Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.
Rigid Motion:Any way of moving all the points in the plane such that
a) the relative distance between points stays the same and
b) the relative position of the points stays the same.
There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.
Translation:In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance. See Image-1.
Rotation:A rotation fixes one point (the roto center) and everything rotates by the same amount around that point. Every rotation has a roto center and an angle. See Image-2.
Reflection:A reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every reflection has a mirror line. See Image-3.
Glide Reflection:A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance. See Image-4.
Therefore,
Simply put, rigid motions are transformations that preserve the side lengths and angles in a shape. You can see any of these transformations by moving an object you may have around you right now. Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.
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The figure shown has two parallel lines cut by a transversal:
A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Use the figure to complete the sentence. (4 points)
∠3 and ____ are alternate interior angles.
∠2
∠6
∠5
∠8
Answer:
∠5
Step-by-step explanation:
If Im not mistaken with the order of angles, ∠5 is the answer because they are both angles in the middle of he transversal making them interior angles, then alternate is pretty self explanatory.
PLEASE HELP!
What is the value of (−14)3 when evaluated?
A. −2,744
B. −196
C. 42
D. 2,744
Answer:
−2,744
Step-by-step explanation:
What is the value of [tex](-14)^{3}[/tex] when evaluated?
A. −2,744
B. −196
C. 42
D. 2,744
The following data values represent a sample. What is the variance of the sample? x = 7. Use the information in the table to help you.
A. 14.4
B. 4.2
C. 18
D. 3.8
X 7 5 11 1 11
(x₁ - x)² 0 4 16 36 16
The variance of the sample mean x = 7 is 18(option c).
Given table:
X 7 5 11 1 11
(x₁ - x)² 0 4 16 36 16
n = number of observations = 5
Variance σ² = 1/n-1 Σ[tex]\ \ n} \atop {i=1} \right.[/tex] ([tex]X_{1}[/tex] - X)²
= 1/5-1 (0 +4 + 16 + 36 + 16)
= 1/4(72)
= 18
Therefore variance σ² = 18
Hence the variance of the sample mean x = 7 is 18.
so option c is correct.
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if two parallel lines are cut by a transversal then each pair of alternate interior angles are congruent or supplementary
if two parallel lines are cut by a transversal then each pair of alternate interior angles are congruent.
Two straight lines are parallel if they intersect a horizontal line so that their corresponding angles are coincident. Two line segments are parallel if they intersect the transverse line so that the alternating interior angles are congruent. When two parallel lines cross a horizontal line, they form an equilateral interior angle, and their sum equals 180 degrees.
The angles are complementary because the sum of the interior angles on equal sides is 180 degrees. The sum of the interior angles formed by one side of a horizontal line is two right angles. Alternating interior angles are formed by a horizontal line intersecting two parallel lines. They lie between two parallel lines, but on opposite sides of the horizontal line, creating two pairs of alternating interior angles four angles total.
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NEED HELP ASAP
Which value is closest to (2.4×103)+(5.7×102)?
A
2.97×102
B
2.97×103
C
8.1×105
D
8.1×106
Answer: C) 8.1 x 105
Which of the following functions translates the graph of the parent function f (2) = 2? left 2 units?
f (x) = x^2, translated left ,2 units
Is a parabola
Vertex is at (0,0)
left translation is (x +2)
(-2 + 2)= 0
Then answer is
Option A ) h(x)= (x+2)^2
find the ratio of 5 days to 60 hours
The ratio of 5 days to 60 hours is 2:1.
What is the ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)The number of common shares each convertible security receives when converted is known as the conversion ratio. The more common shares are exchanged for each convertible security, the higher the ratio.So, the ratio of 5 days to 60 hours:
We know that 60 hours is 2.5 days.Then, ration os 5 days to 2.5 days
5:2.52:1Therefore, the ratio of 5 days to 60 hours is 2:1.
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Solve the compound inequality.
x + 6 <0 or 6x > - 18
Answer: 6x - 18 = 6 • (x - 3)
Step-by-step explanation: Pulling out like terms
9, y = |x-1 table of values?
From absolute value we get the table of values are for x = 0, we get x = 1, we get y = 0, for x < 0, we get y > 1 and for x > 0, we get y > 1
What is absolute value?
The non-negative value of x, regardless of its sign, is referred to as the absolute value or modulus of a real number in mathematics and is denoted by the symbol |x|. For example, displaystyle |x|=x if x is a positive number, displaystyle |x|=-x if x is a negative number, and displaystyle |0|=0 otherwise.
Given y = |x - 1|
When x = 0, we get
y = |0 - 1|
=> y = |-1| = 1
When x < 0, we get
y > 1, as absolute value always give positive value
When x = 1, then we get
y = 0
When x > 0, then we get
y > 1.
Therefore, the table of values are for x = 0, we get x = 1, we get y = 0, for x < 0, we get y > 1 and for x > 0, we get y > 1
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Thank you to who ever answers this question. Have a good rest of your day!
Answer:
Step-by-step explanation:
Answer: HI! I believe that the answer would be this symbol (I put it below)
>
Step-by-step explanation:
So sorry if this is wrong
In the figure above, ABCD is a square. What is the value of x?
Answer:
6x-1 is x=-1
5x+7 is x=7
Step-by-step explanation:
What is greater 1.0079 or 100.8
Answer:
100.8 is the correct answer
Answer:
100.8
Step-by-step explanation:
100.8 > 1.0079
Blank x – 18 = 3( – x – 6 )
We expand the bracket :
3(-x - 6) = 3 x (-x) - (3 x 6)
= -3x - 18.
So, we have :
___ - 18 = -3x - 18
Add 18 to both sides :
___ = -3x
=> The quantity we need to find is -3x.
An airplane flies with a constant speed of 804 miles per hour. How far can it travel in 3 hours?
The distance covered by the aeroplane moving with constant speed is 2412 miles in 3 hours.
What is meant by the speed of the body?The distance moved per unit of time is referred to as speed. It is the rate at which an object moves. The magnitude of a velocity vector is represented by the scalar quantity speed. It lacks a sense of direction. A higher speed indicates that an object moves faster. Lower speed indicates that it is moving more slowly. It has zero speed if it is not moving at all.The formula: is the most common method to count the constant speed of an object traveling in a straight line.The formula for speed is;
Speed = distance/ time
s = d/t
For the given question,
An air plane flies with a constant speed of 804 miles per hour.
speed 's' = 804 mi / hour.
Time 't' = 3 hours.
Put the values in formula.
804 = d/3
d = 804×3
d = 2412 miles
Thus, the distance covered by the aeroplane moving with constant speed is 2412 miles in 3 hours.
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From 1969 through 1977, there were 24 teams in Major League Baseball, and only 4 made the playoffs
each year. Now, there are 30 teams, and 10 make the playoffs. Find the ratio of teams making the
playoffs to those not making the playoffs in 1969 and today.
The 1969 Major League Baseball season was contested from April 7 to October 16, 1969. It included the third Major League Baseball expansion of the decade, with the Kansas City Royals, Montreal Expos, San Diego Padres, and Seattle Pilots each beginning play this season. The season was also celebrated as the 100th anniversary of professional baseball, honoring the first professional touring baseball team, the Cincinnati Red Stockings of 1869.
This was the first season of the "Divisional Era". With each league expanding from 10 teams to 12 teams, both leagues were divided into two six-team divisions. Teams continued to play 162-game schedules, in place since 1962, by now playing the other five teams in their own division 18 times each (90 games) and playing the six teams in their league's other division 12 times each (72 games). The winners of each division would advance to the postseason and face each other in a League Championship Series, then a best-of-five series, to determine the pennant winners that would face each other in the World Series.
The Baltimore Orioles won the AL East with an MLB-best 109–53 record, and then defeated the AL West champion Minnesota Twins in three games in the first American League Championship Series. The New York Mets won the NL East division with an NL-best 100–62 record, and then defeated the NL West champion Atlanta Braves in three games in the first National League Championship Series. The "Miracle Mets", having joined the league in 1962, were the first expansion team to win a pennant.
The upstart Mets went on to upset the heavily favored Orioles in the World Series, four games to one, in what is considered one of the greatest upsets in World Series history.[1]
HOPES THIS HELPS :D
–26.1 as a mixed number.
Answer:
-26 [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
.1 as a fraction is 1/10
Answer:
________________________________________________
Step-by-step explanation:
______________________________________________________________________________________________
Tell which definition, postulate, or theorem gives the justification.
- Geometry
The condition m∠GLA + m∠ALD = m∠GLD is proved by the Angle Addition Postulate.
What is termed as the Angle Addition Postulate?According to the Angle Addition Postulate, the measure of an angle made of two angles adjacent to each other is the sum of the two angles' measures. The Angle Addition Postulate can be employed to compute the angle formed by two or more angles, as well as to compute the assessment of a missing angle. The Angle Addition Postulate states that if two angles are placed side by side, the measure of a resulting angle would be equal to the sum of the original two angle measures. This postulate requires that the vertices, that are the angle's corner points, be placed together.For the given question;
A is the interior angle of ∠GLD.
m∠GLA + m∠ALD = m∠GLD is proved by the Angle Addition Postulate.
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Which expression can be used to check the answer to 56÷(-14)= -4?
the given expression is,
56 /(-14)
[tex]\begin{gathered} =\frac{56}{-14} \\ =-4 \end{gathered}[/tex]so the answer is -4.
you can check the answer
by multiplying the (-14) to -4,
[tex]\begin{gathered} \frac{56}{-14}=-4 \\ 56=-14\times-4 \\ 56=56 \end{gathered}[/tex]LHS = RHS so we use the expression -14 x -4 to check the answer.
HELP PLEASE
Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-51|-3 = -2
O |5x-1| +8 < 6
O 3|x-4|+5 < 4
O 2|x + 7| +3 = 2
For the given absolute value equations and inequalities the following have solution set which is not empty set.
a. |2x-51|-3 = -2 has solution set x = 25 or 26.
b |5x-1| +8 < 6 has empty set.
c. 3|x-4|+5 < 4 has empty set.
d. 2|x + 7| +3 = 2 has solution set x = -15/2 or -13/2.
As given in the question,
Solution set of the absolute value equations and the inequalities are as follow:
a. |2x-51|-3 = -2
⇒ |2x-51| = -2+3
⇒ |2x-51| = 1
⇒ 2x -51 = 1 or 2x -51 = -1
⇒ 2x = 52 or 2x = 50
⇒ x= 26 or 25
Solution set is x = 25 or 26.
b. |5x-1| +8 < 6
⇒|5x-1| < -2
⇒5x -1 < -2 or 5x -1 > 2
⇒ x< -1/5 or x > 3/5
Empty set.
c. 3|x-4|+5 < 4
⇒3|x-4| < -1
⇒x -4 < -1/3 or x -4 > 1/3
⇒ x< -11/3 or x > 13/3
Empty set.
d. 2|x + 7| +3 = 2
⇒2|x + 7| = -1
⇒|x + 7| = -1/2
⇒ (x+7) = -1/2 or (x+7) = 1/2
⇒x= -15/2 or -13/2
Solution set is x= -15/2 or -13/2.
Therefore, For the given absolute value equations and inequalities the following have solution set which is not empty set.
a. |2x-51|-3 = -2 has solution set x = 25 or 26.
b |5x-1| +8 < 6 has empty set.
c. 3|x-4|+5 < 4 has empty set.
d. 2|x + 7| +3 = 2 has solution set x = -15/2 or -13/2.
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Somebody help!!!!! I don’t know the answer
Given expression
[tex][(\cfrac{20}{5}*\cfrac{1}{5})^{-1}]^2[/tex]Step 1Simplify the parenthesis:
[tex][(\cfrac{20}{5}*\cfrac{1}{5})^{-1}]^2=[(\cfrac{4}{5})^{-1}]^2[/tex]Step 2Apply the negative exponent rule:
[tex]a^{-1}=1/a[/tex][tex][(\cfrac{4}{5})^{-1}]^2 = [(\cfrac{5}{4})^{1}]^2[/tex]Step 3Apply the product of a power rule:
[tex](a^b)^c=a^{bc}[/tex][tex](\cfrac{5}{4}})^{1*2}=(\cfrac{5}{4}})^2[/tex]Step 4Apply product of the product law:
[tex]a^2=a*a[/tex][tex](\cfrac{5}{4}})^2=(\cfrac{5}{4}})^(\cfrac{5}{4}})=\cfrac{25}{16}[/tex]11. What is the least common
70 ?
multiple of 30, 40, and
Answer:
i think 840 i searched it up
Step-by-step explanation:
Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with an $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? A = P (1 + r) superscript t
It will take 3 years for Korey to see an overall profit in his business.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Cost of the store to open = $12500
Cost of the operational cost = $8000
Profit store makes each year = $12000
Profit increase each year = 6%
Profit = Income - Total cost
First-year:
Profit = 12000 - (12500 + 8000) = -8500
There is no profit in the first year.
2nd year:
Profit = 2 x (12000 + 6% of 12000) - (12500 + 2 x 8000)
= 25440 - 28500
= -3060
There is no profit in the second year.
Third-year:
Profit = 3 x (12000 + 6% of 12000) - (12500 + 3 x 8000)
= 38160 - 36500
= 1660
We see that there is a profit of 1600 in the third year.
Thus,
It will take 3 years for Korey to see an overall profit in his business.
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Blank x + 16 + x = – 3 x – 4
The value of x from given linear equation is -4.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Given that x + 16 + x = – 3 x – 4
To find the value of x solving the given linear equation
x + 16 + x = – 3 x – 4
⇒ 2x + 16 = -3x - 4
⇒ 2x + 3x = -4 -16
⇒ 5x = -20
⇒ x = -20/5
⇒ x = -4
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(30 points) Circle A is____ to circle B.
A. Tangent
B. Concentric
C. Coplanar
D. Congruent
Answer:Co planar
Step-by-step explanation:
There are different types of relation between circles,
Congruent circles: Two circles are congruent to each other if they have same size( radius, diameter or circumference).
Concentric circles: If two circles have the same center,
Co planar : When the two circles lie on the same plane.
Tangent circle : Circles in a common plane that intersect in a single point.
⇒ They are only co-planer circles.
find 9th term for 2,5,8,11
Answer: 26
Step-by-step explanation:
2+3=5
5+3=8
8+3=11
11+3=14
14+3=17
17+3=20
20+3=23
23+3=26
Simplify m^8 m^ -6
Om^2
0 1/m^2
O-m^14
Answer: The answer is m^2
Step-by-step explanation:
4 x 10 to the power of 5
Answer:
400000
Step-by-step explanation:
Have a Good Day!
please help trying to do a test
(x + 1) a factor of 2x ^ 4 - 9x ^ 3 - 20x ^ 2 + 147x - 180 Find out by using the Factor theorem.
Answer:
Step-by-step explanation:
4
If a location on a graph has an indegree of 5 and an outdegree of 10 what is the total degree?
The total degree when the indegree is 5 and the outdegree of 10 is 15.
The number of head ends next to a vertex is referred to as the vertex's indegree, and the number of the tail ends next to a vertex is referred to as the vertex's outdegree (called branching factor in trees).
The location on a graph has an indegree of 5 and an outdegree of 10.
The sum of the indegree and the outdegree is the total degree of the vertex. The indegree is written as deg−(x) and the outdegree is written as deg+(x).
The total degree will be:
= indegree + outdegree
= deg⁻(x) + deg⁺(x)
= 5 + 10
= 15
The total degree is the sum of in and outdegree is 15.
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Terrell arranges x roses at $3.50 each with 10 carnations at $2.25 each. He makes a bouquet of flowers that averages $3.00 per flower. Choose an equation to model the situation.