Based on a graph below which sequence of transformation is needed to carry ABCD onto its image A’B’C’D?
Answers
Given:
The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).
The vertices of A'B'C'D' are A'(-2,6), B'(-5,3), C'(-8,3) and D'(-8,6).
To find:
The sequence of transformation is needed to carry ABCD onto its image A’B’C’D.
Solution:
The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).
If figure ABCD translated by the rule, [tex](x,y)\to (x,y-9)[/tex], then
[tex]A(2,3)\to A_1(2,-6)[/tex]
[tex]B(5,6)\to B_1(5,-3)[/tex]
[tex]C(8,6)\to C_1(8,-3)[/tex]
[tex]D(8,3)\to D_1(8,-6)[/tex]
Then the figure rotated 180 degrees clockwise about the origin. So,
[tex](x,y)\to (-x,-y)[/tex]
[tex]A_1(2,-6)\to A'(-2,6)[/tex]
[tex]B_1(5,-3)\to B'(-5,3)[/tex]
[tex]C_1(8,-3)\to C'(-8,3)[/tex]
[tex]D_1(8,-6)\to D'(-8,6)[/tex]
So, the required sequence of transformation that is needed to carry ABCD onto its image A’B’C’D is " A translation by the rule [tex](x,y)\to (x,y-9)[/tex] and then a 180° clockwise rotation about the origin".
Therefore, the correct option is D.
Related Questions
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper how many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper
Answers
Given :
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.
To Find :
How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.
Solution :
Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].
Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].
Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.
Percentage of copper in resulting mixture :
[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]
Hence, this is the required solution.
8. A sequence can be generated by using 2n - 11. What are the first four terms in
the sequence?
Answers
Answer:
[tex]\bold{a_1=-9\,,\quad a_2=-7\,,\quad a_2=-5\,,\quad a_4=-3}[/tex]
Step-by-step explanation:
[tex]a_n=2n-11\\\\a_1=2(1)-11=2-11=-9\\\\a_2=2(2)-11=4-11=-7\\\\a_3=2(3)-11=6-11=-5\\\\a_4=2(4)-11=8-11=-3[/tex]
you are selling tickets to a school play. students tickets cost 5.00 dollars and adults tickets cost 7.00. you sell a total of 125 tickets and collect 775.00 dollars. how many of each type of ticket did you sell? PLZ HELP SHOW WORK
Answers
Answer:adult tickets - 75 and student tickets - 50
Step-by-step explanation:
75x7=525 and 50x5=250, therefore 525+250=775
hope this helps
At 9 pm the temperature was -2°C.
By midnight the temperature had gone down by 7 °C.
(b) Write down the temperature at midnight.
Answers
Answer:
-9°C.
Step-by-step explanation:
Simple -2°C - 7°C.
What is the formula for calculating slope? Explain it in full.
Answers
Answer:
Use slope formula
Step-by-step explanation:
To calculate the slope, you can use the slope formula which is the change in the height compared to the change in the width. Using ordered pairs, this is the change in the y-values divided by the change in the x-values or the rise divided by the run.
x - 13 = 22 linear equations
Answers
Answer:
x = 35
Step-by-step explanation:
x - 13 = 22
Add 13 to each side
x - 13+13 = 22+13
x = 35
See attachment for math work and answer.
NEED HELP PLEASE BEGGING PLEASE!!!!
Answers
Answer:
-54
Step-by-step explanation:
[tex]8(-9) - 6(-3)\\[/tex]
Multiply 8 by -9 and 6 by -3
[tex]-72 - (-18)[/tex]
Subtract[tex]Value = -54[/tex]
Hope this helps
plz mark brainliest
Which of the following is r^2 + 4s evaluated for r = 4 and s = 1.5?
14
30
38
22
Answers
Answer:
22
Step-by-step explanation:
Once you fill in the variables your equation will look like this::4^2+4(1.5)::you will the go multiply both parts of the equation leaving you with 16+6 and when you add those together you get 22.
Hope This Helps!
A rectangular tank has a length of 12 feet, width of 8 feet, and height of 5 feet. Frankie filled the tank with water at a rate of 4 cubic feet per minute. At this rate, how long will it take Frankie to completely fill the tank without overflowing it?
Answers
Answer:120 minutes.
Step-by-step explanation:
look, 12x8x5=480, and 480/4-120
3. Samuel tiene 11 cajas con mosaicos cuadrados de 20 cm por
lado y quiere cubrir una pared que mide 3 m de largo y 2 m
de alto. Si en cada caja hay 14 mosaicos, éserá necesario que
compre más cajas?
Matemáticas
Answers
Answer:
Primero veamos el área de la pared, es decir, el área total que Samuel debe cubrir.
La pared es de 3m por 2m.
Entonces el area es:
A = 3m*¨2m = 6m^2.
Ahora veamos los mosaicos.
Cada mosaico es un cuadrado de 20cm por 20cm.
El primer paso sería cambiar las unidades para tener metros aca también.
1cm = 0.01m
entonces.
20cm = 20*0.01m = 0.2m.
Entonces cada mosaico es:
0.2m por 0.2m
El área de cada mosaico es:
a = 0.2m*0.2m = 0.04m^2.
En una caja de mosaicos hay 14 mosaicos, entonces con una caja Samuel puede cubrir 14 veces a, o:
14*0.04m^2 = 0.56m^2.
Y Samuel tiene 11 cajas, entonces tenemos 11 veces lo de arriba:
11*0.56m^2 = 6.16m^2.
Y el área de la pared es 6m^2.
6.16m^2 > 6m^2
Entonces con las 11 cajas de mosaicos podemos cubrir completamente esa pared, y vamos a tener algunos mosaicos sobrantes.
Entonces Samuel no debe comprar mas cajas.
Type your response in the box. We each have a different level of health, and that level of health depends on many factors, including our lifestyles and habits. Some factors, however, might be outside our control. In your opinion, which is the biggest factor in determining how healthy you are? your level of physical activity your diet your level of stress factors outside your control, such as heredity Font Sizes
Answers
Answer:
Diet
Step-by-step explanation:
Health & fitness level has multiple factors. Some internal choice factors, some externally ascribed factors. Eg(s) - Diet, Excercise & Heredity, pollution respectively.
In my opinion, biggest factor affecting health is : Diet. As, it can affects health positively & negatively, by major extent. It can also help overcoming other health detrimental factors - eg lack of excercise, heredity issues, pollution related issues etc.
Each digit 8 in the number 8.888 has a different value placed on its place in the place-value chart. Each 8 is multiplied by its place value. I've made up a song to help you remember this. What is the rule that this is referring to? Write the rule below.
Answers
Answer:
The value of every digit in a decimal figure is given by its position in that figure.
Step-by-step explanation:
The Rule:
The value of every digit in a decimal figure is given by its position in that figure.
For the figure 8.888, from left to right,
The first 8 is in units
The second 8 is in tenth (this means 8/10 = 0.8)
The third 8 is in hundreth (this means 8/100 = 0.08)
The fourth 8 is in thousandth (this means 8/1000 = 0.008)
The sum of the place values of the digits after the decimal point = 0.888
when the unit 8 is added, you then get 8.888
8+($6)+6
Simplify and solve this expression:
Answers
Answer:
6+8=14
14 times 6 is 84
Mutiply 8 by 6 = 48
Add 48 and 6 =54
Answer =54
7) Compare the ratios of the corresponding sides to prove or disprove that the polygons are similar.
Answers
Answer:um thers no picture
Step-by-step explanation:
The equation P=$3.90+$0.10x represents the hourly pay(P) a worker receives for loading x number of boxes onto a truck. What is the slope of the line represented by the given equation?
Answers
Answer:
The slope of the line is 0.1.
Harvy claims that he can map rectangle ABCD to rectangle EFGH. Select all the transformations or series of transformations that support his claim.
Answers
Answer:
Option (B) and (D)
Step-by-step explanation:
To understand the relation between rectangle ABCD and EFGH take a point A from rectangle ABCD which is at E of rectangle EFGH after the series of transformations.
Horizontal distance between A and E = 2 - (-10) = 12 units
Vertical distance between A and E = 4 - 2 = 2 units
If the point A is shifted 12 units right and 2 units up we will find the point E.
Therefore, A translation of 12 right and 2 units up has been done.
Rule for the translation,
(x, y) → (x + 12, y +2)
Moreover this,
If rectangle ABCD is reflected over x = -1 and translated 2 units up, rectangle ABCD will overlap the rectangle EFGH.
Therefore, Options (B) and (D) will be the answer.
Aubrey's dinner cost $85 She tips the waitstaff 30% for excellent service
Answers
Answer:
The total amount she paid would be $105.50.
Answer:
25.5 is the tip -- 110.50 is the total bill.
Step-by-step explanation:
You would calculate .30 (move the decimal over twice to switch from a percentage to a decimale) multiplied with 85 and this gives you 25.5.
85 * .3 = 25.5
Depending on the rest of the question, I added the tip to the amount of the dinner cost to obtain the total bill. You will need to see what the rest of the question is in order to verify which answer you are looking for.
If 6 is an element in the domain of f(x) = 9x-25/5, what is the corresponding element in the range?
Answers
Answer:
Step-by-step explanation:
f(x) = 9x - 25/5
f(x) = 9x - 5
f(6) = 9*6 - 5
f(6) = 54 - 5
f(6) = 49
=================
You might mean
f(x) = (9x - 25)/5
f(6) = (9*6 - 25) / 5
f(6) = (54 - 25) / 5
f(6) = 29/5
f(6) = 5.8
Moral: please use brackets to clarify the question.
what is a frequency table
Answers
Answer: its a method or organizing your info while displaying it
Step-by-step explanation:
Polygons ABCD and A′B′C′D′ are shown on the coordinate grid: A coordinate plane is shown with two polygons represented. Polygon ABCD has vertices A at 2 comma 2, B at 2 comma 4, C at 3 comma 5 and D at 3 comma 1. Polygon A prime B prime C prime D prime has vertices A at negative 1 comma negative 2, B at negative 1 comma negative 4, C at negative 2 comma negative 5, and D at negative 2 comma negative 1. What set of transformations is performed on ABCD to form A′B′C′D′? (4 points) a A translation 1 unit to the left followed by a 180-degree counterclockwise rotation about the origin b A translation 1 unit to the right followed by a 180-degree counterclockwise rotation about the origin c A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right d A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
Answers
Answer:
Answer is A. I get it right. :3
Answer:
a
Step-by-step explanation:
Which equation below represents a horizontal line?
x = 4
y = x – 0
y = x + 0
y = 4
Answers
Answer:
x=4
Step-by-step explanation:
this should be the answer hope it helps
PLEASE ANSWER BOTH QUICK
Answers
Answer:
1.C
2.A
Step-by-step explanation:
dude trust me
Which one?
A. B. C. Or D.
Answers
Answer:
A)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I think..
which expression is equivalent to 0.17w + 0.77 + w? -0.77 + 1.17w
-0.17w + 1.77
-1.94w
-1.6w
Answers
Answer:
113.29w +1.77
Step-by-step explanation:
Write your answer as a whole number and remainder.
73 : 8= R
Answers
Answer:
9 R 1
Step-by-step explanation:
73/8 = 9 R 1
we know 8x 9 = 72 so we know we have a remainder of 1
Mercury is the closest planet to the Sun, with an average distance of 35,000,000 miles. It takes light about 3 minutes to travel from the Sun to Mercury. Neptune is the farthest, with an average distance of 2.8 x 109 miles from the Sun. How many times farther from the Sun is Neptune than Mercury? How long does it take light to reach Neptune? Follow the steps to find out. 1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer.
Answers
Answer:
1.
[tex]2765000000 \: or \: 2.765 \times {10}^{9} [/tex]
2.
[tex]273 \: seconds[/tex]
3.
[tex]3.5 \times {10}^{7} [/tex]
Six less than 2/3 of a
number is eighteen.
Answers
Answer:
36
Step-by-step explanation:
i think
Hope this helps and a Brainliest would be appreciated
Find the missing terms in the sequence:
18, -72, 288,
Answers
Answer:
-1,152Step-by-step explanation:
18 · (-4) = -72
-72 · (-4) = 288
288 · (-4) = -1,152
a and b are positive integers and a+b=2009!
what is the amount of ordered pairs of (a, b)?
Answers
Answer:
[tex]2000 \: and \: 9.[/tex]
[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]
Let's consider a much smaller value and work our way up to the factorial 2009!
Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.
The only solution to a+b = 2 is a = b = 1 as mentioned.
----------
Now move onto a+b = 3. We have two solutions:
a = 1, b = 2
a = 2, b = 1
-----------
Now move onto a+b = 4. We have three solutions
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.
So 'a' counts up to 3, while b counts down from 3.
We cannot reach 4 since 0 is not allowed for a or b.
-------------
The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so
a = 1, b = k-1
a = 2, b = k-2
a = 3, b = k-3
....
a = k-3, b = 3
a = k-2, b = 2
a = k-1, b = 1
Where k > 2
Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.
This confirms there are k-1 solutions listed above.
The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions
Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!
simplify the expression 6(x+4)+1=