Translation 3 units left and 15 units down
Rotation 270° counterclockwise around the origin
Answers
Answer:
W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)
Kindly check the attached image for more reference
Step-by-step explanation:
Given points of WXYZ ( can be identified by looking at the graph )
W : (14,10) X : (12,4)Y : (6,6) Z : (8,12)Applying translation 3 units left , 15 units down
(Note when shifting left , you subtract from the x value , when shifting down, you subtract from the y value.)
Rule for translation (x,y) ===> ( x - 3 , y - 15 )
Applying translation to given points
W : (14,10) ===> (14-3,10-15) ===> (11,-5)X : (12,4) ===> (12-3,4-15) ===> (9,-11)Y : (6,6) ===> (6-3,6-15) ===> (3,-9)Z : (8,12) ===> (8-3,12-15) ===> (5,-3)Applying rotation 270° counterclockwise around the origin
Rotation 270° clockwise rule : (x,y) ===> (y,-x)
Explanation of rule , change the sign of the x values, then swap the x and y values places.
Applying rotation rule to points
W : (11,-5) ===> (y,-x) ===> (-5,-11)X : (9,-11) ===> (y,-x) ===> (-11,-9)Y : (3,-9) ===> (y,-x) ===> (-9,-3)Z : (5,-3) ===> (y,-x) ===> (-3,-5)So the final points of square WXYZ after the two transformations would be W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)
To see this graphed, kindly view the attached image.
The red square represents the square before any transformations
The blue square represents the square following the translation
And the black square represents the coordinates of the square after the full transformation including both the translation and the rotation .
Answer:
Original image:
W = (14, 10)
X = (12, 4)
Y = (6, 6)
Z = (8, 12)
To translate 3 units left, subtract 3 from the x-values (x - 3)
To translate 15 units down, subtract 15 from the y-values (y - 15)
W' = (14 - 3, 10 - 15) = (11, -5)
X' = (12 - 3, 4 - 15) = (9, -11)
Y' = (6 - 3, 6 - 15) = (3, -9)
Z' = (8 - 3, 12 - 15) = (5, -3)
(red square on attachment)
To rotate 270° counterclockwise around the origin (0, 0),
the point (x, y) becomes (y, -x). So, switch x and y and make x negative.
W'' = (-5, -11)
X'' = (-11, -9)
Y'' = (-9, -3)
Z'' = (-3, -5)
(green square on attachment)
Related Questions
How do you write 7.4 × 10–2 in standard form?
Answers
Answer:
740
Step-by-step explanation:
10^2 = 100
So 7.4 * 10^2
= 740
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 2 or 5 on your next turn, you win the game. What is the probability of winning on your next turn? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answers
Answer:
13.9%
Explanation:
Rolling for 2 : (1, 1)
Rolling for 5 : (1, 4), (4, 1), (2, 3), (3, 2)
So, there are (4 + 1) = 5 possible outcomes out of 36 outcomes
Note: There are 36 outcomes when rolling a two fair cubes.
[tex]\sf Probability = \dfrac{possible \ outcomes}{Total \ outcomes}[/tex]
[tex]\rightarrow \sf \dfrac{5}{36} \ x \ 100[/tex]
[tex]\rightarrow \sf \dfrac{125}9} \%[/tex]
[tex]\rightarrow \sf 13.9 \%[/tex]
A new car is purchased for \$49,000$49,000 and over time its value depreciates by one half every 5 years. What is the value of the car 11 years after it was purchased, to the nearest hundred dollars?
Answers
Set it up like 49000(1-0.05)^11
What is the perimeter of ABDE?
Answers
Answer:
answer C.
Step-by-step explanation:
the base of the triangle is 4 units.the other leg is sqrt5.
the last leg is 4 +9 = 13 so it is sqrt 13.
add them all up together and you get 4+sqrt 13 + sqrt 5 which is C.
hey I will guess you are above oklahoma because it is raining(bottom right) and your temp starts with 6
Becky spent h hours studying
plus an additional 2 hours
typing a report for the week. If
her total studying and work
time was 6.5 hours, how many
hours did she study for?
Write an equation to solve.
Answers
Answer:
6.5 = h + 2
h = 4.5
Step-by-step explanation:
We are given h and since she did 2 additional hours of work, we add the 2 hours. and since we are trying to find h, we set the equation equal to 6.5
please help i have no idea what to do
Answers
Answer: D) 80 degrees
Step-by-step explanation:
christian is trown into a swimming pool his mass is 62,000g and his volume is 68,000cm3 what would his density be? (Show solution)
Answers
Answer:
0.91 g/cm³
Step-by-step explanation:
Density Formula
Density = Mass/VolumeSolving
Density = 62,000 g / 68,000 cm³Density = 31/34 g/cm³Density = 0.91 g/cm³A charity received 240 donations. The total amount received was 7,680. If x represents the average donation, which THREE statements are
correct?
Answers
Answer:
x=32
Step-by-step explanation:
In a certain Algebra 2 class of 28 students, 14 of them play basketball and 7 of them
play baseball. There are 2 students who play both sports. What is the probability tha
a student chosen randomly from the class plays basketball or baseball?
Answers
Answer: 19/28
Step-by-step explanation:
p(student plays basketball)= 14/28
p(student plays baseball)= 7/28
2 students play both sports= 2/28
⇒ 14/28+ 7/28 - 2/28 = 19/28
Calculate the range of the data set
33,38,35.5,39.25,31.75
Answers
The range of the given data set, 33, 38, 35.5, 39.25, 31.75, is 7.5. The range represents the spread or the difference between the highest and lowest values in the data set.
To calculate the range of a data set, you need to find the difference between the maximum and minimum values.
Given the data set: 33, 38, 35.5, 39.25, 31.75
To determine the maximum value, we can compare the numbers in the data set and identify the highest one. In this case, 39.25 is the largest number.
To find the minimum value, we compare the numbers and identify the smallest one. Here, 31.75 is the smallest number.
Now, we can calculate the range by subtracting the minimum value from the maximum value:
Range = Maximum value - Minimum value
= 39.25 - 31.75
= 7.5
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What are the coordinates for B?
options:
(4, -4)
(-3, -2)
(2, 2)
(-4, 4)
Answers
Answer:
(2,2)
Step-by-step explanation:
coordinates are written as (x,y)
where x represents the x value of the coordinate and y represents the y value of the coordinate.
If we look at the graph we can tell that "b" has an x value of 2 and a y value of 2
Therefore we can say that "b" is positioned at (2,2)
Answer:
C. (2, 2)
Step-by-step explanation:
A coordinate is used to identify a point on a graph. A coordinate is written in the form of (x, y), where x is the x-value and y is the y-value.
The x-value is the number of units left or right from the origin (0, 0), and it gets negative by going left and positive by going right.
The y-value is the number of units up or down from the origin (0, 0), and it gets negative by going down and positive by going up.
For example, the coordinates (1, -2) indicate that the x-value goes to the right one unit and the y-value goes down two units.
Here, we are asked to find the coordinate of B:
The x-value is positive 2, which means it went to the right two from the origin.The y-value is positive 2, which means it went up two units from the origin.Our coordinate should look like this: (2, 2)Therefore, the correct answer is C. (2, 2)
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The expression above can also be written in the form a=, b=,c=. 3 6/5
The expression above can also be written in the form .
For this expression, a =
, b =
, and c =
.
Answers
The value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
[tex]\rm = 3^{\dfrac{6}{5}}[/tex]
We can write it as:
[tex]\rm = \sqrt[5]{3^6}[/tex]
The value of a = 3,
The value of b = 6, and
The value of c = 5
Thus, the value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
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What change in government did the British demand of Massachusetts?
needs help
Answers
Answer:
They were no longer able to trade with England. They were no longer able to elect their own governor.I need help with this, and a step by step explaination would be very helpful! Thank you!
Answers
Answer:
18
Step-by-step explanation:
The summation symbol is telling you there are 4 terms of the sum. The values of x in the terms range from 1 to 4.
__
The expanded form of the sum is ...
(1 +2) +(2 +2) +(3 +2) +(4 +2)
= 3 +4 +5 +6 = 18
The sum is 18.
_____
Additional comment
The sum can be rewritten as ...
[tex]\displaystyle \sum_{x=1}^4{(x+2)}=\sum_{x=1}^4{x}+\sum_{x=1}^4{2}=\dfrac{4(4+1)}{2}+4\times2=10+8=\boxed{18}[/tex]
This way, you need to know the sum of integers from 1 to n is (n/2)(n+1). It may be easier just to write the terms out as we have done above.
Atheles leaving practice are asked what their favorite sport is. is it sample or random sample and why is it.
Answers
This is not really a random sample. The athletes are heavily biased toward loving sports. Likely they'll pick their favorite sport to be the one they are currently playing.
Example: if basketball players are asked their favorite sport, they likely might pick basketball.
A much better approach is to randomly select names from a hat, use computer software, or a random number table. This will produce a more random sample to help better represent the population.
°116°
56
f
What is the degree measure of f?.
Answers
Answer:
C. 60
Step-by-step explanation:
Find each measurement indicated. Round your answer to the nearest tenth.
Answers
The measure of the angle B is 30 degree after applying the sin law of triangle.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have a triangle shown in the picture:
We can apply the sin law of the triangle to find the angle B
[tex]\rm \dfrac{28}{sin91} =\dfrac{14}{sinB}[/tex]
SinB = 0.499
B = 29.99 ≈ 30 degree
Thus, the measure of the angle B is 30 degree after applying the sin law of triangle.
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If Birr 5000 is invested with a compound interest rate of 4 percent per annum, which of the following is the amount of the future value at the end of a 24th month?
a.
5203.02005 Birr
b.
5634.6205 Birr
c.
5365 Birr
d.
5408 Birr
Answers
Answer:
d. 5408 Birr.
Step-by-step explanation:
24 months = 2 years.
Amount after 2 years = 5000(1 + 0.04)^2
= 5408.
For how many values of x does f(x) = g(x), on the graph shown
below?
a. 0
b. 2
c. 3
d. 6
Answers
Answer:
the answer is C
Step-by-step explanation:
as you can see f(x) cut g(x) 3 time ( sorry for my bad English )
How many integers are between the numbers a = - 6.52 and b = 6.98?
Answers
Answer:
-13.5
Step-by-step explanation:
-6.52-6.98=-13.5
HELP FAST ITS EASY I JUST NEED TO MAKE SURE PLEASE SOMEONE WHO HAS REAL SKILL AND CAN FINSH THIS ANSWER IT PLEASE I BEG U GUYS I NEED TO FINISH (GIVING BRAINLIEST!!)
Answers
Answer: 71/28 or 2 15/28
Step-by-step explanation:
Turn both fractions into improper fractions.
5 1/4 = 21/4
2 5/7 = 19/7 multiply the denominator with the whole then add the numerator, same denominator.
21/4 - 19/7 = ? find common denominator to subtract
4 x 7 = 28 common denominator
Divide the new denominator by previous denominators then multiply by each respective numerator. 28 divided by 4 is 7 multiplied by 21 is 147, the same happens with 19/7.
147/28 - 76/28 = 71/28 or 2 15/28
1.3b + 2 = 12.4 what is b?
Answers
Answer:
b = 8
Step-by-step explanation:
1.3b + 2 = 12.4
- Subtract 2 from both sides
1.3b = 12.4 - 2
- Subtract 2 from 12.4 to get 10.4.
1.3b = 10.4
- Divide both sides by 1.3.
b = [tex]\frac{10.4}{13}[/tex]
- Expand [tex]\frac{10.4}{13}[/tex] by multiplying both numerator and the denominator by 10.
[tex]b = \frac{104}{13}[/tex]
- Divide 104 by 13 to get 8.
Question 1 (Essay Worth 10 points)
(08.01 MC)
Minnie is doing a survey to find the time her classmates spend playing musical instruments. She asks the following question:
Which student spends the most time playing musical instruments?
Part A: Describe the data you would expect her to collect from this question. (5 points)
Answers
Part A: She needs to collect different types of data to form her classmates. It will help her to find which student spends the most time playing musical instruments.
Part B: Yes, it is a statistical question.
What does Zoe need to do?Zoe needs two main data from each of her classmates.
1. Name of her classmates.
2. Which student spends how much time playing musical instruments.
After that, she can make a graph or a chart in order to understand which student spends more time playing musical instruments.
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Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side JG.
Round your answer to the nearest tenth if necessary.
Answers
Answer: 30.5
Step-by-step explanation:
please help!!!! the other boxes under 4 and 15/2 are 10 and 5
Answers
Answer:
see explanation
Step-by-step explanation:
given that x and y are proportional relationships , then
y = kx ← k is the constant of proportionality
divide both sides by x
[tex]\frac{y}{x}[/tex] = k
using corresponding values of x and y from each table to find k
first table
k = [tex]\frac{10}{1}[/tex] = 10
second table
k = [tex]\frac{20}{4}[/tex] = 5
third table
k = [tex]\frac{15}{2}[/tex]
fourth table
k = [tex]\frac{4}{1}[/tex] = 4
hhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
i think its D.
Step-by-step explanation:
i just counted
Find f(5)+j(-2) if f(x)=12-3x and j(x)=x² + 4x - 1.
Answers
Answer:
-8
Step-by-step explanation:
Put the given values where the corresponding variables are, and do the arithmetic.
__
first functionf(x) = 12 -3x
f(5) = 12 -3(5) = -3
__
second functionj(x) = x² +4x -1 = (x +4)x -1
j(-2) = (-2 +4)(-2) -1 = 2(-2) -1 = -5
__
compositionf(5) +j(-2) = -3 +(-5) = -8
Hector would also like to see a professional sumo tournament while he is there, which would cost him ¥5,488. if the conversion rate of us dollars to japanese yen is 1:94.153 at the time of hector’s trip, how will this affect his budget? a. hector can see the sumo tournament and have about $322 left over. b. hector can see the sumo tournament and have about $86 left over. c. hector has exactly enough left in his budget to see the sumo tournament. d. hector cannot afford to see the sumo tournament, because it would put him over budget by almost $12.
Answers
Based on the exchange rate and Victor's budget, hector can see the sumo tournament and have about $322 left over.
How to find cost of Victor's tournament?Amount with Victor = $380Conversion rate of US dollars to Japanese yen = 1 : 94.153
Cost of the trip = ¥5,488Ratio of dollar to Yuan
1 : 94.153 = x : 5,488
1/94.153 = x / 5,488
cross product1 × 5,488 = 94.153x
5,488 = 94.153x
x = 5,488 / 94.153
x = 58.2881055303601
Approximately,
x = $58
Amount left with Victor = Total money with Victor - amount spent
= $380 - $58
= $322
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This graph shows the solutions to the inequalities y> 3x + 14 and y< 3x + 2.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
-10 -8
10
-10
A. There is a solution, and it is shown by region B.
B. There is a solution, and it is shown by region C.
C. There is a solution, and it is shown by region A.
D. There is no solution.
B2
4
FO
C
00
Answers
The system of inequalities have no solutions, option D is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that the graph shows the solutions to the inequalities y> 3x + 14 and y< 3x + 2.
We have to find the system of inequalities have solutions has solutions or not
As we observe the graphs y> 3x + 14 and y< 3x + 2 of these inequalities the shade of both lines are not overlapped.
So the two inequalities does not have solution
Hence, the system of inequalities have no solutions, opton D is correct.
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is −1.28 a rational number?
Answers
The number -1.28 is rational if it is an integer or decimal, so yes it is.
Answer:
we have 1.28 with bar above 28 signifying that the number can also be written as 1.28282828 The mixed number is then equal to,
1 and 28/99 or 1 and 28 over 99
Therefore, the answer to this item is the second choice.
Step-by-step explanation:
My brother helped me with this one