Answer:
The dilation on any point of the rectangle is [tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex].
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
[tex]G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)][/tex] (1)
Where:
[tex]G(x,y)[/tex] - Coordinates of the point G, dimensionless.
[tex]O(x,y)[/tex] - Center of dilation, dimensionless.
[tex]k[/tex] - Scale factor, dimensionless.
[tex]G'(x,y)[/tex] - Coordinates of the point G', dimensionless.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]G(x,y) =(2,-2)[/tex] and [tex]G'(x,y) =(5,-5)[/tex], then scale factor is:
[tex](5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)][/tex]
[tex](5,-5) = (2\cdot k, -2\cdot k)[/tex]
[tex]k = \frac{5}{2}[/tex]
The dilation on any point of the rectangle is:
[tex]P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)][/tex]
[tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex] (2)
The dilation on any point of the rectangle is [tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex].
Algebraic representation of the dilation will be T'(x, y) → T(2.5x, 2.5y).
Dilation of a rectangle about a point not the origin:Let one of the four vertices of a rectangle is (h, k) is dilated about the origin by the scale factor 'k'.Rule for the transformation will be,
[tex]D_{(o,k)}(x,y)\rightarrow (kx,ky)[/tex]
Following this rule,
If one of the vertices of a rectangle is G(2, -2) and it is dilated by a scale factor 'k', image point will be given by,[tex]D_{(o,k)}(2, -2)\rightarrow (2k, -2k)[/tex]
Since, coordinates of the dilated point are G'(5, -5),
Therefore, (2k, -2k) = (5, -5)
⇒ 2k = 5
⇒ k = 2.5
Hence, algebraic representation defining the dilation of the
triangle will be,
T'(x, y) → T(2.5x, 2.5y)
Algebraic representation of the dilation will be T'(x, y) → T(2.5x, 2.5y).
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PLS HALP- Fill in the blanks-sometimes-always-or never-
-Irrational numbers can be expressed by ratio of 2 integers (sometimes-always-or never)
-If a number is a whole number, it is also rational (sometimes-always-or never)
-Rational numbers are also integers (sometimes-always-or never)
-Non-perfect squares are irrational (sometimes-always-or never)
Pls answer correctly ty
Answer:
I think they are all always.
Step-by-step explanation:
They are called rational because they are the ratio, or quotient, of two integers
numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end and does not repeat a pattern.
Please help I’m a little bit confused. If so, could you also tell me why it would be the one it is thank you!!
Answer:
0.44x10^3
Step-by-step explanation:
The number has to be from 1 to 10, not below 1, like 0.44 does.
Mr. Mills is 5 feet and 11 inches tall. How many inches tall is he?
Answer:
71
Step-by-step explanation:
There are 12 inches in a foot:
12 inches x 5 feet = 60
60 + 11 inches = 71 inches total
Answer:
71 inches
Step-by-step explanation:
12 inches in a foot
12*5
60+11
71 inches
Hope this hopes. Have a great day. May it be filled with joy and happiness.
Which number line represents the solution set for the inequality -1/2x>4
Answer: D
Step-by-step explanation: D because if your turn 1/2 into a decimal point it 0.5 (don't forgot to add the negative) and so i then divided -0.5 from x and just got x then you have to do the same for the other side. So i took 4 and divided it by -0.5 and got -8 to the expression would be x is greater then or equal to -8. you plot the dot at -8 and the line goes in front of it because it is lesser or equal to x (remember you reverse the problem if you say it back words so don't get confused), but after my long explanation just pick D
What is the GCF of:
15x^2y and 20xy
Answer:
5xy
Step-by-step explanation:
x and y can only go into both into once
Ava and her children went into a restaurant and will buy hotdogs and tacos. She must buy no less than 8 hotdogs and tacos altogether. Write an inequality that would represent the possible values for the number of hotdogs purchased, hh, and the number of tacos purchased, t.t.
Answer:
h + t ≥ 8
Step-by-step explanation:
h is for hotdogs and t is for tacos and they must buy no less than 8 (buy 8 or more than 8 altogether)
What’s the domain and rangeee
Answer:
the domain is 2, and the range is 1
Step-by-step explanation:
The point G(1,1) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, G'?
The resulting point's coordinates, G', are rotated 90° clockwise around in the origin are (-1 , -1 ).
What is the coordinate plane's location?A coordinate plane is a two-dimensional plane created by the intersection of the y-axis, a vertical line, and the x-axis, a horizontal line. These really are perpendicular lines that cross at zero, which is known as the origin.
What are a plane's quadrants?Quadrant one (QI) is the upper right fourth of a coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's upper left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.
According to the given data:Point G(1,1)
X= 1 ,Y = 1
We can see that the point lies in the first quadrant because the value of X and Y are the positive.
the coordinates of the resulting point, G' is rotated 90° clockwise around the origin.
As we know that the quadrant plane is divided into 4 part but if the point G rotates at 90 clockwise the the point will shift to the 4 quadrant and in the 4 quadrant the value of X and Y change And it became negative.
So
The resulting point's coordinates, G', are rotated 90° clockwise around in the origin are (-1 , -1 ).
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Find the coordinates of the reflection: B (8,-1) is reflected over the y-axis
Answer:
good for u
Step-by-step explanation:
please help!! i don’t understand how to do this.
Answer:
C= 5/9 * (F -32)
Move 5/9 to the left which makes it 9/5
9/5 * C = (F -32)
Move the -32 to the left
9/5 * C +32 = F or to make it read left to right
Fahrenheit = 9/5 * Celsius + 32
Step-by-step explanation:
In the equation X=(3y-9)^2 solve for y.
Answer:
y=radical x/3 +3
y=-radical x/3 +3
Step-by-step explanation:
This is the 3rd time I'm posting this with no response. The last time someone commented something completely unrelated to the topic so please no one do that again but I really need help with this. I'd really appreciate it. Thanks!
Answer:
20 pts
Step-by-step explanation:
PLS HELP I ALREADY GOTTA FINISH!!!!
Answer:
C.
Step-by-step explanation:
Add whole numbers: 8+9=17
Combine Fractions: 3/4+2/8= 1
= 17+1 =18
Answer:
Step-by-step explanation:
Make them have common denominators and combine.
[2((8 x 3)+3) ]/8 + [(9 x 8)+2]/8 = C.) 18.
40+[3{18÷(9-3)-11-9}+4]
Step-by-step explanation:
= 40 + [ 3 { 18 ÷ ( 9 - 3 ) - 11 - 9 } + 4 ]
= 40 + [ 3 { 18 ÷ 6 - 11 - 9 } + 4
= 40 + [ 3 { 3 - 20 } + 4
= 40 + [ 3 {- 17 } + 4
= 40 + ( - 51 ) + 4
= 40 + 4 - 51
= 44 - 51
= - 7
[tex]...[/tex]
☘☘☘....
Answer:
[tex] \sf \large \: - 7[/tex]
Step-by-step explanation:
40+3(18/9−3−11−9)+4
=40+3(18/6−11−9)+4
=40+3(3−11−9)+4
=40+3(−8−9)+4
=40+(3)(−17)+4
=40+−51+4
=40+−47
=−7
I need the answers please can anyone solve this one?
Answer:
This is it.
HI=8
GH=15
GI=17
Somebody please help! Due today! Whoever does best get's brainliest and 5/5 stars
Answer:
x=30
5x/6=25
5x=25x6
5x=150
x=150/5
x=30
The temperature falls from -7°C to -20°C. What is the change in these temperatures?
Answer:
13 degrees Celsius
Step-by-step explanation:
To solve this question, you need to subract -20 from - 7.-7-(-20) is 13.
I need help with this question ASAP
Answer:
Step-by-step explanation:
If you had both parts of the whole kite you would multiply but because you don't have both parts, you have to divide to find the other part so:
15.5 (whole) / 1.5 (part)= 10.3 (part)
Hope this helps!! :) have a good evening!
MARKING BRAINLIEST! A machine pumps 4 1/2 gallons of water every hour. How many gallons of water does it pump after 2 2/3 hours?
Answer:
12 gallons
Step-by-step explanation:
You just multiply both of the numbers.
Answer:
12 Gallons of Water!
___________________________________________________
4.5= 1 hour
9= 2 hours
4.5/3=1.5
So every 1/3 hour equal 1.5 gallons of water!
9+1.5*2= 12
The table shows values for a linear function, f(x). What is an equation for f(x)?
Answer:
f(x) = -3(x) + 4
Step-by-step explanation:
Option C. 3/4.
the slope is 3/4 for any two adjacent points.
Then use the point-slope formula y-y1=m(x-x1) where m slope and (x1, y1) point
y-1=(3/4)(x-11)
y=(3/4)x-(29/4), distributing and moving the 1 over.
What is F x in a linear function?A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).
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Enter a positive common factor (other than 1) of the fractions numerator and denominator 15/25
A study concluded that among people with a certain virus, 99.2% of tests conducted were (correctly) positive, while for people without the virus, 97.9% of the tests were (correctly) negative. If 32% of patients actually carry the virus, what's the probability that a patient testing negative is truly free of the virus?
Answer:
Following are the solution to the question:
Step-by-step explanation:
The probability of virus P(V) =0.32
No virus P(NV) =0.66
Patient testing of negative P(TN) = virus, and negative testing+no virus and negative testing
[tex]=0.32(1-0.992)+0.66 \times 0.979 \\\\=0.00256+0.64614\\\\=0.6487[/tex]
This is why the likelihood of a patient being free of the virus is negative.
[tex]= \frac{P(NV) \times\ tested \ negative }{P(TN)}[/tex]
[tex]= \frac{0.66 \times 0.979}{0.6487}\\\\= \frac{0.64614}{0.6487} \\\\=0.996053646[/tex]
Lavasha and Keisha travel separately to their grandmother’s house, 114 miles away. Keisha leaves from the same place 30 minutes after Lavasha. If Lavasha is travelling at 40 mph and Keisha travels at 55 mph, how many minutes will it take Keisha to catch up to Lavasha?
Help! [tex]\frac{x}{3} +5=x-1[/tex]
[tex]\frac{x}{3}+5=x-1[/tex]
Whenever there's a denominator. Multiply all whole equation with the denominator. For example, the denominator here in the equation is 3. So we multiply the whole equation by 3.
[tex]\frac{x}{3}(3)+5(3)=x(3)-1(3)\\x+15=3x-3[/tex]
Moving the x to the same term which goes for the same as the constant for easier in solving.
[tex]15+3=3x-x[/tex]
Moving to the another side, changing the sign/operator to opposite (From plus to minus, from multiply to divide.)
[tex]18=2x\\2x=18\\[/tex]
Move 2 to another side, aka to divide 18.
[tex]x=\frac{18}{2}\\x=9[/tex]
Therefore, the answer is x = 9.
A cab service charges $4 plus $1.50 per mile. Kate wants to spend no more
than $28 on cab fare. In this inequality, m represents the greatest number of
miles Kate can travel in the cab.
28 > 4+1.5m
Solve the inequality. What is the value of m?
O A. 8
O B. 16
O C. 28
O D. 30
Answer:
b
Step-by-step explanation:
took the test i got bj : fz wf
The value of m in the inequality 28 > 4+1.5m is 16
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
To solve for m, we need to isolate it on one side of the inequality.
We can start by subtracting 4 from both sides:
28 - 4 > 1.5m
Simplifying:
24 > 1.5m
Next, we can divide both sides by 1.5:
16 > m
So Kate can travel at most 16 miles in the cab if she wants to spend no more than $28 on cab fare.
Therefore, the value of m in the inequality 28 > 4+1.5m is 16
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Objective: Write expressions to represent scenarios. If x represents the amount Rita earns each week, which expression represents the amount she earns in a year? Select the correct answer.
A. x + 52
B. 52 – x
C.
D. 52x
statistical studies are not concerned with understanding the sources of variability in data, only with describing the variability in the data
False.
Variability in statistics is the degree to which data in a set varies, or how much difference there is in a single set of data. The variability definition also refers to the consistency of the pattern in a set of data.
There are many measures of variability to help researchers determine how much variability is contained within a set of data. A simple measure of variability is the range, the difference between the highest and lowest scores in a set.
A concern when using a simple range measure is the existence of outliers, individual scores that are not grouped with the rest of the scores.
Current statistical studies are modern and have a wealth of analysis tools and software to understand the data. Statistics has a wide range of objectives, which aim not only to understand the variability of the data, but also its origin and motivation. For example, if an election poll shows a variation from a previous poll, statisticians will seek to understand the causes of these variability and not just present the variation in the data.
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A car travels at a rate of 50 miles per hour for 3 hours. Let y be the distance, in miles, the car travels for a given amount of time, x, in hours. This situation can be modeled by a function.
What is the domain of the function?
A.
0 ≤ x ≤ 3
B.
0 ≤ x ≤ 50
C.
0 ≤ y ≤ 3
D.
0 ≤ y ≤ 50
The smallest composite number that can be written as a product of 4 different prime number are
option a) 120
option b)210
option c)240
option d)180
Pls give me brainliest
Do all 3 to get brainliest
Answer:
1.C
2. C
3.D
Step-by-step explanation:
Answer:
CCD
Step-by-step explanation: