equation.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (52 -80)/(3 -5)(x -5) +80 . . . . . fill in the given values

  y = (-28/-2)(x -5) +80 . . . . . simplify a bit

  y = 14x -70 +80 . . . . . eliminate parentheses; next, collect terms

  y = 14x +10

Plz, Help me with this question.

Answers

the answer is A 41 5x4=20 7x3=21 . 20+21 =41. please mark me brainlesist

what is the slope of the line
PLSSS HELPPP

Answers

Gradient = rise/run = 8/5 = 1.6

Slope = 1.6

A juggler tosses a ball into the air. The balls height, h, and the t seconds can be represented by the equation h(t)=16t^2+40t+4. Suppose the juggler missed and the ball hit the ground. Find the maximum height of the ball and the time it took the ball to reach the ground. Round all answers to the nearest hundredth

Answers

Answer:

h= -20

t = -0.104 and -2.39s

Step-by-step explanation:

A juggler tosses a ball into the air. The balls height, h, and the t seconds can be represented by the equation h(t)=16t^2+40t+4. Suppose the juggler missed and the ball hit the ground. Find the maximum height of the ball and the time it took the ball to reach the ground. Round all answers to the nearest hundredth

The velocity of the body at its maximum height is zero

V= dh/dt

dh/dt = 32t + 40

0 = 32t+40

-32t = 40

t = 40/-32

t = -1.25s

Substitute t = -1.25 into the expression

h(t)=16t^2+40t+4.

h(-1.25)=16(-1.25)^2+40(-1.25)t+4.

h = 16(1.5625)-50+5

h = 25-45

h =-20

Hence the maximums height is -20m

The ball will reach the ground at h = 0

Substitute

h(t)=16t^2+40t+4.

0 = 16t^2+40t+4

Divide through by 4

0 = 4t²+10t+1

Factorize

-10±√10²-4(4)/2(4)

t = -10±√100-16/8

t = -10±√84/8

t =-10+9.17/8

t = -0.83/8 and -19.17/8

t = -0.104 and -2.39s

Please help im bad at this pls dont just steal my points =(

Answers

Answer:

the slope is a positive and the point is (-1,-2) the equation is 3=(×1,2)

Step-by-step explanation:

if im wrong im so sorry

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