10. What is a composition of rigid motions and a dilation that maps APZY onto ARST
I’m confused on this subject please explain to me how you got an answer thank you
Answers
Answer:
dilation by a factor of 1/2reflection over the line y = -xStep-by-step explanation:
You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.
DilationFirst of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.
The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...
k = RS/PZ
Counting grid squares in the figure, we see this ratio is ...
k = 2/4 = 1/2
Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.
Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.
ReflectionWhen we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.
The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.
We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.
Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.
This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.
__
RotationIf we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.
So, another sequence of transformation that will make the required mapping is ...
dilation by a factor of 1/2reflection across the y-axisrotation 90° CCWThe order of reflection and rotation is important. The dilation can occur anywhere in the sequence.
Alternate solutionPerhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...
dilation by a factor of 1/2reflection across the x-axisrotation 90° CWIf you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.
__
Additional comment
Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.
Tracing paper and/or transparencies can be helpful for these exercises.
Related Questions
What is 2/3 plus 1/5 equal
Answers
Answer: 13/15
Step-by-step explanation: Hope this helps, please mark brainliest and give thanks!
2/3+1/5
15÷3*2+15÷5*1
10+3/15
13/15
What is the value of n?
n = 5
-5 only
0 and 5
5 only
-5 or 5
Answers
Answer:
5 only
Step-by-step explanation:
Answer:
5 only
Step-by-step explanation:
The square root parent function is translated so that it has an endpoint located at (4,-1), then
vertically compressed by a factor of 1/3. Write an equation that could represent this function.
PLEASE HELP
Answers
Answer:
Step-by-step explanation:
[tex]parent~function~f(x)=\sqrt{x-4} -1\\new ~function ~g(x)=\frac{1}{3} \sqrt{x-4}-1[/tex]
Using translation concepts, an equation that could represent this function is:
[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]
The square root parent function is given by:
[tex]f(x) = \sqrt{x}[/tex]
The endpoint is (0,0).What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.After the translation:
The endpoint is (4,-1), hence it was shifted 4 units right and 1 unit down, which means that the equation is now:[tex]f(x) = \sqrt{x + 4} - 1[/tex]
Vertically compressed by a factor of [tex]\frac{1}{3}[/tex] means that it was multiplied by [tex]\frac{1}{3}[/tex], hence:[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]
You can learn more about translation concepts at https://brainly.com/question/4521517
 Please tell me what question 4
Answers
Step-by-step explanation:
In my opinion I think the answer for this question is B you don't have to choose it because it might be wrong
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and 51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
Answers
If we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given that the values in database A are 0 from 100 and have a mean of 50 and Database B has entries from 49 to 51 and also has a mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding the mean. The square of a standard deviation is known as a variance.
Database A has values from 0 to 100 and has a mean of 50. Because the values are somewhat very larger than 50 and database B has values from 49 to 51, there are more chances that the standard deviation of database B will have a smaller value than the standard deviation of database A.
Hence if we compare the given values then we can find that database B is more likely to have a smaller standard deviation.
Learn more about standard deviation at
brainly.com/question/475676
#SPJ1
-k -(-8k)
HELP PLS !!
Answers
Answer:
7k is the answer
Step-by-step explanation:
-k -(-8k)
-k+8k
7k
Mr. Harmon ordered calculators for his math class to use. He ordered a case of 24 calculators and paid a total
of $199.20.
What is the unit rate per calculator that Mr. Harmon paid?
$4.78
$8.30
$12.05
$17.52
HELP ME PLEASE
Answers
so the unit rate was $8.30
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
264cm^3
Step-by-step explanation:
8 × 5 × 5 = 200
8 × 1 × 8 = 64
200 + 64 = 264
how many lines of symmetry dose this picture have??
Answers
Answer:
1 line of symmetry
Step-by-step explanation:
picture has only vertical symmetry
Anyone read tgcf/heaven officials blessing??
Answers
Y=(x-3)^2+3
vertex form to standard form
Answers
Answer:
y = x² -6x +12
Step-by-step explanation:
You want the quadratic equation Y=(x-3)^2+3 written in standard form.
Standard formDepending on where you go to school, the given equation may already be in standard form.
Other places, standard form means the equation is simplified and terms are written in order of decreasing degree.
y = (x -3)² +3 = (x² -6x +9) +3
y = x² -6x +12
Ben is walking 150 miles in 31 days to raise money for a charity. He wants to walk the same distance each day. How far should he walk each day?
Explain what you did with the remainder and why.
Answers
150/31 = 4.8 miles per day
You're creating plans for a building project, and you use a T-square to create a set of angles from lines that are perpendicular, meaning the lines are at right angles to each other, or ______ degrees? a. 225, b. 45, c. 180, d. 90
Answers
Answer:
d. [tex]90^{\circ}[/tex]
Step-by-step explanation:
This is the definition of perpendicularity.
(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0
Answers
Answer:
(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0
2mx^2+x^2-2mx+5x+2m+1=0
3mx^2+5x+1=0
That's as far as you can get simplifying it.
Step-by-step explanation:
Multiply the fractions. Select the answer that is in simplest form.
1
1
5- X 1 = ?
2
4
OA.
1
5
8
OB
1
6
4
OC.
7
6-
8
Answers
Answer:
1 is factors of this question
Answer:
a.option is your answer
The perimeter of a rectangular lawn is 108 meters it is 35 meters long how wide is it
Answers
Answer:
19 meters
Step-by-step explanation:
1. 35×2= 70
2. 108-70=38
3. 38÷2=19
I hope that helped☺
Find the value of the trigonometric ratio.
Answers
Answer:
A) 12 / 13
Step-by-step explanation:
The Sine of a number is defined as the ratio of the length of the side opposite the angle, divided by the length of the hypotensue.
What is an angle that is supplementary to HDI?
Answers
Answer:
hde
Step-by-step explanation:
they both add up to 180 since they're both on line BI
Answer:
<EDH
Step-by-step explanation:
When two angles are supplementary they sum to 180. This means together they form a straight line. So, to find the answer find the angle that connects to <HDI to create one straight line. In this case, that is <EDH because line EI is straight and the two aforementioned angles are the ones that create the line.
if a sample proportion is 0.85, which range of possible values best describes an estimate for the population parameter?
A. (0.8, 0.85)
B. (0.8, 0.89)
C. (0.85, 0.9)
D. (0.8, 0.9)
Answers
Answer:
The correct answer is (0.8, 0.9)
(0.8+0.9) divide by 2 = 85
:) hope this helps
Step-by-step explanation:
Josephine wrote the numbers 1-100 and placed them in a bag.If she selects a number without looking what is the probability that the number is greater than 78
Answers
Easy Cooking is a cooking supply company. Last year, the company sold 32,010 ovens. This year, they sold 30% fewer ovens than that. How many ovens did they sell this year?
Answers
Answer:
9,603 ovens
Step-by-step explanation:
Given:
Last year ---> 32,010 ovens
This year ---> 30% of last year
Question:
How many ovens did they sell this year?
Work:
To find out how many ovens they sold this year, all of you have to do is just multiply 30% by 32,010, the amount of ovens they sold last year
32,010 * 0.3 = 9,603
Solution:
Easy Cooking sold 9,603 ovens this year.
Hope this helped! :D
Given that cot 0 =
5
-, find csc 0.
√11
Answers
According to the given cosecant function the value of csc 0 is equal to 6/5.
What is the cosecant function?The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.
It is given that:
[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
According to trigonometric identity,
[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]
Therefore the value of csc 0 is equal to 6/5.
Complete question;
Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
find csc 0.
To learn more about trigonometric identities visit:
brainly.com/question/24496175
#SPJ1
darius and dakota re roommates. together they have 238 books. if darius has 50 more books than dakota, how many books does dakota have? write an algebraic equation using x for a variable for the situation and solve for x
Answers
Answer:
Dakota has 94 books, while Darius has 144.
Step-by-step explanation:
Given that Darius and Dakota are roommates, and together they have 238 books, if Darius has 50 more books than Dakota, to determine how many books does Dakota have the following calculation must be performed:
Dakota = X
Darius = X + 50
X + X + 50 = 238
2X + 50 = 238
2X = 238 - 50
X = 188/2
X = 94
Therefore, Dakota has 94 books, while Darius has 144.
PLS PLS HELP I HAVE A D IN MATH AND NEED HELP GETTING MY GRADE UP
Answers
Answer:
1/6 bcause
Step-by-step explanation:
it is a 4 by 3 block so if your going to count cont by the side answe is 1/6
A pile of sand has a weight of 90 kg.
The sand is put into a small bag, a medium bag and a large bag
in the ratio 2:3:7.
Work out the weight of sand in each bag.
but
Answers
Answer:
i hope it helps
mapriend
Answer:
Step-by-step explanation:
divide 90 by 2, 3, 7
small bags 90 ÷ 2 = 45
medium bag 90 ÷ 3 = 30
large bag 90 ÷ 7 = 12.8 round it to nearet whole number = 13
a bank account grows by 7% each year .by what percentage dose it grow each decade
Answers
Answer:
Each decade it grows by 10% because a whole decade is 10 years
In a week, an airline operates a flight from San Francisco to New York once a day. The total travel times for this week are:
Sunday: 343 min.
Monday: 314 min.
Tuesday: 401 min.
Wednesday: 341 min.
Thursday: 359 min.
Friday: 407 min.
Saturday: 378 min.
What was the range of flight times for the route that week?
a. 66 min
b. 93 min
c. 29 min
d. 87 min
Answers
Answer:
To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.
Step-by-step explanation:
will give 33 poits and will be marked brainliest please solve this and post answer is it and explain how you got it.
Answers
Answer:
9.85
Step-by-step explanation:
With all the data we get:
0.4+1+0.6+0.85+0.85+0.95+2+1.05+1.05+1.1
Add them all up and you get:
9.85
I did not do this on paper, but on a calculator, to make sure my answers were correct.
happy learning!
--Applepi101
Answer:
9.85 inches
Step-by-step explanation:
Total amount rain that fell in desert :
Amount of rain in inches * number of times recorded in the year
Amount of rain is on the horizontal axis
Number of times is given by the number of dots on each Rainfall amount.
Therefore ;
(1*0.4) + (2*0.5) + (1*0.6) + (2*0.85) + (1*0.95) + (2*1) + (2*1.05) + (1*1.1)
= 9.85 inches
Without looking, you get to choose twice. You will not put them back
each time, because that would be gross.
A) What kind of event is this (independent or dependent)?
B) What is the probability that you would draw 2 reds?
show your work and answer
Answers
A) This is an independent event.
B) The probability that you would draw 2 reds is 0.017
What is probability?The likelihood of an event occurring is known as probability. You can determine how likely something is by asking someone what the probability of something happening is.
When people purchase lottery tickets, the likelihood of winning is typically stated, and it occasionally may be as low as 1/10,000,000. (or even worse). This informs you that there is a low likelihood that you will succeed.
There are 4 reds out 0f 30 colours
The probability of drawing red the first time is 4/30 = 2/15
The probability of drawing red on the 2nd time is 4/30 = 2/15
The probability of drawing red on the both draw is = 2/15 × 2/15
= 4/225
= 0.0170
Thus, The probability of drawing red on the both draw is 0.0170.
Learn more about probability
https://brainly.com/question/30034780
#SPJ1
The cost of an amusement park ticket has been increasing by the same percentage since 2000.
a. The equation c(t)=80(1.03)^t represents the cost of a ticket in dollars as a function of tea the number of years since 2000 explain what the 80 and 1.03 tells us about the situation
b. what is the percent increase in to get prize from year to year?
what does c(5) mean in the situation? find its value and show your reasoning
Answers
b. c(5) means what the cost of the ticket in 2005 is, it’s value is 92.74 because 80(1.03)^5 is 92.74