A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1. What is the scale factor of dilation?
Answer:
The scale factor of dilation from ΔPQR to ΔP'Q'R' is 1/3
Step-by-step explanation:
The given information are;
The vertices of ΔPQR are;
P(-6, 6), Q(-6, 3), and R(-3, 3) and the coordinates of ΔP'Q'R' are P'(-2, 2), Q'(-2, 1), and R'(-1, 1)
Given that the length, l, of each side of the triangles is given by the formula for calculating length given the vertices we have;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For side PQ, we have;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-6, 3)
Given that the points have equal y-values, the length is the difference of their x-values as follows;
[tex]l_{PQ}[/tex] = 6 - 3 = 3
Similarly, length QR is the difference in the y-values, since the x-values are equal. therefore, we have;
[tex]l_{QR}[/tex] = -3 - (-6) = 3
Length PR is given as follows;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-3, 3)
[tex]l_{PR} = \sqrt{\left (3-6 \right )^{2}+\left (-3-(-6) \right )^{2}} = \sqrt{18} = 3\cdot \sqrt{2}[/tex]
[tex]l_{PR}[/tex] = 3·√2
For P'Q', we have
P'(-2, 2), Q'(-2, 1)
[tex]l_{P'Q'}[/tex] = 2 - 1 = 1
[tex]l_{P'Q'}[/tex] = 1
For Q'R', we have
Q'(-2, 1), R'(-1, 1)
[tex]l_{Q'R'}[/tex] = -1 - (-2) = -1 + 2 = 1
[tex]l_{Q'R'}[/tex] = 1
For P'R', we have;
P'(-2, 2), R'(-1, 1)
[tex]l_{P'R'} = \sqrt{\left (1-2 \right )^{2}+\left (-1-(-2) \right )^{2}} = \sqrt{2} = \sqrt{2}[/tex]
[tex]l_{P'R'}[/tex] = √2
Therefore, given that we have
PQ/(P'Q') = PR/(P'R') = 3/1 = 3 and QR/(Q'R') = 3·√2/(√2) = 3
The scale factor of dilation from ΔPQR to ΔP'Q'R' = 1/3.
3 2/3 x 4 1/8 x 2 1/2
Answer:
=2/3^x62
Step-by-step explanation:
32/3^x41/8x21/2
PLEASE HELP I DONT KNOW HOW TO DO THIS AND ITS DUE IN 30 MINUTEs
Answer: Can you include a picture please.
Step-by-step explanation:
(Help ASAP!!)
You play a game on your phone. For every correct move you make, you
receive 50 points. For every second that it takes you over 2 minutes to complete the
game, you lose 3 points. You complete the game in 2 minutes 10 seconds using
3 correct moves. What is your score?
Answer:
120 is the score
Step-by-step explanation:
3 correct moves X 50 points for a correct move = 150 points
-3 points for every seconds over the time X 10 seconds over 2 minutes = 30 points lose -30
150 - 30 = 120
if tiffany drove 21 miles using 7 gallons of gas, how many miles did she drive per gallon.?
Answer: she drove 3 miles per gallon
Step-by-step explanation:
21 / 7 = 3 i hope this helps
[tex] \frac{1}{11} \times x = [/tex]
NEED THIS NOW/URGENT
i dont know how to simplify with fractions please need this right now!
Answer:
1/11x
Step-by-step explanation:
Answer: it is [tex]\frac{1}{11}x[/tex] or [tex]\frac{x}{11}[/tex]
On Saturday, Kim's softball team will be having a family picnic. Hamburger patties
are sold at the local store with 12 patties in a package. Hamburger buns, however,
are only sold in packages of 9 hamburger buns. Kim's team wants to buy the exact
same number of packages for patties and buns
What is the least number of packages of patties and hamburger buns that Kim's
team should buy to have exactly the same number of patties as hamburger buns? If a
package of hamburger patties cost $4.98 and a package of hamburger buns cost
$2.16, what was the total expense?
Answer:
See below
Step-by-step explanation:
The patties (3 packs)
12x3= 36
The buns (4 packs)
9x4= 36
cost:
3x$4.98= $14.94
4x$2.16= $8.64
Add them to equal the total cost
= $ 23.58
Maggie‘s brother is 11 years younger than four times her age. The sum of their ages is 54. How old is Maggie?
Answer:
Maggie is 13
Step-by-step explanation:
Honestly, I just kept trying ages starting from 10 because I knew it wasn't going to be less than that. Then I did whatever age, in this case 13, and multiply it by 4. Then minus 11 from that number. Then take that end number and add it to the beginning number(maggies age) and you should get 54.
Math Equation Explanation:
13*4 = 52 (Maggies Age) x 4
52-11= 41 The question stated that Maggie's brother was 11 -------------------------------------years younger than her age times 4.
41 + 13 =54 The sum of both their ages.
£1=$1.62
£650 in dollars
$405 in Pounds
605 pounds is 840.25 dollars
405 dollars is 313.30 pounds
Answer:
£650= 840.25$
$405= 313.30£
Step-by-step explanation:
do any of you know how to do algebra 2 ?
Answer: Were is the math problem at?
what is 64x64? and I know if you use a calculator =)
Answer:
4096
Step-by-step explanation:
Given m//n, find the value of x
Answer:
117 is the value of you Question
Step-by-step explanation:
if you place a 37 foot ladder against the top of a 12 foot building, how many felt will the bottom of the ladder be from the bottom of the building
Answer:
Would it be 25 that’s what I got
Step-by-step explanation:
Before i thought the dividing functions
Please solve that problem my homework is due ✨
Answer:
1,100 miles traveled in 2 hours, 3,300 miles in 6 hours
Step-by-step explanation:
if the plane is moving at a constant speed, to find the miles per hour divide the distance traveled over the time (1650/3). this would get you 550 miles per hour. So, to get the distances at the other times multiply the times by the speed to get distance traveled. (2*550) and (6*550)
Tell me a cool, fun fact, best fact gets. Brainliest
Answer:
The moon has moonquakes.
Step-by-step explanation:
The heads on Easter Island have bodies.
Please help! I'm in a hurry.
Answer:
13
Step-by-step explanation:
15 and 13 have the same angle because they are opposit each other on the intersection of both lines.
2x + 3y = 6
y = 2/3x - 2
y = 2/3x + 2
y = -2/3x - 2
y = -2/3x + 2
Answer:
y= −2/3x+2
Step-by-step explanation:
2x+3y=6
Add -2x to both sides.
2x+3y+−2x=6+−2x
3y=−2x+6
Divide both sides by 3.
3y/3=−2x+6/3
a printer can print 12 pages in 9 seconds what is the closest estimate of the number of pages it can print in 1 min
Answer:
estimated number of pages it can print will 80 in 1 min.
Step-by-step explanation:
If 12 pages/9 Seconds then by multiplying by 60 secs as there are 60 secs in 1 min.
we get
12/9 then multiply by 60 you will get 80 pages in 1 minute.
Number of pages a printer can print in 9 seconds = 12 pages
Number of pages than can be printed in 1 second =
= 12/9
= 1.3 pages
Number of pages that can be printed in 1 second = 0.75 page
Number of pages that can be printed in 1 minute =
= 1 minute = 60 seconds
Number of pages that can be printed in 60 seconds =
= 1.3 × 60
= 78 pages
Rounding off 78 , we get 80 .
Therefore , 80 pages can be printed in 1 minute .
julie is having a nail salon day.She needs to spend $5 for nail polish, $3 for nail polish remover, and $2 for cotton balls.if she does 5 of her friends' nails for $10 each, what will her profit be?
Answer:
Her profit will be $40
Step-by-step explanation:
Answer:
Her profit would be $50
Step-by-step explanation:
The nail polish is $5, Remover is $3, Cotton balls are $2, That all adds up to ten.
And She has 5 of her friends so Ur multiplying 10 by 5
$10 times 5 equals to $50
I really need help..
Thanks!
The distance light travels in one year is known as a light year. A light year is equal to 5.87 × 1012 miles. The closest that Earth ever gets to Jupiter is 3.65 × 108 miles. What is a correct representation of the number of years it will take light to travel from Earth to Jupiter at this distance? Check all that apply.
Answer:
[tex]6.21\times 10^{-5}\ \text{light years}[/tex]
Step-by-step explanation:
The distance light travels in one year is known as a light year.
[tex]1\ \text{light year}=5.87\times 10^{12}\ \text{miles}[/tex]
The closest that Earth ever gets to Jupiter is [tex]3.65\times 10^8\ \text{miles}[/tex]
[tex]3.65\times 10^8\ \text{miles}=\dfrac{1}{5.87\times 10^{12}}\times 3.65\times 10^8\ \text{light years}\\\\=6.21\times 10^{-5}\ \text{light years}[/tex]
Hence, the distance it will take light to travel from Earth to Jupiter at this distance is [tex]6.21\times 10^{-5}\ \text{light years}[/tex]
HIN
The cliff dwellings in Mesa Verde
National Park are accessible to visitors
only when accompanied by a park
ranger. Billy is at a cliff dwelling in
Mesa Verde National Park. So, Billy
(is, may be, is not) with a park ranger.
Deductive reasoning
Answer: Be careful !
Billy is with a park ranger. Should be correct BUT
It is not given that Billy is visiting the cliff dwelling.
Billy may be the Park Ranger.
So Billy may be with a park ranger.
Step-by-step explanation:
Hannah starting playing video games as soon as she got home from school. She played video games for 20 minutes. Then, it took Hannah 1 hour and 35 minutes to finish her homework. When Hannah finished her homework, it was 4:40 P.M. What time did Hannah get home from school?
Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa
A portion of a map with cities A and B is shown. The map uses a scale of 1 inch =15 miles. You are making a map with a scale of 2 inches = 25 miles How far apart are cities A and B on your map?
PLEASE HELP THERE ARE TWO PARTS!!
The graph shows the relationship between the United States dollar and
the euro, the currency of the European Union, in December 2011. Part A:
What is the constant of proportionality shown in the graph? *
Exchange Rate (December 6, 2011)
VA
(400, 300)
300
Number of euros
200
(250, 187.50)
100
(120,90)
100 200 300
400
Number of US dollars
I
Answer:
The constant of proportionality of the graph is 0.75
Step-by-step explanation:
The coordinates of the points on the lines are;
(400, 300), (250, 187.5), and (120, 90)
Which can be written in a tabular form as follows;
Number of US dollars [tex]{}[/tex] Number of euros
120 [tex]{}[/tex] 90
250 [tex]{}[/tex] 187.5
400 [tex]{}[/tex] 300
Given that the graph is a straight line graph, we can represent the graph with the straight line equation, y = m·x + c
Where;
c = The y-intercept (where the graph meets the y-axis) = 0
m = The slope = The constant of proportionality
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m =\dfrac{300-90}{400-120} = \dfrac{210}{280} = 0.75[/tex]
We have, y = m·x = 0.75·x.
Therefore, the constant of proportionality of the graph = 0.75.
in a survey 8 out of 32 students preferred vanilla ice cream if 252 students are surveyed how many should theoretically prefer vanilla ice cream make a prediction?
Answer:
63
Step-by-step explanation:
8 / 32 = 0.25
Multiply 0.25 with 252
0.25 * 252 = 63
This process simply applies the same ratio from the first test to the second test.
What is the solution set of the equation below? 3|5 − x| + 2 = 29
Answer:
x=-4
x=14
Step-by-step explanation:
Absolute Value Equation entered :
3|5-x|+2=29
Step by step solution :
STEP
1
:
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
3|-x+5|+2 = 29
Another term is moved / added to the right hand side.
3|-x+5| = 27
STEP
2
:
Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is 3|-x+5|
For the Negative case we'll use -3(-x+5)
For the Positive case we'll use 3(-x+5)
STEP
3
:
Solve the Negative Case
-3(-x+5) = 27
Multiply
3x-15 = 27
Rearrange and Add up
3x = 42
Divide both sides by 3
x = 14
STEP
4
:
Solve the Positive Case
3(-x+5) = 27
Multiply
-3x+15 = 27
Rearrange and Add up
-3x = 12
Divide both sides by 3
-x = 4
Multiply both sides by (-1)
x = -4
Which is the solution for the Positive Case
STEP
5
:
Wrap up the solution
x=14
x=-4
Solutions on the Number Line
Two solutions were found :
x=-4
x=14
I need help
Indicate the quadrant in which the point belongs.
(-18, -12)
Answer:
3rd quadrant is where the point is