Graph the polygon and its image after a dilation centered at C(1,1)
with scale factor k=0.5
.
J(3,1), K(5,−3), L(5,5), M(3,7)
Answers
Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
DIlations are defined by the follwing operation:
[tex]P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.[tex]k[/tex] - Dilation factor.[tex]P(x,y)[/tex] - Original point of the polygon.[tex]P'(x,y)[/tex] - Dilated point of the polygon.If we know that [tex]O(x,y) = (1,1)[/tex], [tex]k = 0.5[/tex], [tex]J(x,y) = (3,1)[/tex], [tex]K(x,y) = (5, -3)[/tex], [tex]L(x,y) = (5,5)[/tex] and [tex]M(x,y) = (3,7)[/tex], then the coordinates of the new polygon are:
[tex]J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)][/tex]
[tex]J'(x,y) = (1,1)+0.5\cdot (2,0)[/tex]
[tex]J'(x,y) = (1,1) +(1,0)[/tex]
[tex]J'(x,y) = (2,1)[/tex]
[tex]K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)][/tex]
[tex]K'(x,y) = (1,1) +0.5\cdot (4,-4)[/tex]
[tex]K'(x,y) = (1,1) +(2,-2)[/tex]
[tex]K'(x,y) = (3,-1)[/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)][/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot (4,4)[/tex]
[tex]L'(x,y) = (1,1) + (2,2)[/tex]
[tex]L'(x,y) = (3,3)[/tex]
[tex]M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)][/tex]
[tex]M'(x,y) = (1,1) +0.5\cdot (2,6)[/tex]
[tex]M'(x,y) = (1,1) +(1,3)[/tex]
[tex]M'(x,y) = (2,4)[/tex]
Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
We kindly invite to check this question on dilations: https://brainly.com/question/13176891
Related Questions
Factorise fully
gcse maths
please help
Answers
Answer:
Step-by-step explanation:
Numbers: HCF of 18 and 30
18: 2 * 3 * 3
30:2 * 3 * 5
HCF: 2 and 3 = 6
a: a * a and a.
HCF = a
b: b
c: c and c*c
HCF: C
Answer: 6*a*b*c(3a + 5*c)
Note: for this question one of the factors is the HCF and the other is what remains when the HCF is taken out.
Question 1
25 pts
What is the total cost to run the cookie shop when rent is $50.00, insurance is $50.00 and the cost
to make the cookies is $100.00?
O $50.00
O $100.00
O $200.00
O $4.00
Answers
Answer:
200
Step-by-step explanation:
50 for rent and 50 for insurance is 100 plus 100 to make them
A jar contains 35 coins made up of 20c and 50c coins only. Then total value of the coins is
$13.90.
(I) If there were x 20c coins, write an equation in x for the number of 50c coins.
(ii) Using the given information, write an equation in terms of x for the total sum of money
the jar holds.
(iii) Solve the equation to find the number of each type of coin in the jar.
Answers
There are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
Let x represent the number of 20 cent ($0.2) coins
i) Since there are 35 coins in total:
Number of 50 cent coins = 35 - x
ii) The total value of the coins is $13.90. Hence:
0.2x + 0.5(35 - x) = 13.90
iii) 0.2x + 17.5 - 0.5x = 13.90
0.3x = 3.6
x = 12
Number of 50 cent coin = 35 - x = 35 - 12 = 23
Therefore there are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
Find out more at: https://brainly.com/question/21105092
WILL GIVE BRAINIEST IF YOU GET IT RIGHT PLEASE HELPP!!!
Translation: with the digits 1,2,3 you can form three-digit numbers like 123,231,312 ... determine the sum of all possible numbers
Answers
Answer:
d
Step-by-step explanation:
po ang tamang sagon po
Which statement is a true conditional with a converse that is also true?
If an angle measures more than 90 degrees, then the angle is obtuse.
If x = 4, then x2 = 16.
If a figure is a square, then it is a quadrilateral.
If two angles are complementary, then the angles have a sum of 180 degrees.
Answers
That is true
what is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first
Answers
the value of y varies directly with X. Which function represents the relationship between X and Y if y equals 15/6 when x equals 20
Answers
Answer:
y = (1/8)x
Step-by-step explanation:
The relevant basic formula is y = kx, where k is the constant of proportionality.
We must find k. To do this, let y = 15/6 and x = 20 in the above formula:
15/6 = k(20)
We solve for k by dividing both sides by 20: 15/(6*20) = k = 1/8
Then the specific formula for this situation is y = (1/8)x
Three bowls of frozen yogurt cost 8.25. At the same rate how much do 9 bowls of frozen yogurt cost.
Answers
Answer:
$24.75
Step-by-step explanation:
$8.25 is for 3. So triple that cost gets you $24.75
Matthew's bedroom has an area of 72 square feet. The bedroom is 8 times as many square feet as Matthew's closet. If the closet is 3 feet wide, what is the length of the closet?
Answers
Answer:
3
Step-by-step explanation:
72÷8=9
3×y=9
3=y
I hope this helps
please help!! thanks!
Answers
Answer:
A.) Yes
Step-by-step explanation:
Plug in (3,2) into both equations ....
2(3) - 3(2) = 0
2(3) + 2 = 8
Then solve ....
2(3) - 3(2) = 0
6 - 6 = 0
0 = 0
2(3) + 2 = 8
6 + 2 = 8
8 = 8
Since both equation are true the solution (3,2) is true
A car agency shows a new car with a price of AED 45,000. The company predicted that the cost of the
car would depreciate 10% each year for three years and then depreciate 8% each year after that. Find
the value of the vehicle in 8 years.
HELP ME PLSSS
Answers
Answer:
$8640
Step-by-step explanation:
Step 1:
The total amount of the car currently is $45,000. The car depreciates by 10% for the next 3 years. Then multiply 3 to 45,000.
3 × 45,000 = 135,000
The price then decreases by 10%. So, find 10% of 135,000
[tex]10\% = \frac{10}{100}[/tex]
[tex]135000=\frac{135000}{1}[/tex]
[tex]\frac{10}{100}\times \frac{135000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{10}{1}\times \frac{1350}{1}[/tex]
Multiply across
[tex]10\times1350 = 13500[/tex]
Therefore, for the three years, the cars price is now $13,500.
Step 2:
The next step is the same as the first one. But now the car currently is $13,500. And The car depreciates by 8% for the next years. We have to find the value in 8 years. Then multiply 8 to 13,500.
8 × 13,500 = 108,000
Now, find 8% of 108,000
[tex]8\% = \frac{8}{100}[/tex]
[tex]108000=\frac{108000}{1}[/tex]
[tex]\frac{8}{100}\times \frac{108000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{8}{1}\times \frac{1080}{1}[/tex]
Multiply across
[tex]8\times1080 = 8640[/tex]
Therefore, the value of the vehicle in 8 years is $8640.
rail fares go up by 10%, and josie’s new season ticket to london costs £1342. calculate how much more she has to pay now than she did before the 10% increase was added
Answers
Answer:
£134.2 more
Step-by-step explanation:
Divide 1342 by 100
Then you get 13.42
Times that by 10 and £134.2 is 10%
x-3y=-14
x-y=-2
substution method
Answers
Answer:
(4, 6 )
Step-by-step explanation:
x - 3y = - 14 ( add 3y to both sides )
x = - 14 + 3y → (1)
x - y = - 2 → (2)
Substitute x = - 14 + 3y into (2)
- 14 + 3y - y = - 2
- 14 + 2y = - 2 ( add 14 to both sides )
2y = 12 ( divide both sides by 2 )
y = 6
Substitute y = 6 into (1)
x = - 14 + 3(6) = - 14 + 18 = 4
solution is (4, 6 )
Find x and y.
Answers
Answer:
x = 36°y = 48°Step-by-step explanation:
Given:
ΔABC ≅ ΔFDEWe can tell that y = 48° because ΔABC ≅ ΔFDE. We can also tell that ∠DEF = 108 because ΔABC ≅ ΔFDE.Let's first try to simplify ∠CAB in ΔABC. Then we can find the 'x' in ΔFDE with the help of ΔABC.
ΔABC = 108 + 48 + ∠CAB = 180°
=> 156 + ∠CAB = 180°
=> ∠CAB = 24°
=> 48 + 108 + 2x - 48 = 180°
=> 108 + 2x = 180°
=> 2x = 72°
=> x = 36°
So, after working on this problem, we can conclude that 'x = 36°' and 'y = 48°'. Hoped this helped.
Answer: x=36, y=48
Step-by-step explanation:
The sum of the angles in a triangle is 180. From triangle ABC we see that:
108 + 48 + Z = 180, where Z is the unknown third angle.
156 + Z = 180
Z= 24 (angle CAB).
Since the triangles are similar, we can say angle EDF(y) is equal to angle CAB (48). Thus,
y = 48
we can also say that angle CAB is the same as angle DFE:
24 = (2x-y)
24=2x-48
72=2x
x=36
Last month of the visitors at the zoo saw the panda. This month of the visitors at the zoo saw the panda. What fraction more of the visitors saw the panda this month? Simplify the answer if possible.
A. 1/12
B. 1/4
C. 1/6
D. 3/4
Answers
Answer:
There is no way of finding out.
Step-by-step explanation:
9.
3
Here is a recipe for making 10 chocolate chip cookies.
Chocolate Chip Cookies
Makes 10 cookies.
100 g of flour
60 g of sugar
50 g of margarine
40 g of chocolate chips
g
2 eggs
Work out the amounts needed to make 15 chocolate chip cookies.
Answers
Answer:
you will half the recipe, so
50g flour
30g sugar
25g margarine
20g chocolate chips
1 egg
then add together. recipe for 15 cookies will be;
150g flour
90g sugar
75g margarine
60gr chocolate chips
3 eggs
6m in the ratio 7:3:5
Answers
Step-by-step explanation:
which one of the 3 categories represent the 6m ?
the 7 ? the 3 ? or the 5 ?
I suspect it is the 3 (the middle), because it is the only one working with 6 using only integer numbers.
you really have to be more careful about putting all relevant information here for a question.
so,
in general, we see that a "whole" set of distance types has 7 + 3 + 5 = 15 parts (in our case equally long distance segments).
the length of the first type (whatever it is) is 7 parts of the whole 15 parts. = 7/15
the length of the second type is 3 parts of the whole 15 parts (and we suspect this type to be 6m). = 3/15
and the length of the third type is 5 parts of the whole 15 parts. = 5/15
since we now know (or rather assume) that 6m = 3 parts, we can then calculate that 1 part of the 15 is 6/3=2m.
aha !
so then 7 parts are 2×7 = 14m.
and 5 parts are 2×5 = 10m
I guess that's what you needed to find, right ?
just to practice : what would it be, if 6m stands for the 7 ?
we still have the 15 parts of the whole.
but now 7 parts stand for 6m.
1 part is then 6/7m.
3 parts would then be 3×6/7 = 18/7m
5 parts would be 5×6/7 = 30/7m
you see now, why I think the 6m were meant for the 3 part category ?
Combine Like Terms:
7X + 3M - 2(2X + 8) + 24 + 8M - X
so hard
Answers
Answer:
11M + 2X + 8
Step-by-step explanation:
Hope this helps!! :))
Answer:
11M + 2x + 8
I did the math
it rights tho
Help !! I don’t understand
Answers
Answer: .8, -.9, -.5, .9 (estimates)
Step-by-step explanation: correlation coefficients are between -1.0 and 1.0.
-1.0 means a perfectly negative correlation, which will be a straight line going down from left to right
0 means no correlation, it's just random points on the graph with no sense of direction or relationship
1.0 means a perfectly positive correlation, which will be a straight line going up from left to right
the more line-like the shape the data points make are, the further away the correlation coefficient is from 0. you can tell if it's negaitive or positive from the direction of the line.
Write a two paragraph summary of what you are learning in your current math class.
Answers
Answer:
what are you even learning?
Answer:
what is your topic in math class..?
What is the area of this tile? in. in? 4 in. I in.
Answers
Answer:
1*4 = 4 in^2
Step-by-step explanation:
The area for this shape is calculated by multiplying width and length:
1*4 = 4 in^2
Use the pattern in the sequence to determine the next two terms.
-16, 8, -4, 2. . .
Answers
Answer:
-1 , 1/2
Step-by-step explanation:
Each term is obtained by dividing by (-2)
-16/-2 = 8
So, the next two terms are:
2/-2 = -1
-1/-2 = 1/2
I need help with Goemetry. Can you help me with this?
Thank you.
Answers
Answer:
1) (4,5.5) which is (4, 5 [tex]\frac{1}{2}[/tex])
Step-by-step explanation:
Graph it do the equation, (mx2+nx1 divided by m+n , my2+ny1 divided by m+n )
m being 1 and n being 5. Plug in the points and you get the answer to be, (4,5.5). So the answer is 1)
f(x)={x+4….
for f(x)
Answers
Answer:
x+4 x<5
8 5<_x<7
2x -1 7<_x<_10
Evaluate each question below
Answers
Answer:
b=29 a=5.5 n=-13 r=12
Step-by-step explanation:
a: 5+8(4)=5+24=29
b: 3-5(-0.5)=3+2.5=5.5
c: 2(-2)^2-5=2(-4)-5=-8-5=-13
d= -3(-1-3)=-3(-4)=12
substitute the variable with the number and pedmas
variable is the letters in the equation: y=5+8x
Your parents gave you $50 to take your brother and sister to the movies. Your ticket cost $8.25 and your siblings cost $4.25. If you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
$50
$13.25
$39.75
$10.25
Answers
Identify the slope and y-intercept of the
equation 2x + 5y = 20
Answers
Answer:
Slope = - ⅖
Y-intercept = (0, 4), where b = 4
Step-by-step explanation:
Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:
Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.
Subtract 2x from both sides:
2x -2x + 5y = - 2x + 20
5y = -2x + 20
Divide both sides by 5 to isolate y:
[tex]\frac{5y}{5} = \frac{-2x + 20}{5}[/tex]
y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4. The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).
What is a set builder notation
Answers
Answer:
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.
Step-by-step explanation:
For example, C={2,4,5} denotes a set of three numbers: 2, 4, and 5, and D={(2,4),(−1,5)} denotes a set of two pairs of numbers. ... Another option is to use set-builder notation: F={n3:n is an integer with 1≤n≤100} is the set of cubes of the first 100 positive integers.
Answer:
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.
Step-by-step explanation:
No Explanation
write an quadratic equation with the x-intercepts of (0,0) and (16,0)
Answers
Answer:
y = x^2 - 16x
Step-by-step explanation:
The given roots are x = {0, 16}
y = (x - 0)(x - 16)
y = x(x - 16)
y = x^2 - 16x
5 - 6 - 9 - 8 - 5 - 4 + 5 - 5 -5 -5 - 32 = ?
Answers
5 - 6 = -1
-1 - 9 = -10
-10 - 8 = -18
-18 - 5 = -23
-23 - 4 = -27
-27 + 5 = -22
-22 - 5 = -27
-27 -5 = -32
-32 -5 = -37
-37 - 32 = -69
Answer = -69