(2.05 MC) Triangle PQR is transformed to Triangle P'Q'R'. Triangle PQR has vertices P(4,0), Q(0,-4) and R(-8,-4). Triangle P'Q'R' has vertices P'(1,0), Q'(0,-1), and R'(-2,-1). Part A: What is the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' Part B: Write The Coords of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis Part C: Are the two Triangles PQR and P"Q"R" congruent?

Answers

Answer 1

Answer:

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

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent

Step-by-step explanation:

The coordinates of triangle PQR are;

P(4, 0)

Q(0, 4)

R(-8, -4)

The coordinates of triangle P'Q'R' are;

P'(1, 0)

Q'(0, -1)

R'(-2, -1)

Part A:

The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;

The ratio of the x, and y coordinates of the points are;

P'/P  = x'/x = 1/4, y'/y =0/0

R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4

Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4

Part B: For reflection across the y-axis, we have;

Pre-image (x, y) becomes the image, (-x, y)

Therefore, we have;

Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)

Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)

Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.

Answer 2

(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 = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]

Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]

from distance formula we can write that

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

PQ = [tex]4\sqrt{2}[/tex]

Similarly

P'Q'= [tex]\sqrt{2}[/tex]

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

[tex](x,y ) \; as \; (-x,y)[/tex]

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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Related Questions

answer it answer it answer it.

Answers

Answer:

C.   p = 3/q

Step-by-step explanation:

An inverse proportion has the form:

y = k/x

Your problem uses p and q, so you need the form

p = k/q

Answer: C.   p = 3/q

please hurry!!!! Show that (2, 1) is a solution of the system of equations. x + 3y = 5, y = –x + 3 Substitute (2, 1) into x + 3y = 5 to get 1 + 32 = 5 . Simplify the equation to get . Substitute (2, 1) into y = –x + 3 to get . Simplify the equation to get .\

Answers

Answer:

see below

Step-by-step explanation:

x + 3y = 5,

y = –x + 3

Substitute the point into each equation and verify that it is true

x + 3y = 5,  2 +3(1) = 5   5 = 5  true

y = -x +3    1 = -2+3     1=1  true

(2,1) is a solution

Answer:

D,A,A,A,

Step-by-step explanation:

that's the real answer

1d

2a

2a

2a

God bless

how do you solve 6 – 5c = -29

Answers

Answer: C = 7

Step-by-step explanation:

6 -5c = -29  make the variable be by itself by subtracting 6 on both sides.

-5c = -35  divide -5 on both sides, when dividing if both numbers are negative they become positive.

c = 7  

C=7 hope this helps:)

Need help ASAP!!!! THX

Answers

Answer:

C

Step-by-step explanation:

f(x) = x - 2

f(2) = (2) - 2

f(2) = 0

A + B are wrong cuz..

f(-2) = -2 - 2

f(-2) = -4

A landscaper is designing a wall of white bricks . The pattern consists of 130 white bricks in the bottom row , 110 white bricks in the second row , and 90 white bricks in the third row . How meany white bricks will the 6th row have

Answers

Answer:

30 Bricks in the 6th row

Step-by-step explanation:

i found the answer online

Answer:

b: 30

Step-by-step explanation:

took test

5. Name the property of real numbers illustrated by the equation. (-2)(3 + ) = (-2)( + 3)

Answers

Answer:

Commutative property

Step-by-step explanation:

You can switch the places of -2 and 3 without changing the output.

This property is called the commutative property

hey gouys I need help on this to plz help mee

Answers

Answer:

d. 3√6 = 7.348

Step-by-step explanation:

1. simplify each expression

a. √150 / 2 = 6.124

b. π + 4 = 7.142

c. 2π = 6.283

d. 3√6 = 7.348

the largest number will be the closest to 8. therefore, point W is expression D.


[tex] {x}^{3} - {x}^{2} \div x[/tex]

Answers

Answer

x(x^2 - 1)

Explanation

Order of Operations is BIDMAS

Therefore division before subtraction.

x^2 / x^1

Use law of indices where

x^m / x^n = x^m-n

So

x^2 / x^1 = x^2-1 = x^1 = x

x^3 - x is no possible as they aren’t like terms, However you can factorise to obtain

x(x^2 - 1)

29. A painter leans a ladder against the side of a
house that is 3 feet from the base. If the top
of the ladder reaches 16 feet, how long is the
ladder ?

HELP! answer if you can!​

Answers

Answer:

16.2788 feet

Step-by-step explanation:

a²+b²=c²

3²+16²=c²

9+256=c²

265=c²

c=√265

c=16.2788 feet

If the ladder is 3 feet from the base of the house and the top is 16 feet from the base then the length of ladder is approximately 16.2788 feet long.

What is pythagoras theorem?

Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to the sum of squares of base and perpendicular of that respective triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex] where H is hypotenuse, P is perpendicular, B is base of triangle.

How to find length of ladder?

If a painter leans a ladder against a wall then it forms a right angled triangle so in this we will apply pythagoras theorem to find the length of ladder.

let the length of ladder be h so,

[tex]h^{2} =3^{2} +16^{2}[/tex]

[tex]h^{2} =9+256[/tex]

[tex]h^{2} =265[/tex]

h=[tex]\sqrt{265}[/tex]

h=16.2788 feet.

Hence the length of ladder is 16.2788 feet.

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congruent complements theorem

Answers

Answer:

Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other.

HOPE THIS HELPS

MARK IT BRAINLIEST!!!!

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

Answers

This question is incomplete because the options are missing; here is the complete question:

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

A. He can randomly survey 50 boys in the school.

B. He can survey 30 students in the school band.

C. He can randomly survey 50 6th graders in the school.

D. He can survey 20 friends from his neighborhood.

The correct answer is C. He can randomly survey 50 6th graders in the school.

Explanation:

A representative sample is a portion of a population that shows the characteristics of all the population. In this context, for a sample to be representative it needs to include only individuals of the population that is studied. Also, ideally, individuals should be selected randomly as this guarantees the sample is not influenced by the researcher. According to this, option C is the best as this is the only one that focuses on the target population (6th graders) and the sample is random, which contributes to the sample being objective and representing the behavior of 6th-graders.

Answer:

He can randomly survey 50 sixth-graders in the school.

Step-by-step explanation:

Which formula would you use to calculate the total enclosed space of Firm 1’s structure. Explain your choice.
What is the total enclosed space of Firm 1’s structure

Answers

Answer:

Total enclosed space = 6597.35 ft³

Step-by-step explanation:

Firm 1's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,

Volume = πr²h

where r = radius of the structure

h = height of the Firm

By substituting the values of 'r' and 'h' in the given formula,

V = [tex]\pi (\frac{70}{2})^{2}(60)[/tex]

  = [tex]\pi (35)\times 60[/tex]

  = 6597.345

  ≈ 6597.35 cubic feet

Total enclosed space of Firm 1 is 6597.35 cubic feet.

Answer:

pi*r sqrq

Step-by-step explanation:

bc its a cirlce

total SA=10445.8 units sqrt

ur welcome

Which transformations will change Figure A into Figure B?

Answers

Answer:

To transform figure A into figure B, you need to reflect it over the y-axis and translate one unit to the left. A sequence of transformations that will accomplish this is (x, y) + (-x, y) and (x, y) + (x - 1,y).

The figures informed are in different scales and mirrored in this way it will be necessary to rotate 180 about the origin, dilate by a scale factor of 2/3.

What is figure rotation?

Rotation is the "turn" of a shape around a point called the center of rotation. The distance to the center of rotation remains constant and the measure of rotation is called the angle of rotation.

In this case, first the figure must be rotated 180 degrees since the images are mirrored and then change the scale so that a dilation of 2/3 occurs.

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The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answers

[tex] d \propto v^2[/tex]

$\implies d=kv^2$

substitute the given values, $5=k(10)^2\implies k=\frac1{20}$

now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$

A big blunder from my side, now fixed!

A baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of$458. How many apples pies did they sell and how many blueberry pies did they sell

Answers

The total number of apple pies is 22 and the total number of blueberry pies is 17.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of $458.

Asumme the total number of apple pies be 'x' and the total number of blueberry pies be 'y'.

The linear equation that represents the total number of pies is:

x + y = 39

x = 39- y   --- (1)

The linear equation that represents the total amount collected is:

10x + 14y = 458--- (2)

Substitute the value of 'x' in equation (2).

10(39- y) + 14y = 458

y = 17

Then Substitute the value of 'y' in the equation (1).

x = 39 - 17

x = 22

Learn more about equations here;

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Solve for x: 3(x + 1) = -2(x - 1) + 6. (1 point)

Answers

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 1

First: distribute 3(x+1)= -2(x-1)+6

3x+3=2(x-1)+6

Then you have too distribute again

3x+3=2(x-1)+6

3x+3= -2x+2+6

Third: add the numbers

3x+3= -2x+2+6

3x+3= -2x+8

Fourth: add the same term to both sides of the equation

3x+3= -2x+8

3x+3-3= -2x+8-3

Fifth: Simplify 3x= -2x+5

Sixth: add same term to both sides of the equation

3x= -2x+5

3x+2x= -2x+5+2x

Seventh: simplify again

5x =5

Eigth: divide both sides of the equation by the same term

5x=5

5x/5 =5/5

Last: Simplify

X=1

Please show your work. I will give brainliest to the right answer!

Answers

Answer:

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

SOLUTION:

Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]

[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

10.The sum of first 16 terms of the AP: 10, 6 ,2, ....is



− 320− 320

320320

640640

 − 352 − 352


Answers

Answer:

              - 320

Step-by-step explanation:

a₁ = 10

a₂ = 6

d = a₂  - a₁ = 6 - 10 = -4

n = 16

a₁₆ = a₁ + (n-1)•d = 10 + (16-1)•(-4) = 10 - 60 = -50

[tex]S_{n}=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{16}=\dfrac{10-50}{2}\cdot 16=-40\cdot8=-320[/tex]

Please give me the correct answer

Answers

Answer:

Step-by-step explanation:

slant height = l = 15 mm

radius = r = 7 mm

Surface area of cone = πr (l + r) square units

                                  = 3.14 * 7 *(15 + 7)

                                  = 3.14 * 7 * 22

                                 = 483.56 square mm

what is the answer to (x+1)(3x+2)

Answers

The answer is 3x2+5x+2

A bag contains 2
2
blue marbles, 2
2
red marbles, and 2
2
yellow marbles.

If Jenna randomly draws a marble from the bag (and puts it back) 15
15
times, how many times should she expect to pull a yellow marble?

Answers

Answer:

5 times

Step-by-step explanation:

Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.

49*32’55” + 37*27’15” = ?

Answers

Answer:

87°10''

Step-by-step explanation:

In 49°32'55'', we convert 32' to degrees. So. 32/60 = 8/15. We also convert 55'' to degrees. So, 55 × 1/60 × 1/60 = 55/3600 = 11/720

In 37°27'15'', we convert 27' to degrees. So. 27/60 = 9/20. We also convert 15'' to degrees. So, 15 × 1/60 × 1/60 = 15/3600 = 1/240

We now add the fractional parts plus the whole part of the angles together.

So,

49 + 8/15 + 11/720 + 37 + 9/20 + 1/240 = 49 + 37 + 8/15 + 9/20 + 11/720 + 1/240 = 86 + 59/60 + 7/360.

We now convert the fractional parts 59/60 to minutes by multiplying by 60 and convert 7/360 to seconds by multiplying by 3600

86° + 59/60 × 60 + 7/360 × 3600 = 86° + 59' + 7 × 10 =86° + 59' + 70'' = 86 + 59' +  1'  + 10''= 86 + 60' + 10'' = 86 + 1° + 10'' = 87° 10''

So, 49°32'55'' + 37°27'15'' = 87°10''

HHHHEEEEELLLLLPPPPPPP PLEASEEE ANSWER #1 AND #2

Answers

Answer:

37 = -3 + 5(k +6)

37 = -3 + 5k + 30

37 = 27 + 5k

10 = 5k

k = 2

-2 = -(w - 8)

-2 = -w + 8

-10 = -w

w = 10

Answer:

37=-3+5(k+6)                                            

37=-3+5k+30

37=27+5k

37-27=5k

5k=10

k=10/2

k=5

***********************************************************************************

-2= -(w-8)

-2=-w+8

-2-8=-w

-w=-10

w=10

The Three Stooges are having a pie eating contest. In 3 hours, Moe can eat 36 pies, Larry can eat 30, and Curly can eat 60. How many hours does it take them to eat 126 pies?

Answers

Answer:

3 hours

the information states in 3 hours they eat 36+30+60 = 126 pies.

Answer:

Altogether, the three stooges will consume 126 pies in three hours.

Step-by-step explanation:

1. In one hour, the three stooges can eat their total divided by three: Moe can eat 12 in one hour, Larry can eat 10 in one hour, and Curly can eat 20 in one hour. Therefore, the three stooges can eat 42 pies in one hour altogether. So, we have the equation 126 = 42h where h = the number of hours. Solving for 126 gives us 126/42 = h. h = 3. The three stooges can eat 126 pies in three hours.

HELPPP MEEE

Ying was planning how to seat guests at a dinner. There were between 50 and 100 people coming. Ying noticed that they could be seated with 8 people to a table and no seats left empty. She also noticed that they could be seated with 12 people to a table with no seats left empty. How many people were coming?

Answers

Answer:

96 people were coming

Step-by-step explanation:

In this question, we want to determine the number of people who were coming to the party.

First of all, we were made to know that this number is between 50 and 100. So whatever figure we will be giving as answer will be something within that range.

We were told that if 8 or 12 people sat at a table, there would be no remainder left. So basically what we need to do here is to calculate the highest multiple of 8 and 12 which is between 50 and 100.

we could have 24, 48 and 96 as multiples of both. But that multiple that sits between 50 and 100 is 96. So therefore, our answer is 96.

Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m

Answers

Answer:

x = 2√41 m

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

a² = b² + c²

where a is the hypotenuse

From the question x is the hypotenuse

So we have

[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]

Find the square root of both sides

We have the final answer as

x = 2√41 m

Hope this helps you

Answer:

2 sqrt(41) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10^2 = c^2

64+ 100 = c^2

164 = c^2

take the square root of each side

sqrt(164) = sqrt(c^2)

sqrt(4*41) = c

2 sqrt(41) =c

I WILL GIVE BRAINLIEST!
80 patients gave information about how long they waited to see the doctor.
1. Work out an estimate of the mean time that the patients waited.

2. The doctor says, “70% of our patients wait less than 30 minutes to be seen.” Is she correct?

Answers

Answer:

No, 68.75% waited less than 30mins

I don't really know about the other one, but i tried my best, soooo sorry

soz

Hope that helped!!! k

15 points! :( help asap!:(
(-1,-5)
(0,-3)
(4,5)
(9,15)

Answers

Answer:

(0,-3)

Step-by-step explanation:

You can plug in x and y into the equations to see if it works.

(-1,5)

2(-1)-(-5)=-2+5=3 Yes

(-1)+2(-5)=-1-10=-11 No

So (-1,5) Does NOT work.

(0,3)

2(0)-(-3)=0+3=3 Yes

(0)+2(-3)=0-6=-6 Yes

So (0,-3) DOES work.

The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for dailytransportation. What is the standard deviation of the amount spent?b. What is the probability that a household spends between $4000 and $6000?c. What is the range of spending for the 3% of households with the highest daily transportationcost?

Answers

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312

           [tex]\sigma[/tex] = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

                      P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           [tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]                

                            [tex]\sigma=\frac{-\$5312}{-1.645}[/tex]  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)

 P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

                    P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           [tex]\frac{x-\$6312}{3229.18}=1.88[/tex]                

                         [tex]{x-\$6312}=1.88\times 3229.18[/tex]  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Find the value of x. A. 53–√ in B. 241−−√ in C. 55–√ in D. 9

Answers

Answer:

x = 5√3 inches

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

where a is the hypotenuse

Substitute the values into the above formula

The hypotenuse is 10 inches

We have

[tex] {10}^{2} = {5}^{2} + {x}^{2} [/tex]

[tex] {x}^{2} = {10}^{2} - {5}^{2} [/tex]

[tex] {x}^{2} = 100 - 25[/tex]

[tex] {x}^{2} = 75[/tex]

We have the final answer as

x = 5√3 inches

Hope this helps you

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