In geometry, transformations are used to move points from one position to another.
The transformation is a rigid transformation given by [tex](x,y) \to (x + 1, y-2)[/tex]. It preserves lengths and anglesThe preimage is given as:
[tex]S =(-3,4)[/tex]
[tex]T = (3,4)[/tex]
[tex]U = (-1,0)[/tex]
The image is given as:
[tex]S' = (-2,2)[/tex]
[tex]T' =(4,2)[/tex]
[tex]U' = (0,-2)[/tex]
Using points S and S' as our reference point, we have:
[tex]S =(-3,4)[/tex] and [tex]S' = (-2,2)[/tex]
Calculate transformation
[tex](x,y) \to S -S'[/tex]
[tex](x,y) \to (-2,2)-(-3,4)[/tex]
Rewrite as:
[tex](x,y) \to (-2--3,2-4)[/tex]
[tex](x,y) \to (-2+3,2-4)[/tex]
[tex](x,y) \to (1,-2)[/tex]
So, the transformation from the preimage to image is:
[tex](x,y) \to (x + 1, y-2)[/tex]
Calculate the lengths of the sides of the preimage and the image
Using the following distance formula, we have:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]ST = \sqrt{(-3 - 3)^2 + (4 - 4)^2} = 6[/tex]
[tex]SU = \sqrt{(-3 - -1)^2 + (4 - 0)^2} = \sqrt{20[/tex]
[tex]TU = \sqrt{(3 - -1)^2 + (4 - 0)^2} = \sqrt{32[/tex]
and
[tex]S'T' = \sqrt{(-2 - 4)^2 + (2 - 2)^2} = 6[/tex]
[tex]S'U' = \sqrt{(-2 - 0)^2 + (2 -- 2)^2} = \sqrt{20[/tex]
[tex]T'U' = \sqrt{(4 -0)^2 + (2 -- 2)^2} = \sqrt{32[/tex]
Since
[tex]ST = S'T'= 6[/tex]
[tex]SU = S'U'= \sqrt{20[/tex]
and
[tex]TU = T'U'= \sqrt{32[/tex]
Then, the transformation preserves length
From the graph of [tex]\triangle STU[/tex] and [tex]\triangle S'T'U'[/tex]
Since
[tex]\angle S = \angle S' = 76^o[/tex]
[tex]\angle T = \angle T' = 45^o[/tex]
[tex]\angle U = \angle U' = 59^o[/tex]
Then, the transformation preserves angle measure.
Read more about transformation at:
https://brainly.com/question/12865301
Describe the transformation of y = f(x) for the new function
y = -f(x)
A. The graph of y = f(x) was flipped horizontally across the y axis.
B. The graph of y =f(x) was shifted up
C. The graph of y = f(x) was flipped vertically across the x axis.
D. The graph of y = f(x) was shifted down
AWARDING BRAINIEST TO THE FIRST RIGHT ANSWER
PLEASE EXPLAIN TO ME HOW TO SOLVE THIS QUESTION
Answer: -2sin θcos θ -cos θ +sin θ -1
Step-by-step explanation:
I hope it helps! The attachment is down there…. If you have any more questions ask me!
List all the factors of 48. List all the
factors of 64. What are the common
factors of 48 and 64? What is the
greatest common factor of 48 and 64?
Answer:
the GCF of 64 and 48 is 16
Step-by-step explanation:
Factors of 64: 1, 2, 4, 8, 16, 32 and 64.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Common factors of 48 and 64: 1,2,4,8,16
the GCF of 64 and 48 is 16
Answer:
the GCF of 64 and 48 is 16
Step-by-step explanation:
Step-by-step explanation:Factors of 64: 1, 2, 4, 8, 16, 32 and 64.Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.Common factors of 48 and 64: 1,2,4,8,16the GCF of 64 and 48 is 16
Hong needs to memorize words on a vocabulary list for Russian class. He has 14 words to memorize, and he is one-half done. How many words has hong memorized so far?
Step-by-step explanation:
He has done one half = ½
Finding ½ of 14
½ × 14
7
Hence, Hong has memorized 7 words
An electrician charges $40 to come to your house. She also charges $55 for each hour that she works. The electrician charges you a total of $205. How many hours does the electrician work at your house? Use h for the number of hours.
Answer:
$40 + h = $190
190 - 40 = 150
150 ÷ 55 ≈ 2.70 = 3
SO the electrician worked about 3 hours at your house.
h ≈ 3
Hope I helped ya!!
A bakery sells six cookies for every one cake. Yesterday the store
sold 154 cookies and cakes combined. How many cakes were sold?
Answer:
22 cakes were sold.
Step-by-step explanation:
In order to solve this, add the cookies and cakes together (6+1=7) to get 7. Next, divide the cookies and cakes sold combined and divide that by the 7. 154/7=22. You sold 22 cakes and 132 cookies.
To check this answer multiply 6*22=132. Then multiply 22*1=22.
And add; 132+22=154.
Hope this helps!
A cookie recipe says to mix 1 and a half cups of sugar with 1 and three quarter cups of flour. How much of this mixture will there be in all?
what is 8w + 9 < –31
Answer:
w < -5
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!!
Triangle DEF will be rotated 180° clockwise. Choose the TRUE STATEMENT:
The image will be congruent but the orientation will change.
The image will be congruent and the orientation will stay the same.
The image's size and orientation will change.
The image's size will change but the orientation will stay the same.
Answer:
hhhhhhhhhhhhhhhh
Step-by-step explanation:
hhhhhhhhhhhhhhhhhhhh
3.
Find the common ratio of the sequence. 2, –10, 50, –250, . . .
A. –12
B. 12
C. 1/-5
D. –5
Answer:
D. –5
Step-by-step explanation:
Given 1000x = 1000, what is x?
Answer:
x = 1
Step-by-step explanation:
Given
1000x = 1000 ( divide both sides by 1000 )
x = [tex]\frac{1000}{1000}[/tex] = 1
The given equation is,
→ 1000x = 1000
Let's find the required value of x,
→ 1000x = 1000
→ x = 1000/1000
→ [x = 1]
Therefore, 1 is the value of x.
PLZ HELP I REWARD BRAINLIEST PLZ!!
Answer:
.......................
Step-by-step explanation:
a) x=14°
b) x=23°
Please answer by September 7th
Write two conditionals from each biconditional.
SEE EXAMPLE 6
30. A month has exactly 28 days if and only if it
is February
Answer:
If a month has exactly 28 days then it is February
If the month is February then it has exactly 28 days.
Step-by-step explanation:
There is no such thing as two conditional statements however there is the conditional statement and the converse statement so I wrote those for your answer.
anyone solve these questions plz
Answer:
5)7:8=180
84:96=180
6)4:5=90
40:50=90
7)a). q=135
p=45
b).a=70
b=110
supplementary angle=sum of two angle 180°
complementary angle=sum of two angle 90°
Answer:
5) Ans;The two angle 7 and 8 —> 7x and 8x
Sum of two supplementary angle is 180°
7x +8x =180
15x =180
x= 180/15
x = 12°
7x =7(12)= 84°
8x = 8(12)= 96°
The angles; 84° , 96°
6) Ans;The two angle 4 , 5 —> 4x and 5x
Sum of two complimentary angle is 90°
4x+5x =90
9x =90
x=90/9
x=10
4x—> 4(10) = 40°
5x —> 5(10) = 50°
The angles; 40° , 50°
7) Ans;q= 135 ( Vertically Opposite angles)
q+p = 180
135+p=180
p=180-135
p = 45°
_______o_____o_____
a= 70° ( Alternate angles)
a+ b = 180
70 + b = 180
b =180 - 70
b = 110
So ; angle a=70° , b = 110°
I hope I helped you^_^
What is the number 0.000706 written in scientific notation?
Answer:
7.6 x 10^-4
Step-by-step explanation:
Jill runs 18.8 miles in 2 hour. How fast does she run per minute? Round your answer to the hundredth place.
Answer:
0.157
Step-by-step explanation:
im pretty sure thats the answer
express -3/5 as a rational number with denominator of 20
Show full work !
Answer:
- [tex]\frac{12}{20}[/tex]
Step-by-step explanation:
To obtain a denominator of 20 requires the numerator and denominator to be multiplied by 4 , that is
- [tex]\frac{3}{5}[/tex] = - [tex]\frac{3(4)}{5(4)}[/tex] = - [tex]\frac{12}{20}[/tex]
Select the correct answer.
Which statement best defines an angle?
A.
two rays that share a common endpoint called the vertex
B.
two line segments that intersect at a point called the vertex
C.
two lines that intersect at a point called the vertex
D.
two lines that share a common line segment called the vertex
Answer:
A.
two rays that share a common endpoint called the vertex
Step-by-step explanation:
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
The best statement which defines an angle is "Two rays that shares a common endpoints called vertex".
What is an angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
From the definition of an angle, a figure which is formed by two rays or lines that shares a common endpoints is called an angle.
Hence, the best statement which defines an angle is "Two rays that shares a common endpoints called vertex".
Learn more about angle here:
https://brainly.com/question/13954458
#SPJ2
I can't understand. Please help
Answer:
Step-by-step explanation:
i.
(10y+x) - (10x+y) = 63 ---> This subtracts the original from the number with the reversed digits, and makes it equal to 63, so the number increases by 63
y - x = 7 ---> We have to prove this is true, so put it into the original equation
y = 7 + x ---> manipulate the above equation, and substitute it into the original equation
[10 (7 + x) + x] - [10x + (7 + x)] = 63
(70 + 11x) - (11x + 7) = 63
63 = 63 ---> Solve the equation, and because it comes out to be true, you proved that y - x = 7
ii. a.
(10x + y) + (10y + x) = 99 ---> The sum of the original and reversed numbers
x + y = 9
y = 9 - x ---> substitute this into the original equation
[10x + (9 - x)] + [10 (9 - x) + x] = 99
(9x + 9) + (90 - 9x) = 99
99 = 99
ii. b.
infinitely many solutions
factor the expression completely (please help!)
Step-by-step explanation:
6x - x²x ( 6 - x)hope this helps
Answer:
x(6-x)
Step-by-step explanation:
6x - x²
= x(6-x)
first u must find what is the similirity between the 2 eqn “6x and x²”
they both have x, therefore u have to bring the x outside the bracket
What the answer is ansjjfjcjcjjcjcjc
Solve the following equation:
X+m=p-n for p
Answer:
p = m + n + x
Step-by-step explanation:
x + m = p - n
x + m + n = p
p = m + n + x
what are factors of -12 that add up to -2
Answer:
Step-by-step explanation:
the only factors of -12 is: 12 and -1 or -12 and 1, 2 and -6 or -2 and 6, and finally 3 and -4 or -4 and 3. There is no even factor of 12 that adds to -2, unless you use decimals which even then I don’t think there is an awnser. So the awnser would be nonfactorable.
express algerbraically
Four fifths of the product of x squared and y
x^2*y/(4/5)
I think they just wanted you to write it out right?
An ice cream truck driver used the equation Y=KX to show how much money he made selling 9 ice cream bars. He determined he'd make $24.93. How much did he make per bar sold?
Answer:
$2.77 per bar sold
Step-by-step explanation:
Hi there!
We're given that selling 9 ice cream bars could make the truck driver $24.93. To find how much he'd make per bar sold, divide $24.93 by 9 ice cream bars:
24.93 ÷ 9 = 2.77
Therefore, the truck driver would make $2.77 per bar sold.
We could also find this answer using the given equation, y=kx.
y=kx
Let y equal the earnings. Let x equal the number of ice cream bars sold. Let k equal how much the driver would make per bar sold.
24.93=k(9)
24.93=9k
x=2.77
I hope this helps!
I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Problem Situation: Donelle is selling bread for $3 per loaf.
He also sells one specialty cake for $36.
He makes a total of $117.
How many loaves of bread does he sell?
Select the equation that represents this situation.
The letter b represents the number of loaves of bread Donelle sells.
Answer:
36 + 3b = 117
Step-by-step explanation:
36 is the one specialized cake he sold.
3 is the cost and b is how many it represents
117 is your total, so we piece it together.
36 + 3(b) = 117
Answer:
36 + 3b = 117
Step-by-step explanation:
36 is the one specialized cake he sold.
3 is the cost and b is how many it represents
117 is your total, so we piece it together.
36 + 3(b) = 117
Solve the system of equations –2 + y = 14 and -5x – 7y = 10 by
combining the equations.
Answer:
[tex](x,y)=(-\frac{122}{5}, 16)[/tex]
Step-by-step explanation:
Substitute the value of y
[tex]\left\{{{y=16} \atop {-5x-7y=10}}\right.[/tex]
Solve the equation
[tex]-5x-7*16=10[/tex]
A possible solution is
[tex]x=-\frac{122}{5}[/tex]
Check the solution
[tex](x, y) = (-\frac{122}{5}, 16)\\[/tex]
Simplify
[tex]\left \{ {{-2+16=14} \atop {-5*(-\frac{122}{5})-7*16=10}} \right.[/tex]
The ordered pair is a solution
[tex]\left \{ {{14=14} \atop {10=10}} \right.[/tex]
What is this? I don’t know the answers plz help
Answer:
C
Step-by-step explanation:
Answer:
c.
Step-by-step explanation:
Starting with the multiplications, first the multiply matrix A by -4, so we multiply every value in the matrix by -4 and we get
16 16 -4
-4 -16 -28
-8 -12 -12
Then we do the next multiplication which is 8 by matrix B, so once again we multiply every value in the B matrix by 8
16 72 -72
64 64 -16
32 80 8
Now that we did both multiplications, just need to sum the results, so we sum each value of matrix A with the value on the matrix B that's on the same spot
16 + 16 16 + 72 -4 + (-72)
-4 + 64 -16 + 64 -28 + (-16)
-8 + 32 -12 + 80 -12 + 8
And the final result is
32 88 -76
60 48 -44
24 68 -4
So it's option c
A scientist needs 10 liters of 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?
Answer:
4.3L of the 40% solution and 5.7L of the 5% solution
Step-by-step explanation:
hope this helps
