Discuss the transformation of g(x)=2 (x−3)2 + 4 compared to the original function f(x)=x2. Select all that apply.
Group of answer choices
The graph is shifted right 4 units.
The graph has a horizontal stretch by a factor of 2.
The graph is shifted right 3 units.
The graph has a vertical stretch by a factor of 2.
The graph is shifted left 3 units.
The graph is shifted up 4 units.
The graph is shifted down 3 units.
The graph is shifted down 4 units.
The graph has a horizontal compression by a factor of 1/2.
Answers
The graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function is:
f(x) = x²
First transformation:
x → (x- 3)
The graph is shifted right to 3 units.
F(x) = (x- 3)²
Second transformation:
F(x) → 2F(x)
The graph has a horizontal stretch by a factor of 2.
h(x) = 2(x- 3)²
Third transformation:
h(x) → h(x) + 4
The graph is shifted up 4 units.
g(x) = 2(x- 3)² + 4
Thus, the graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
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Related Questions
If f(x) = 2x + 1 and g(x) = x 7, find (++ g)(x). h
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Therefore Option B is correct
1.Write a linear equation of the form y1 = mx + b for your first set of data.2.Write a linear equation of the form y2 = mx + b for the other equation in your system.3.Explain the Point of Intersection. (X,Y)
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First, find the actual number of miles per round trip in each case.
-Hyperloop
[tex]distanceH=speed*time=760*0.583=443.08miles[/tex]-Airplane
[tex]distanceA=535*1.25=668.75miles[/tex]Then, the cost (round trip) would be related to the constant b in both cases since it is a fixed rate. Multiply it by the maximum number of passengers,
[tex]\begin{gathered} b_H=40*28=1120 \\ b_A=88*360=31680 \end{gathered}[/tex]Then, multiply the rate of consumption by the fuel costs for each mean of transportation,
[tex]\begin{gathered} \frac{1}{m_H}=2*16.8*1=33.6 \\ \frac{1}{m_A}=2*2736*2.98=16306.56 \end{gathered}[/tex]Notice that it is multiplied by 2 since the rate of consumption row is given in one-way unitsThus,
[tex][/tex]Score: 0 of 1 pt1 of 16 (0 complete)Instructor-created questionA rectangle is 3times as long as it is wide. If the width of the rectangle is2inches, what is the rectangle's area in square inches?6O A. 10OB. 12O C. 16OD. 6O E. 7Click to select your answer and then click Check AnswerAll parts showingClear All0
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The length of the rectangle is 3 times it width. The width size is given as 2 inches.
Therefore,
width = 2 inches
length = 3(2) = 6 inches
The area of the rectangle can be calculated below
[tex]\begin{gathered} \text{area}=\text{length}\times\text{width} \\ \text{area}=6\times2 \\ \text{area}=12inches^2 \end{gathered}[/tex]The answer is B.
Write an equation for a parabola with x-intercepts (-3,0) and (4,0) which passes through the point (2,-40)
Answers
An equation for a parabola with x-intercepts (-3,0) and (4,0) which passes through the point (2,-40) is 5(x+3)(x-4)
Quadratic equationQuadratic equations are equation that has a leading degree of 2. The standard quadratic equation is given as:
y = a(x-a)(x-b)
where a and b are the x-intercepts of the function
Given the x-intercepts (-3,0) and (4,0), the equation will below:
y = a(x-(-3)(x-4))
y = a(x+3)(x-4)
If the curve pass through the y-intercept (2,-40)
-40= a(2+3)(2-4)
-40 = a(4)(-2)
-40 = -8a
a = 5
Substitute the value of a into the resulting function to have:
y = 5(x+3)(x-4)
This gives the required quadratic equation.
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The entire graph of the function f is shown in the figure below.Write the domain and range of fusing interval notation.
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Domain = the set of possible values along the x axis.
Domain = (-5 , 3 ]
Range = the set of possible values along the y axis.
Range = (-3 , 5 ]
Grant orders a $55 bouquet of flowers to be delivered to his sister. He pays the bill plus a 6.5% sales tax and a 15% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive to the nearest cent, if he pays the delivery driver with a $100 bill?
Answers
The change that Grant received to the nearest cent after giving the delivery driver with a $100 bill is $ 32.6.
This is a question of percentages.
Given that:-
Price of bouquet of flowers = $ 55
Sales tax % = 6.5 %
Tip % = 15 %
Delivery fee= $10
We have to find the change that Grant received to the nearest cent after giving the delivery driver with a $100 bill.
Sales tax = (6.5/100)*55 = $3.575
$55 + $3.575 = $58.575
Tip = (15/100)*58.575 = $ 8.78625
Total money paid by Grant = 55 + 3.575 + 8.78625 = $ 67.36125 ≈ $ 67.4
Hence,
Change received by Grant = 100 - 67.4 = $ 32.6
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Need help on #3 Please help me on my hw
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Factor the left hand side:
[tex]\begin{gathered} \frac{6}{6}\cdot\frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \frac{1}{1+2x}\ne\frac{1}{1+12x} \\ \end{gathered}[/tex][tex]1+12x\ne1+2x[/tex]Subtract 2x from both sides:
[tex]\begin{gathered} 1+12x-2x\ne1+2x-2x \\ 1+10x\ne1 \end{gathered}[/tex]Sutract 1 from both sides:
[tex]\begin{gathered} 1+10x-1\ne1-1 \\ 10x\ne0 \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10x}{10}\ne\frac{0}{10} \\ x\ne0 \end{gathered}[/tex]Therefore, the equation is correct for every x different from 0.
Find the area of the polygon with the given vertices.
X(-1, 2), Y(-1, -3), Z(4, -3)
square units
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Check the picture below.
I need help with all these questions as I don't know what to do with any of them.
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answer: 4) -10
Help me with question 2, thank you!
Answers
Given the function f(x):
[tex]f(x)=3x^2-5x-4[/tex]We will find the point on the given parabola where the slope of the tangent is horizontal
The horizontal line has a slope = zero
The slope of the line is the first derivative of the function
So, we will find the first derivative and equate it to zero
[tex]\begin{gathered} f^{\prime}(x)=0 \\ 3(2x)-5(1)-(0)=0 \end{gathered}[/tex]solve the equation to find (x):
[tex]\begin{gathered} 6x-5=0 \\ 6x=5 \\ x=\frac{5}{6} \end{gathered}[/tex]substitute with the value of (x) into the given function to find the y-coordinate
[tex]y=3(\frac{5}{6})^2-5(\frac{5}{6})-4=\frac{-73}{12}[/tex]So, the answer will be the point will be as follows:
[tex](x,y)=(\frac{5}{6},\frac{-73}{12})[/tex]See the following figure:
Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
p is greater than or equal to negative twenty over three
p is less than or equal to negative twenty over three
p is greater than or equal to negative forty four over three
p is less than or equal to negative forty four over three
Answers
Value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
As given in the question,
Given inequality:
Three fourths times p plus 8 is greater than or equal to 3 is written as
(3/4)p + 8 ≥ 3
Simplify inequality to get the value of p
(3p + 32)/4 ≥ 3
⇒ 3p + 32 ≥ 12
⇒ 3p ≥ 12 -32
⇒ 3p ≥ -20
⇒ p ≥ -20 /3
Therefore, value of p for given inequality of three fourths times p plus 8 is greater than or equal to 3 is p is greater than or equal to negative twenty over three.
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Jose wants to earn at least S61 trimming trees. He charges $7 per hour and pays $9 in equipment fees. What are the possible numbers of hours Jose could trim
trees?
Use for the number of hours.
Write your answer as an inequality solved for t.
Answers
Answer:
That depends on what exactly is meant by "$3 in equipment fees". Is that per hour, per day or what?
Assuming per hour, he makes $7 per hour but pays $3 for a profit of $4 per hour. So, to make at least $39, he'd have to work 39/4 or 9 3/4 hours.
Now, if his equipment fee is daily, then he would need to earn at least $42 in a day to profit at least $39. Thus, he'd have to work at least 42/7 or 6 hours to make that much profit.
Step-by-step explanation:
Members of a softball team raised $1186.50 to go to a tournament. They rented a bus
for $842.50 and budgeted $21.50 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Answers
The equation to determine the number of players the team can bring is $842.50 + $21.50y = $1,186.50
The team can bring 16 players to the tournament.
To go to a tournament, softball team members raised $1186.50 and rented a bus for $842.50, and the cost of meals of each player is $21.50.
Let y represent the number of players.
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50 × y = $1,186.50
$842.50 + $21.50y = $1,186.50
Subtracting $842.50 from each side.
$21.50y = $1,186.50 - $842.50
$21.50y = $344
Divide both side of the equation by $21.50.
x = $344 / $21.50
x = 16 players
As a result, the team is allowed to enter 16 players into the competition.
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how do you tun the area of a rectangle into its side lengths?
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In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.
To do so, first let's find the zeros a1 and a2, then we can factor as follows:
[tex]k(a-a_1)(a-a_2)[/tex]Where k is the coefficient of the quadratic term (so k = 12).
Using the quadratic formula, we have:
[tex]\begin{gathered} 12a^2+4a-5=0 \\ a_{}=\frac{-4+\sqrt[]{4^2-4\cdot12\cdot(-5)}}{2\cdot12} \\ a_1=\frac{-4+16}{24}=\frac{1}{2} \\ a_2=\frac{-4-16}{24}=-\frac{5}{6} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 12(a-\frac{1}{2})(a+\frac{5}{6}) \\ =(2a-1)(6a+5) \end{gathered}[/tex]Therefore the factors are 2a-1 and 6a+5.
Hello I need help please :)
Answers
Given: The system of equations below...
[tex]\begin{gathered} y=2x-2 \\ -4x-y=26 \end{gathered}[/tex]To Determine: The value of x and y
Using substitution method, Substitute for y in the second equation
[tex]\begin{gathered} -4x-y=26 \\ -4x-(2x-2)=26 \\ -4x-2x+2=26 \\ -6x=26-2 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Substitute for x in the first equation to solve for y
[tex]\begin{gathered} y=2x-2 \\ y=2(-4)-2 \\ y=-8-2 \\ y=-10 \end{gathered}[/tex]ence,
x = -4; y = -10
G
please help, thank you!!! photo attached with problem
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From the given table, it is found that:
a. The weight function is linear, as it has a constant rate of change.
b. The equation for the linear function is: W(x) = 0.85x + 2.22.
What are linear functions?Linear functions are modeled according to the following rule:
y = mx + b.
In which the coefficients are:
m is the slope of the function.b is the y-intercept of the function.The slope is the rate of change, and it has to be constant for the relation to be a linear function.
Relating the number of cans x and the cost of the cans C(x), the slope can be calculated as follows:
m = (5.19 - 3.99)/(12 - 8) = 0.3.m = (5.99 - 3.99)/(15 - 8) = 0.286.m = (9.99 - 3.99)/(24 - 8) = 0.375.Different slopes, hence the cost function is not linear.
For the weight function, the slope can be calculated as follows:
m = (10.2 - 6.8)/(12 - 8) = 0.85.m = (12.75 - 6.8)/(15 - 8) = 0.85.m = (20.4 - 6.8)/(24 - 8) = 0.85.Due to the constant rate of change, the weight function is a linear function.
Considering the slope of m = 0.85, the weight function can be written as follows:
W(x) = 0.85x + b.
When x = 8, W(x) = 6.8, hence the intercept b is found as follows:
8 = 0.85(6.8) + b
b = 8 - 0.85 x 6.8
b = 2.22.
Then the function is:
W(x) = 0.85x + 2.22.
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Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π =3.14
A: 0.38 in²
B: 126.39 in³
C: 353.88 in³
D: 88.47 in³
Answers
The total volume taken by the coins is 88.47 cubic inches, so the correct option is D.
How many cubic inches are taken up by the coins?The coins are cylinders with a radius of 1.4 inches and a height of 0.0625 inches.
Remember that the volume of a cylinder is given by:
volume = (height)*pi*(radius)^2
Where pi = 3.14
Then here the volume of each coin is:
V = (0.0625 in)*3.14*(1.4 in)^2 = 0.384 in³
And there are 230 coins, so the total volume is:
V = 230*0.384 in³ = 88.47 in³
So the correct option is D.
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Answer: D: 88.47 in³
Step-by-step explanation: So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h
Take 1.4 and times it by itself
1.4 x 1.4 = 1.96
Now multiply 1.96 by 0.0625
1.96 x 0.0625 = 0.1225
And times 0.1225 by pi, or in this case, 3.14
0.1225 x 3.14 = 0.38465
Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.
0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³
That is your answer.
Also I took the same test and I picked 88.47 inches cubed and got it right.
Proof:
Have a good day :)))
7 1
92. _ _ _
+6,39 0. ————
6,5 32
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PLSSSS HELP Which number is not in the correct location?
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We can conclude that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
What are whole numbers?Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.Integers:
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.As we can read the definitions whole numbers do not include negative numbers and integers do include negative numbers, so we can conclude that the number -7 in the given Venn diagram is not in the correct location.
Therefore, we can infer that the position of the number -7 in the provided Venn diagram is incorrect as -7 is an integer but, not a whole number.
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there are 60 minutes in one hour and 60 seconds in one minute using this information explain how you could convert 20 miles per hour to feet per second
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20 miles per hour converted to feet per second is 88/3 feet per second.
It is given in the question that there are 60 minutes in one hour and 60 seconds in one minute.
We have to convert 20 miles per hour in feet per second.
We know that,
1 mile = 5280 feet
1 hour = 60 minutes
1 minute = 60 seconds
Hence, we can write,
1 hour = 60*60 = 3600 seconds
1 mile per hour = 5280/3600 feet per second = 22/15 feet per second
Using unitary method, we can write,
20 miles per hour = 20*(22/15) = 88/3 feet per second or 29.3334 feet per second.
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Find the sum 40 +41 +42 +43 +...+ 124 + 125.
The sum is
Please help I’ll mark you as brainliest if correct!
Answers
Answer: 415
Step-by-step explanation:
??
The equation for a projectile's height versus time is h(t) = -16+2 +Vot+to. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height? Round to the nearest hundredth.
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Given the equation of a projectile to be:
[tex]h(t)=-16t^2+v_0t+h_0[/tex]Initial height = 2 feet
Initial speed = 110 feet per second.
That is,
[tex]h_0=2,v_0=110\text{ f}eet\text{ per second}[/tex]Substitute the initial height and speed into the projectile equation,
[tex]h(t)=-16t^2+110t+2[/tex]The graph of the projectile is shown below:
From the graph, the time it takes the ball to attain maximum height to the nearest hundredth is 3.44 seconds
What is the distance, d, between the points(2,7/2) and (5/3,1)?
Enter your answer in the box. Enter your answer in simplest radical form.
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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}[/tex]
I have available 1500mg/250mL ordered is 1500mg to be given over 90 minutes. What is the pump setting?
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Please solve the question. I am leaving but I will refer the answer typed by you teacher tomorrow, as I am going to sleep. Bit please solve.
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To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)
Step 1
[tex]\begin{gathered} Preimage\text{ of }triangle\text{ ABC} \\ A(1,3) \\ B(2,1) \\ C(1,1) \end{gathered}[/tex]Step 2
The new ordered pair of the image after rotation
[tex]\begin{gathered} \Delta A^{\prime}B^{\prime}C \\ A^{\prime}(3,-1) \\ B^{\prime}(1,-2) \\ C(1,-1) \end{gathered}[/tex]Step 3
Image of the coordinateStep
Step 4
Label of the points
Find the scale factor from triangle A to triangle B:
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From the figure of triangles, scale factor of A and B, the value of x = 3
According to the question, given that
when two triangle are same, then we easily get missing value x
From the figure, two triangle are similar in it thus,
[tex]\frac{x}{1}[/tex] = [tex]\frac{9}{3}[/tex] {property of triangles which are similar}
x = [tex]\frac{9}{3}[/tex] .
x = 3
Therefore, we get scale factor of triangle A and B, the missing value of missing x = 3.
What is a Scale Factor?Scale factor is the proportion of an original object's scale to a new one that is a representation of it but is a different size (bigger or smaller).
For example, if we have a rectangle of sides 4 cm and 6 cm, we can enlarge it by multiplying each side by a number, say 4. The new figure we get will be similar to the original figure, but all its dimensions will be twice that of the original rectangle.
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Please help me I was sick today and missed out on class and I don’t understand this question
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
the 2 angles are vertically opposite angles and are congruent
(c)
since they are congruent , then
7x + 6 = 6x + 18 ( subtract 6x from both sides )
x + 6 = 18 ( subtract 6 from both sides )
x = 12
(d)
then
7x + 6 = 7(12) + 6 = 84 + 6 = 90
6x + 18 = 6(12) + 18 = 72 + 18 = 90
Which points are solutions to the system of inequalitiesshown below? Check all that apply.y> xy> 2X> 4O A. (6,4)B. (9,-2)C. (9, 10)O D. (4,2)E (5,6)F(8,1)
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We take a look at the inequalities y > 2 and x >4. This means that the solutions must have values that has x > 4 and y > 2. Letters A, C, and E are candidates to be solution since they satisfy the inequalities provided. Using the inequality y > x, this means that the y value must be greater than the x value that we have. Letter A has higher x value than y value, hence, it will be crossed out. Both C and E has higher y values compared to their x values. Hence, the points that are solution to the system of inequalities provided are C. (9, 10) and E. (5, 6).
What is the correct answer
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1) [tex]m\angle A=76^{\circ}[/tex] (given)
2) [tex]m\angle B=76^{\circ}[/tex] (base angles theorem)
3) [tex]m\angle BCA=28^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle ECD=28^{\circ}[/tex] (vertical angles)
5) [tex]m\angle DEC=90^{\circ}[/tex] (perpendicular lines)
6) [tex]m\angle D=62^{\circ}[/tex] (sum of angles in a triangle)
NO LINKS!!! Part 1 Please help me with this similarity practice
Answers
Answer:
C' = (13, 4)
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units right.
Step-by-step explanation:
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)If two triangles are said to be similar:
Their corresponding angles are congruent.Their corresponding sides are in the same ratio.To keep the corresponding angles of both triangles the same and maintain similarity, dilate triangle ABC.
If we compare the coordinates of B (1, 4) and B' (5, 8), the y-value has been multiplied by 2.
Therefore, the first step of the transformation is a dilation by a scale factor 2 with the origin (0, 0) as the center of dilation.
⇒ (1 × 2, 4 × 2) = (2, 8)
After multiplying the coordinates of B by two, the difference between the x-values of the dilated point and B' is 3, so the second step of the transformation is a translation of 3 units right.
Therefore, the series of transformations is:
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation.Translation of 3 units right.Mapping Rule: (x, y) → (2x+3, 2y)
Therefore, the coordinates of point C' are:
⇒ C' = (2(5) + 3, 2(2)) = (13, 4)
Answer: (13, 4)
Infinitely many answers are possible.
====================================================
Explanation:
See this similar question
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because I'll be using the same steps and ideas. There are also diagrams that might help visualize what's going on.
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The translation vector from B(1,4) to C(5,2) is <4,-2> since we move to the right 4 units, and down 2 units. It's the shorthand way of writing [tex](x,y) \to (x+4,y-2)[/tex]
Double the coordinates of the translation vector <4,-2> to get <8,-4>
If we started at point B'(5,8) and followed the pathway "right 8, down 4" then we arrive at C'(13,4) as one possible answer.
We could express the steps like this
[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}-4)\\\\(5,8)\to(5+8,8-4)\\\\(5,8)\to(13,4)\\\\[/tex]
As I mentioned in the link above, there are infinitely many answers because we can change the scale factor to any nonnegative real number. For instance we could triple the coordinates of <4,-2> to get <12,-6> and follow the same outline of steps to get C'(17,2) as another possible answer.