Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
Given that,
Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.
An isometry of R² is a mapping T:R²⇒R² which preserves distance.
The formula for the distance between x and y is
d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²
The preservice means,
d(x,y)=d(T(x),T(y))
A translation is an isometry.
Since,
d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)
The rotation matrix, for rotating by an angle Θ, is defined as,
cosΘ -sinΘ
sinΘ cosΘ
Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
To learn more about translation visit: https://brainly.com/question/28825586
#SPJ4
Can somebody help asap I need the steps as well !!!
The total addition of numbers is, 53975687481.
What is addition of numbers?
The other three fundamental arithmetic operations are subtraction, multiplication, and division. Addition is one of these four operations. The total sum or value obtained by adding two whole numbers is the result of the addition.
For the given addition first add the digits on 1st place.
7 + 7 + 7 + 7 + 2 + 2 + 2 + 1 + 8 + 7 + 1 = 51
Take 1 as it is and add 5 on the 10th place numbers.
Now add 10th place numbers,
6 + 6 + 8 + 8 + 2 + 3 + 4 + 4 + 6 + 6 + 5 = 58
Take 8 as it is and add 5 to the 100th place numbers.
Now, 9 + 9 + 9 + 1 + 2 + 4 + 4 + 0 + 7 + 4 + 5= 54
Take 4 as it is and add 5 to the 1000th place numbers.
Now, 4 + 4 + 4 + 7 + 6 + 7 + 7 + 0 + 1 + 2 + 5 = 47
Take 7 as it is and add 4 to the next addition.
Now, 9 + 6 + 7 + 4 + 8 + 3 + 1 + 2 + 4 + 4 = 48
Take 8 as it is and add 4 to the next addition.
Now, 8 + 7 + 7 + 9 + 7 + 2 + 2 + 4 = 46
Take 6 as it is and add 4 to the next addition.
Now, 7 + 6 + 6 + 2 + 6 + 1 + 3 + 4 = 35
Take 5 as it is and add 3 to the next addition.
Now, 4 + 9 + 4 + 3 + 4+ 3 = 27
Take 7 as it is and add 2 to the next addition.
Now, 7 + 4 + 2 + 4 + 2= 19
Take 9 as it is and add 1 to the next addition.
Now, 9 + 3 + 1 = 13
Take 3 as it is and add 1 to the next number.
4 + 1 = 5.
Now take the last numbers one by one from step by step.
⇒ 53975687481
Hence, the total addition of numbers is, 53975687481.
To know more about addition of numbers, click on the link
https://brainly.com/question/5982761
#SPJ1
Andrea's record label released her new album. Andrea wants to know when she has sales of at least $20,000 per week. She uses the related equation below to determine when sales will be at least this amount, where t represents time in weeks.
please finish the other half
Answer:
10 ≤ t ≤ 20 or t ∈ [10; 20]----------------------------
The other half is:
t - 15 ≥ - 5t ≥ - 5 + 15t ≥ 10The answer, considering both halves, is:
10 ≤ t ≤ 20or
t ∈ [10; 20]Answer:
[tex]10 \leq t \leq 20[/tex]
Step-by-step explanation:
Given absolute value inequality:
[tex]1000(-2|t-15|+30) \geq 20000[/tex]
Isolate the absolute value on one side of the equation:
[tex]\implies \dfrac{1000-2|t-15|+30)}{1000} \geq \dfrac{20000}{1000}[/tex]
[tex]\implies -2|t-15|+30 \geq 20[/tex]
[tex]\implies -2|t-15|+30-30 \geq 20-30[/tex]
[tex]\implies -2|t-15|\geq -10[/tex]
[tex]\implies \dfrac{-2|t-15|}{-2}\geq \dfrac{-10}{-2}[/tex]
[tex]\implies |t-15|\leq 5[/tex]
[tex]\textsf{Apply absolute rule:\quad {If} $|u| \leq a, \;a > 0$ \;then\; $-a \leq u \leq a$}[/tex]
[tex]\implies -5 \leq t-15\leq 5[/tex]
Solve both equations:
[tex]\begin{aligned}\underline{\sf Equation\;1} && \underline{\sf Equation\;2}\\t-15 &\geq -5 \quad & t-15& \leq 5\\t-15+15& \geq-5+15 &\qquad t-15+15& \leq 5+15\\t&\geq10 & t &\leq20\end{aligned}[/tex]
Merge the overlapping intervals:
[tex]10 \leq t \leq 20[/tex]
URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
identify the conic section represented by the equation (x+1)^2+(y-2)^2=8
Step-by-step explanation:
A circle with a center of (-1,2) and a radius
of
[tex]2 \sqrt{2} [/tex]
a researcher obtained a random sample of 100 smokers and a random sample of 100 non smokers. after interviewing all 200 participants in the study, the researcher compared the rate of depression among the smokers with the rate of depression among nonsmokers
observational study
Based on the study, the researcher may develop a hypothesis that smoking is associated with an increased risk of depression.
What is Hypothesis?An explanation that is put up for a phenomena or a group of facts is called a hypothesis. It is a speculative explanation that needs more testing and improvement because it is supported only by a small body of data. A hypothesis is not a tested theory, but rather a point of departure for more research. A hypothesis is examined in scientific study by testing and observationit. The purpose of hypothesis testing is to evaluate the likelihood that the suggested explanation is accurate and to spot any discrepancies or holes in the available data. The act of testing and improving hypotheses is a crucial component of the scientific method since it ensures that scientific ideas are supported by reliable data.
How to solve?
This hypothesis can then be tested through further research, such as conducting a larger study with more participants, or conducting experiments to evaluate the potential mechanisms by which smoking may affect the development of depression.
The researcher may also use statistical methods to analyze the data collected from the study, in order to determine the significance of the relationship between smoking and depression.
If the hypothesis is supported by the evidence, the researcher may conclude that smoking is a risk factor for depression, and may recommend interventions or preventative measures to reduce the risk of depression among smokers.
To learn more about hypothesis, visit:
https://brainly.com/question/17246563
#SPJ4
Need a Detailed explanation
Answer:
The dividend in the synthetic division below is x+2:
4 | -6 -5 4 -7
- --------------
- -1 -1 1 -5
0 | -5 -4 3 -2
- --------------
2 | x+2
In synthetic division, the numbers in the top row represent the coefficients of the polynomial being divided, and the number in the bottom row represents the value of the dividend. In this case, the dividend is x+2 because it is the only number in the bottom row that is not a result of the division operation
CAN SOMEONE HELP WITH THIS QUESTION?✨
a) The exponential function that models the population in t years after 2000 is of: P(t) = 14300(1.06)^t.
b) The estimate for the population in 2008 is of: 22792.
How to define the exponential function?Considering it's standard format, the increasing exponential function is defined as follows:
P(t) = P(0)(1 + r)^t.
In which the parameters of the function are defined as follows:
P(0) is the population in the reference year of 2000.r is the growth rate, as a decimal.Hence the values of these parameters are given as follows:
P(0) = 14300, r = 0.06.
Thus the function is given by:
P(t) = 14300(1.06)^t.
2008 is eight years after 2000, thus the estimate is P(8), which is obtained as follows:
P(8) = 14300 x (1.06)^8 = 22792.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
write 500;000 in expanded form in tow different ways
Answer:
500,000 can be written in expanded form in two different ways:
500,000 = 500,000
500,000 = 5 x 100,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 0 x 1
In both cases, the expanded form shows the value of each digit in the number. The first way simply lists the number itself, while the second way breaks down the number into its component parts and shows the value of each digit in relation to the place value it holds in the number.
to create a pivottable layout, you can drag fields from the field list to an area box in the pivottable fields pane
a. true
b. false
Yes , we can drag fields from the field list to an area box in the pivot table fields pane in order to create a pivot table. Hence , true.
The four sections of the pivot table
Report FilterColumn LabelsRow LabelsValuesare located at the bottom of the PivotTable Field List window.
The fields will appear in the corresponding region of the worksheet's pivot table layout when you drag them into these locations.
Only the fields included in the PivotTable Field List can be moved in Excel 2007. If you try to drag the Promo field onto the pivot table in the screen photo below, the cursor displays an X. The drag-and-drop function is broken.
You can alter a setting in the pivot table options if you'd like to drag the pivot fields onto the worksheet layout.
To access the PivotTable Options menu, right-click a cell in the pivot table.Put a checkmark next to Classic PivotTable Layout on the Display tab.PivotDrag02To close the PivotTable Options dialogue box, click OK.To learn more about pivot table
brainly.com/question/26467935
#SPJ4
Answer this! You'll get brainliest!
Answer:
See below
Step-by-step explanation:
Please help ASAP I don;t understand it
Answer:
the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).
Step-by-step explanation:
A point (x,y) falls on a line where the constant of proportionality is k if y is equal to k times x. In other words, the equation for the line is y = kx.
Given this, we can determine which of the given points fall on a line where the constant of proportionality is k by evaluating whether the y-coordinate of each point is equal to k times the x-coordinate.
For example, if k = 2, then the point (6,8) falls on the line y = 2x because 8 is equal to 2 times 6. Similarly, the point (3,2) falls on the line y = 2x because 2 is equal to 2 times 3.
On the other hand, the point (6,4) does not fall on the line y = 2x because 4 is not equal to 2 times 6.
Therefore, the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).
Note that if k is not specified, then any of the given points could potentially fall on a line where the constant of proportionality is k, depending on the value of k.
Kristin spends 30% of her savings on a watch and 60% of the
remainder on a dress. What percentage of her savings is left?
Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
Given that,
Kristin spends thirty percent of her savings on a watch and sixty percent on a dress.
We have to find what portion of her savings is still available.
We know that,
Kristin spends thirty percent of her savings on a watch.
Sixty percent on a dress.
The money she has a 100% in that if she spend 30% on watch she get 70% then if she spend 60% on dress she will have 10%
Therefore, Kristin left with the 10% of the savings when she spends thirty percent of her savings on a watch and sixty percent on a dress.
To learn more about percent visit: https://brainly.com/question/28840349
#SPJ1
Draw the image of triangle ABC under a dilation whose center is A and scale factor is 4.
The image of triangle ABC under a dilation whose center is A and scale factor is 4 is as follows.
What is dilation?
Dilation involves changing the size of a shape.
Main body:
Assume point P is the center of origin, then we have the following coordinates of ABC
A= (1,0)
B= (-2,0)
C= (0,2)
The scale factor (k) is given as:
K = 4
So, the dilation rule is represented as:
(x, y) = 4 *(x,y)
Using the above dilation rule, the following coordinates represent the image of triangle ABC
A' =(4,0)
B' =(-8,0)
C' =(0,8)
See attachment for the image of the dilation.
Read more about dilation at:
brainly.com/question/8532602
#SPJ1
A contractor bought 6.4ft^2 of sheet metal. has used 2.1ft^2 so far and has $129 worth of sheet metal remaining. The equation 6.4x - 2.1x = 129 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
30$ per ft^2
Step-by-step explanation:
6.4x-2.1x=129
4.3x=129
x=30
:]
What is the value of x in the figure
shown?
37°
y
(3x + 1)
Answer:
x=4
Step-by-step explanation:
x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123
The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.
The angle is formed by two rays and a common point.
To calculate the value of x using the diagram attached below:
∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°
On substituting the values from the figure,
∠AOC=3x-7
∠COD=55
∠BOD=x+20
∠AOC+∠COD+∠BOD =3x-7+55+x+20
3x-7+55+x+20=180
4x+68=180
4x=112
x=28
Thus, the value of x is 28 for the figure attached below.
Learn more about angles, here:
https://brainly.com/question/14569348
#SPJ6
Find the mean and standard deviation for each uniform continuous model. (Round "Mean" answers to 1 decimal place and "Standard deviation" answers to 4 decimal places.) Mean a. U(0, 15) b. U(90, 230) c. U(4, 92)
The mean and the standard deviation of the distributions are
Mean = 7.5, Standard deviation = 4.3301Mean = 160. Standard deviation = 40.4145Mean = 48, Standard deviation = 25.4034How to determine the mean and the standard deviation?The distribution is given as:
A uniform continuous model
The mean and the standard deviation of this type of model are
Mean = (a + b)/2
Standard deviation = (b−a)/√12
Using the above formulas, we have
a. U(0, 15)
Mean = (0 + 15)/2 = 7.5
Standard deviation = (15−0)/√12 = 4.3301
b. U(90, 230)
Mean = (90 + 230)/2 = 160
Standard deviation = (230 − 90)/√12 = 40.4145
c. U(4, 92)
Mean = (4 + 92)/2 = 48
Standard deviation = (92 - 4)/√12 = 25.4034
Hence, the standard deviation of U(4, 92) is 25.4034
Read more about mean and standard deviation at
https://brainly.com/question/17019045
#SPJ1
Use the information to answer questions 8-10.
The time in minutes a factory needs to make a cell phone parts in a single day is modeled by th
inequality y-0.0005² ++20, for the domain 0 ≤ ≤ 1000.
8. What does the ordered pair (200, 100) represent?
Type a response
4
the longest it will take the factory to make 600 cell phone parts?
Since y<-0.0005x^2+x+20 and y represents the time in minutes needed to make x cell phone parts, the longest it will take the factory to make 600 cell phone parts will be y=-0.0005(600)^2+600+20
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
A number is a solution to an inequality in x if it can be used to replace x with a statement that is true. Therefore, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the solution set for an inequality.
Wealth inequality, treatment and responsibility disparity, political inequality, life inequality, and membership inequality are the five systems or sorts of social inequality.
In mathematics, larger than symbol (>), less than symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols.
To learn more about inequality refer to:
https://brainly.com/question/25275758
#SPJ1
Please help me on math very easy graphing! thank you!! due soon
Linear regression is a system of plotted points which shows a relationship between two given variables. The required linear equation is: y = 4x.
A graph is a plotted coordinate on a Cartesian plane which shows the relationship between two variables. A system of plotted points in relations to variables that shows a linear relationship is termed linear regression.
In a linear regression, the plotted points can be described by an equation:
y = bx + c
where: y is the dependent variable
x is the independent variable
b is the slope of the graph
c is the intercept
Therefore, considering the given question;
the slope of the graph = [tex]\frac{change in y}{change in x}[/tex]
= [tex]\frac{12 - 4}{3 - 1}[/tex]
= [tex]\frac{8}{2}[/tex]
slope of the graph = 4
While there is no intercept, thus intercept is zero.
Therefore, the required equation that shows the relationship between liters of water and number of minutes is:
y = 4x
Learn more about description of the relationship between two variables using linear regression at https://brainly.com/question/26755306
#SPJ1
- 4y + 11 = -3(2y + 1)
Answer: y=-7
Step-by-step explanation:
Answer: y=-7
Step-by-step explanation:
The population of Greenville was 4,870 people. Six years later, the population had
grown to 5,080 people. What was the average rate of change in Greenville's
population for this six-year period?
The average rate of change in Greenville's population for this six-year period is 35 person per year
What's the math rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.
Given that:
Greenville population = 4,870
Greenville population after 6 years = 5,080
Difference of population = 5080 - 4870 = 210
Average rate = Population / Years = 210/6 = 35 person per year
Learn more about rate
https://brainly.com/question/119866
#SPJ1
Is the following statement linear or exponential?
Lalo's hair is also known to grow rapidly. It began at a length of 6 in and grew at a constant rate of 1 in per month. HELP PLEASE Nobody is helping me :(
Answer:
Step-by-step explanation:
exponential
Find the degrees of freedom if N is 12.
The degrees of freedom is [tex]12N[/tex]
What is degrees of freedom?
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.
[tex]\text { Least Common Multiplier of } N, 12: 12 N[/tex]
Find Least Common Multiplier of [tex]$N, 12$[/tex]
Lowest Common Multiplier [tex](LCM)[/tex]
The LCM of [tex]$a, b$[/tex] is the smallest multiplier that is divisible by both [tex]$a$[/tex] and[tex]$b$[/tex]
Factor 12
[tex]$2^2 \cdot 3$[/tex]
Multiply each factor with the highest power:
[tex]12 \mathrm{~N}[/tex]
To learn more about degrees of freedom visit:
https://brainly.com/question/16254305
#SPJ1
Write the following equation in slope-intercept form and identify the slope and y-intercept.
6x - 4y = 11
Answer:
Step-by-step explanation:
This in standard form (Ax + By = C.) In order to make this slope-intercept form, you need to isolate y.
y = -1.5x + 2.75
y=mx + b is slope intercept, where m is the slope and b is the y-intercept.
In this case, -1.5 is the slope and 2.75 is the y-intercept.
Hope this helps!!
HELPPPP!!! 30 POINTSSSSSS!!!!!!
Find the line of best fit for the set of data:
x y
-2 2.9
-3.5 2
1.4 4.8
-4.2 1.5
0 4
2.8 6
-1.5 3.5
A. y = .613x + 4.142
B. y = -.613x - 4.142
C. y = -.613x + 4.142
D. y = .613x - 4.142
Answer:
[tex]\boxed{\tt A. \;y = .613x + 4.142}[/tex]
Step-by-step explanation:
Equation: (y-y_1)=y_2-y_1/x_2-x_1 (x-x_1)
Here,
[tex]\tt (x_1,y_1):(-2,2.9)[/tex]
[tex]\tt (x_2,y_2): (-3.5,2)[/tex]
[tex]\tt y-2.9=\cfrac{(2-2.9)}{(-3-5-(-2))} (x-(-2))[/tex]
[tex]\tt y-2.9=\cfrac{-0.9}{-1.5} (x+2)[/tex]
[tex]\tt y-2.9=0.6(x+2)[/tex]
[tex]\tt y-2.9=0.6x+1.2[/tex]
[tex]\tt y=.613x+4.142[/tex]
___________________
Hope this helps you!
Have a nice day!
Directions: construct equations for the following and evaluate for X .
The value of x is 13 and value of x in second question is 28, in the angle of line. The angle between a line's inclination and the x-axis's positive direction is known as the inclination.
How do you calculate inclination?The angle between a line's inclination and the x-positive axis's direction is known as the inclination. This angle's value ranges from 0° to 180°. It is measured counterclockwise around the positive x-axis direction. The slope of a line is the tangent of the angle of inclination if the inclination angle is known. Take the tangent of the angle produced between the line and the x-axis to get the degree of inclination.Angle B, which is the opposite of angle A and measures 100 degrees, will also be 100 degrees. This indicates that the sum of the two angles is 200 degrees.From first fig :
26° = 2x °
x = 26 / 2 = 13
Second fig :
134° = 4x + 22
x = 134 - 22 / 4 = 28
To learn more about inclination refer :
https://brainly.com/question/29360090
#SPJ1
Jane's family divided up their garden so that 2/3 of garden will have vegetables. Jane and her sister will plant2/3 of the vegetable portion of the garden. How much will the sisters plant?
3/2 part of the garden is planted by both the sisters.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
Jane's family divided up their garden so that 2/3 of garden will have vegetables.
Jane and her sister will plant2/3 of the vegetable portion of the garden
2/3 is the vegetable portion
In this vegetable portion 2/3 part is of the vegetable portion of the garden
3/2/2/3
3/2×3/2
6/4
3/2
Hence, 3/2 part of the garden is planted by both the sisters.
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ1
PLEASE HELP ASAP!!! Will IMMEDIATELY give Brainliest to the correct answer!! 100 pt question!!
The function f(x)=∣x−3∣ can be used to determine how far a number x is away from the number 3 on the number line. Find and interpret the given function values and determine an appropriate domain for the function.
Answer:
The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. To find the function value for a given x, we first need to subtract 3 from x and then take the absolute value of the result. For example, if x = 5, then the function value would be f(5) = |5 - 3| = |2| = 2.
The domain of the function is the set of all possible values of x that we can plug into the function to get a real number result. In this case, the function will work for any real number value of x, so the domain of the function is the set of all real numbers, which can be written as:
Domain: (-∞, ∞)
In other words, the function f(x) = |x - 3| can be used to determine how far any real number x is away from the number 3 on the number line.
A family buys a studio apartment for $200,000 . They pay a down payment of $20,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would an $80,000 down payment be?
Answer:hope i helped A. 20% B.45%
A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45
Step-by-step explanation:
3. What is the best description of the function in Item 2?
Answer:
Could you give a little more context. I can help.
Reflect (8,
-6) across the x-axis.
Then reflect the result across the y-axis.
What are the coordinates of the final point?l
Answer:
(-8.6)
Step-by-step explanation: If you look at a graph and pinpoint the location of (8,-6) by going up 8 and then going to the left 6. so the point of (8.-6) is in the top left box and if we are reflecting over the x-axis and the y-axis the point will be at the lower right box therefore the answer is (-8.6).
Find all angles, 0°≤θ≤360° that solve the following equation.
sin θ=-1
The solution for the given equation is, θ = 270°.
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition stated by the equation, is known as solving an equation in mathematics. Solutions typically consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.
Consider, the given inequality
sinθ = -1
The general solution for sinθ = -1 is
θ = 270° + 360°n
But the condition is, 0° ≤ θ ≤ 360°
Hence, the solution for the given equation is, θ = 270°.
To know more about solution of an equation, click on the link
https://brainly.com/question/22688504
#SPJ4