LESSON 3 WORK WITH SEQUENCES OF TRANSFORMATIONS AND CONGRUENCE
Activity Thinking About Sequences
Have you ever rearranged furniture in a room? When you
move a chair from one side of the room to another, this can
How many ways can you describe the movement of
the furniture between the before and after pictures?
LESS
Before
Ex
Tri
of Transformations Around You
> Do this activity together to describe sequences of
transformations in the real world.
Pre
tra
yo
be described as a sequence of transformations!
?
After
Answers
9514 1404 393
Answer:
an infinite number of ways
Step-by-step explanation:
The transformation involves a series of reflections, rotations, and translations. Any reflection and translation can be described an infinite number of ways, depending on what you choose for the line of reflection (and how many reflections you choose), and how far you do each translation. Similarly, any rotation can described an infinite number of ways, depending on the amount of rotation and the chosen center point.
So, the answer to the question asked is, "You can describe the movement of the furniture an infinite number of ways."
__
One way to describe it is this:
The upper chair was translated to the right, then reflected* across the horizontal centerline. The couch was rotated 90° about the center of the room and translated upward. The coffee table was rotated -90° about its center and translated to the right.
__
* As a practical matter, a piece of furniture cannot be reflected. It can only be rotated or translated. However, the pillows in the upper chair are moved from the left arm to the right arm, so the appearance is that of a reflection. One might say the chair was rotated 180°, and the pillows were translated.
Related Questions
What is the simplest form of 4a + 8b/12
Step by step pls
Answers
Answer:
4a + 2b/3
Step-by-step explanation:
focus on 8b/12 first:
factor 8b/12 by 4 ---> 8b/12 = 4(2)b/4(3) ----> cancel 4 in the denominator and the nominator ---> 8b/12 = 4(2)b/4(3) = 2b/3
then, go back to 4a:
4a is in its simplest form, it can't be factor
therefore, plus 4a and 2b/3 = 4a + 2b/3
20=-7+1/2x what are the values
Answers
Answer:
X = 54
Step-by-step explanation:
20=-7 + 1/2x
+7 +7.
27 = 1/2x
*2 *2
x = 54
At El Rodeo it costs $8 for a burrito and $5 for a taco. Last week, El Rodeo made $1123 from selling burritos and tacos. If 76 burritos were sold, write and solve a linear equation to find how many tacos were sold.
SOLUTION:
Question Blank
type your answer...
tacos were sold
Answers
Answer:
103 tacos were sold
Step-by-step explanation:
8(76)+5x=1123
608+5x=1123
-608 -608
5x=515
/5 /5
x=103
Determine whether side-angle-angle (SAA) is a valid means for establishing triangle congruence. In this case, you know the measure of a side, an adjacent angle, and the angle opposite to the side. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn't work and give an explanation. If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
20 points
Answers
SAA = corresponding angle
the answer is 28 degree
There are 3 consecutive integers that have a sum of 36. What are the integers?
Answers
Answer:
11, 12, 13Step-by-step explanation:
The consecutive integers are increasing by 1
k ← the smallest integer
k+1 ← the middle integer
k+1+1 = k+2 ← the largest integer
k + k+1 + k+2 = 36
3k + 3 = 36
÷3 ÷3
k + 1 = 12
-1 -1
k = 11
k+1 = 11 + 1 = 12
k+2 = 11 + 2 = 13
-x²-8x-16=0
what is the solutions by solving by quadratic equations
Answers
Answer:
x = - 4
Step-by-step explanation:
Given
- x² - 8x - 16 = 0 ( multiply through by - 1 to clear the leading negative )
x² + 8x + 16 = 0 ← this is a perfect square
(x + 4)² = 0 ( take the square root of both sides )
x + 4 = 0 ( subtract 4 from both sides )
x = - 4
the sum of three consecutive even numbers is 114. what is the smallest of the three numbers?
Answers
Answer:
36
Step-by-step explanation:
Let's let n be any number.
If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n must be even. Therefore, let 2n be our first number.
So, the consecutive even number will be (2n+2) followed by (2n+4).
We know that their sum must be 114. Therefore, we can write the following equation:
[tex](2n)+(2n+2)+(2n+4)=114[/tex]
Solve for n. Combine like terms on the left:
[tex]6n+6=114[/tex]
Subtract 6 from both sides:
[tex]6n=108[/tex]
Finally, divide both sides by 6. Therefore, the value of n is:
[tex]n=108/6=18[/tex]
Therefore, our first even number is 2n or 2(18) which equates to 36.
And the consecutive even numbers will be 38 and 40.
So, the smallest of them, the first term, is 36.
Let the three consecutive even numbers be x, x + 2 and x + 4 .
[tex] \longrightarrow \rm x + x + 2 + x + 4 = 114[/tex]
[tex] \longrightarrow \rm 3x + 6 = 114[/tex]
[tex] \longrightarrow \rm 3x = 108[/tex]
[tex] \longrightarrow \bf x = 36[/tex]
Smallest number = 36
A factory made 357,945 baseball bats over the last 2 years. During that time, the factory made 490,867 little league baseballs and 389,839 major league baseballs. How many more baseballs than bats were manufactured during the 2 years? Liliana's answer to this question is below. Her teacher says her answer is not reasonable. Look over her work before answering (a) and (b).
Answers
Answer:
522,761 baseballs
Step-by-step explanation:
Number of baseball bats produced over the last 2 years = 357, 945
Number of little league baseballs produced over the last 2 years = 490,867
Number of major league baseballs produced over the last 2 years = 389,839
Total number of baseballs produced over the period = 490,867 + 389,839
= 880,706
Number of baseballs manufactured more than bats = 880,706 - 357945
= 522,761
There are 522,761 baseballs produced more than bats during the 2 years.
5 plus 5 and 6 plus 6
Answers
Answer:
5+5=10
6+6=12
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
5+5=10
6+6=12
add them up
22
PART 1 40 points+brainless
i need help with these 5 questions
Answers
1) 1/243 (Fraction)
2) Equal to 1
3) 1/x^7 (1 over x, x to the power of 7)
4) 4
5) Equal to 1
Hope I helped
What is the slope of this line?
A. 3
B. -1/3
C. -3
D. -2
E. 4
Answers
Answer:
-3
Step-by-step explanation:
Pick two points on the graph, lets go with (0, 4) and (1, 1)
y = mx + b
m is the slope and to figure it out use below formula
m = (y₂ - y₁) / (x₂ - x₁)
= (1 - 4) / (1 - 0)
= -3 / 1
= -3
Answer:
C. -3
Explanation:
Given problem;
To solve for the slope of the line;
The slope of a line is the vertical distance to the horizontal displacement on a line.
Slope = [tex]\frac{Vertical distance}{horizontal displacement}[/tex]
For lines such as this, we use the formula below;
Slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
To find the slope reference the image attached;
point 1 (0,4) x₁ = 0 y₁ = 4
point 2 (2,-2) x₂ = 2 y₂ = -2
Now input the parameters and solve;
Slope = [tex]\frac{-2 - 4}{2 - (0)}[/tex] = [tex]\frac{-6}{2}[/tex]
Slope = -3
The slope of the line is -3
(-14) + (-7) = ?*
Your answer
Answers
Answer:
-21
Step-by-step explanation:
-21
Explanation
Um justtttt um it’s the answer
What is the distance between the points (-3, 1) and (1, 3)?
Answers
Answer:
4.47
Step-by-step explanation:
a^2+b^2=c^2
2^2+4^2=c^2
4+16=c^2
20=C^2
[tex]\sqrt{20}[/tex]= [tex]\sqrt{c^2}[/tex]
4.47=c
True or false. The solution to an equation in two variables such as y = 3x - 9 is the value of x that makes the equation true.
Answers
ok wait i think you are in my math class lol... this is on my quiz i just took
What is the solution to this equation? 2 x + 3 = x − 4
Answers
Answer:
the answer is -7
Step-by-step explanation:
hope this helps
Answer:
-7
Step-by-step explanation:
Answer to get points.
Answers
Answer:
I think it's B ////////////
if y=198 when x=22, find y when x=182.
Answers
Answer:
y = 1638
Hope that helps
Simplify
9/17 - 8/17
A 9/17. B 1. C 0. D 17/34
Answers
Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3 ? (1 point) 27 to the power of 1 over 3 equals 9 to the power of 3 to the power of 1 over 3 equals 9 to the power of 3 multiplied by 1 over 3 equals 9 27 to the power of 1 over 3 equals 3 to the power of 9 to the power of 1 over 3 equals 3 to the power of 9 multiplied by 1 over 3 equals 3 27 to the power of 1 over 3 equals 3 to the power of 4 to the power of 1 over 2 equals 3 to the power of 4 multiplied by 1 over 2 equals 9 27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3
Answers
Step-by-step explanation:
27^1/3
=(3^3)^1/3
=(3^3)×1/3
=3, so your final answer is D.)27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3
Or
27^1/3=?
To find the answer, I will use one formula from Laws of Exponent
a^p/q
=q√a^p
Apply the same steps to 27^1/3
27^1/3
=³√27¹
=³√27
=3. Hope it help!
Answer:
27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3Step-by-step explanation:
Use of formula: (a^b)^c = a^(bc)Solution
27^(1/3) =(3^3)^(1/3) =3^(3*1/3) =3This is matching the last answer option
27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3help please because i am very dumb
Answers
B) 20000
C) 300000
Answer:
A.7,000
B20,000
c.300,000
Step-by-step explanation:
The weights of certain candles are normally distributed with a mean of 720mg and a standard deviation of 20mg. What proportion of candles weigh between 695mg and 734mg?
Answers
Answer:
ufoufoydiyd8yf86fiyxitdkydyofiyd8yfoyfoycoycoycoycoyfiyfiyfyocyiciycigxitc8txitditxt8xtix8tx8td8yd8yc8yyc8yf58d8txt7x85d85duts7td8txits
Step-by-step explanation:
yfid8yydyofoyf0
Please help me with this math problem
Answers
Answer:
28x
Step-by-step explanation:
i took the test
A cookie recipe calls for 4.5 cups of flour, makes 3 dozen cookies. How much flour is needed to make 6 dozen cookies?
Group of answer choices
Answers
Answer:
9 cups
Step-by-step explanation:
3 dozen of cookies : 4,5 cups
6 dozen : more
6
--- × 4,5 = 9 cups
3
29. Find the measure of each angle.
E
с
(5x + 2)
3x
B
Answers
Answer:
The measure of each angle is :
3x° = 33°
(5x+2)° =57°
Step-by-step explanation:
From the diagram, angle <ABC is a right-angle triangle with a measure of 90°
This means the sum of the two angles <ABE + <CBE =90°
Given from the question :
<ABE = 3x°
<CBE = (5x+2)°
For an equation for sum of the two angles as;
<ABE + <CBE =90°
3x° + (5x+2)° = 90° ------collect like terms after opening the brackets
3x° +5x° + 2° =90°
8x°=90°-2°
8x°=88°
x°=88°/8° = 11°
Measure of the angles will be:
<ABE = 3x° = 3*11° = 33°
<CBE = (5x+2)° = (5*11° +2° ) =55°+2°= 57°
Answers are :
3x° = 33°
(5x+2)° =57°
Which numbers round to 7.91 when rounded to the nearest hundredth? Select all that apply.
A. 7.914
B. 7.905
C. 7.901
D. 7.915
E. 7.909
Answers
Answer:
A. 7.914
B. 7.905
E. 7.909
Answer: A D AND E
Step-by-step explanation:
There the answers i took that test
Which equation has the same solution as 10x-x+5=4110 x − x + 5 = 41?
Answers
Answer:
d
Step-by-step explanation:
The equation having same solution as linear equation 10x -x + 5 =41 is equation: 9x +5 = 41
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.
Given equation 10x -x + 5 =41
⇒ (10-1) x = 41-5
⇒9x = 36
⇒ x= 36/9 = 4
From given options :
1. 10x + 5 =41⇒ 10x = 36 ⇒ x = 36/10 = 3.6
2. 10x - 5 +x = 41 ⇒ 11x = 41+5⇒ 11x = 46 ⇒ x = 46/11
3. 9x = 46 ⇒ x = 46/9
4. 9x +5 = 41⇒ 9x = 41-5 = 36 ⇒ 9x = 36 ⇒ x = 36/9 = 4
Therefore, the equation 9x +5 = 41 has same solution x= 4 as the given solution.
Also, learn more about linear equation from the link below:
https://brainly.com/question/24145091
#SPJ2
Choose the correct answer :
0,2444... and 0,244
1 ) 0,2444...=0,244
2) 0,2444...<0,244
3) 0,2444...>0,244
Answers
Answer:
2
Step-by-step explanation:
HELP THiS IS DUE In 30 MINUTES
Answers
Answer:
undefined
Step-by-step explanation:
The x coordinate of the two points are the same, while the y values are different. This means that the line is vertical. A vertical line does not have a defined slope, because the change in y divided by the change in x is dividing by zero. Therefore, the answer is "undefined"
Answer:
The slope of the line is undefined.
Step-by-step explanation:
Using the point slope formula, in the end, you will get -7 over 0. Since a zero is in the bottom, the slope is considered undefined.
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis.?
y + 2 =y plus 2 equals StartFraction one-third EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
y – 2 = y minus 2 equals StartFraction one-third EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
y + 3 = y plus 3 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)
y – 3 = y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis.(x – 2)
Answers
Answer:
B. y - 2 = 1/3(x - 3)
Answer:
B.
Explanation:
If you actually do the math you get B
0.82 divided by what = 0.0082
Answers
Answer:
100
Step-by-step explanation:
You move the decimal to the left, 2 times.
You can only move it over like that if you are working with 10, 100, 1,00, ect.
If you were multiplying you would move it to the right.
Answer:
100
Step-by-step explanation: