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Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).


Plot triangles PQR and P′Q′R′ on your own coordinate grid.


Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)


Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)


Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/4

(B) Coordinates of Δ P"Q"R"

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (4,0),

Q(0,-4)

R(-8,-4)

Coordinates of P'Q'R' are

P'(1,0)

Q'(0,-1)

R'(-2,-1)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula =

Where D = Distance between two points

from distance formula we can write that

PQ =

Similarly

P'Q'=

PQ /P'Q' = 4

hence the scale factor of dilation is 1/4 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

So the Coordinated of Δ P"Q"R" can be written as

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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A. 4n - 1.5

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C. 1.5n - 4

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Actually answer and don't ask for brainliest
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Use the table of randomly generated letters to answer the questions about this scenario. The letter P represents personal reasons, and B represents business reasons.

BBB PBB BPB PPB BBP
BBP PBB PPB PBB BBP
BBP BPB BBB BBB BBB
PPB BPB PBP BPB BBP
BPB PBP PPB PBB BBB
Based on this data, the estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is .

The estimated probability that it takes at least four guests to find one who is staying for personal reasons is .

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The barge has an empty weight of 24 tons. The average weight of the railroad cars is 4 tons each. How many railroad cars can the barge haul?

2. In order for the barge operator to meet his expenses, he has to haul
at least 120 tons of freight. How many railroad cars must the barge operator haul on each trip to at least break even?


3. Write a compound inequality that gives the range of the number
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Please help I will reward brainliest

Answer this question please and thank you

What is the slope of this line of best fit?


17

−67

−16

16

Thirty seventh graders each took a random sample of 10 middle school students and asked each student whether or not he likes pop music. Then, they calculated the proportion of students who like pop music for each sample. The dot plot below shows the distribution of the sample proportions.

Based on the dot plot, do you think the proportion of the middle school students at this school who like pop music is 0.5? Explain why or why not.
Question 1 options:

Find the area of 3/4 of the circle (radius = 6)

ASAP HELPP PLSSSSSSSSSSSSSS

Pls helppp 3 part question

Edgar ran 18 2/5 miles and walked 10 1/2 miles. How much further did Edgar run than walk?

Which are equivalent ratios to 3:4?
Check all that are true.

6:8

15:20

9:12

9:15

16:20

What is the fractional equivalent of 1.37?

What is the slope of the line that goes through the points (6, 4) and (8, -2)?


-6

-3

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3

Use the trend line in the following graph to predict the profits a bagel shop will make 22 months after opening.
A.
$28,000
B.
$13,000
C.
$12,500
D.
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Which table shows a proportional relationship between weight and price?
PLS HELP MEE!! I'LL MARK IF RIGHT!!

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Gabby mixes ½ tablespoon of paprika for every ¾ teaspoon of salt. Calculate a unit rate to represent the amount of paprika per 1 tsp of salt.

PLEASE ANSWER I NEED HELP~The scale drawing below is being used to build a wooden table. The scale in this drawing is 1 cm = 3 feet.
You change your mind and want the left edge of table to be 3 feet instead of 6 feet.
How many centimeters should the left edge of the table measure in your scale drawing now?

EXPERT HELP: EXPLAIN THE ANSWER AND DON'T GUESS

Sixty percent of students in your school own a bike. Of a sample of students in your school, the ratio of students who own a bike to students who do not own a bike is 4:10. Does the sample closely estimate the percentage of students in your school who own a bike?

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Can someone help me with this exempalar? The requirements for this are...
What I need to find (I did it so you do not need to do it)
My plan (what to do like multiply or divide)
Solution (your work)
Answer and explanation (answer it and explain)
That’s all! Thank you for helping :)

please help!!!!!!!!!!!!!!!!!