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parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
What is a parabola in math?
Drawing a parabola for the quadratic function f(x) = ax2 + bx + c results in a U-shaped curve.When an is smaller than zero, the parabola's graph is downward (or opens downward).When the value of an is greater than 0, the parabola's graph ascends (or opens up). The locus of points in that plane that are equally spaced apart from the direct x and the focus is known as the parabola.A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.A parabola's general equation is written as y = a(x - h)2 + k or x = a(y - k)2 + h.Vertex here is indicated by (h, k).The typical form is y = a(x - h)2 + k.-9(x_6)²_1
= -9(x-6)1
=-9x+54
Differentiate x
-9
-9(x-6)²
Subtract
d/dx(-9(x-6)
Calculate x-6
d/dx (-9x+54)
-9x1-1
-9x
=-9
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Related Questions
Curious about people's recycling behaviors, Franco put on some gloves and sifted through some recycling and trash bins. He kept count of the plastic type of each bottle and which bottles are properly dispensed. Correctly placed Incorrectly placed Plastic #2 3 Plastic #4 3 3 What is the probability that a randomly selected bottle is made of plastic #2 or is correctly placed? Simplify any fractions.
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Solution
Note: The event here is Mutually Exclusive,, meaning the 2 events can happen at the same time
Total number = 4 + 3 + 3+3 = 13
[tex]\begin{gathered} P\mleft(A\mright)+P\mleft(B\mright)-P\mleft(AnB\mright) \\ \frac{7}{13}\text{ + }\frac{7}{13}-\frac{4}{13} \\ \frac{7+7-4}{13} \\ \frac{10}{13} \end{gathered}[/tex][tex]F\text{inal Answer = }\frac{10}{13}\text{ }[/tex]i dont really get what it means by pattern can u help me understand
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Well the principals patterns are that the equations are quadratic equations, and the graphs are parables and that the equations and the graphs are related.
how much of a 2 gram sample of silver-105 would remain after 86 days? round to three decimal places
Answers
We know that the half life of this element is 41.3 days.
We have to find how much will remain of a sample of 2 grams after 86 days.
The half life of 41.3 days means that the mass after 41.3 days will become half of what it was.
We can express this as:
[tex]\frac{M(t+41.3)}{M(t)}=\frac{1}{2}[/tex]As this is represented with an exponential model like this:
[tex]M(t)=M(0)\cdot b^t[/tex]we can use the half-life to find the parameter b:
[tex]\begin{gathered} \frac{M(t+41.3)}{M(t)}=\frac{1}{2} \\ \frac{M(0)\cdot b^{t+41.3}}{M(0)\cdot b^t}=\frac{1}{2} \\ b^{t+41.3-t}=\frac{1}{2} \\ b^{41.3}=\frac{1}{2} \\ b=(\frac{1}{2})^{\frac{1}{41.3}} \end{gathered}[/tex]Then, knowing that the initial mass M(0) is 2 grams, we can express the final model as:
[tex]M(t)=2\cdot(\frac{1}{2})^{\frac{t}{41.3}}[/tex]We then can calculate the mass after t = 86 days as:
[tex]\begin{gathered} M(86)=2\cdot(\frac{1}{2})^{\frac{86}{41.3}} \\ M(86)\approx2\cdot0.236 \\ M(86)\approx0.472 \end{gathered}[/tex]Answer: the mass after 86 days will be 0.472 grams.
A number divides equally into another number called ______. A.Remainder
B.divisible
C.Multiplier
D.Divisor
Answers
Answer: Divisor
Step-by-step explanation:
The the answer to a division problem is called the quotient. The number that is doing the dividing is called the divisor. The number that gets divided up is called the dividend.
Example: If 3 boys ask to mow your yard for $24, then each boy would get $8.
24 divided by 3 is 8. (24 / 3 = 8 )
24 is the dividend (the number getting divided up)
3 is the divisor (the number that is doing the dividing)
8 is the quotient.
What is the slope of the line represented by 4x-2y=10?
Answers
ANSWER:
2
STEP-BY-STEP EXPLANATION:
We have the following equation of line:
[tex]4x-2y=10[/tex]The equation of the line in its slope and intercept form is like this:
[tex]\begin{gathered} y=mx+b \\ \text{where, m is the slope and b is the y-intercept} \end{gathered}[/tex]Therefore, we must solve for y to know the value of the slope (m), like this:
[tex]\begin{gathered} 4x-2y=10 \\ 2y=4x-10 \\ y=\frac{4x-10}{2} \\ y=\frac{4x}{2}-\frac{10}{2} \\ y=2x-5 \\ \text{therefore,} \\ m=2 \end{gathered}[/tex]The slope is 2
PLEASEEE HELP I"LL GIVE LOTS OF POINTSS
and don't scam me
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Answer:
The difference in the depths is equal to 5ft
Step-by-step explanation:
A) snapper (-10 ft) : (b) redfish (-3ft): (c) clam (0 ft) : (d) Hermit Crab (2 ft)
B The comparison of the depth of hermit crab and redfish,
D = hermit crab - redfish = 2 - (-3) = 5 ft
In order would be 1 snapper) 2 red fish) 3 clam)4 hermit
Answer:
a) Flounder, Bluefish, Clam, Hermit Crab
b) The bluefish is deeper than the hermit crab.
Sketch the graph of the equation. Label the vertex and the intercepts.
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Given,
The expression of the function is,
[tex]y=x^2+4x+3[/tex]Required
The graph of the function.
Take x = 1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = 2 then the value of y is,
[tex]y=2^2+4(2)+3=15[/tex]Take x = 0 then the value of y is,
[tex]y=(-1)^2+4(-1)+3=0[/tex]Take x = -1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = -2 then the value of y is,
[tex]y=(-2)^2+4(-2)+3=-1[/tex]The graph of the function is,
The vertex of the graph is (-2, -1).
The x - intercept of the graph is -1 and -3.
The y - intercept of the graph is at 3.
Hence, the graph of the function is obtained.
A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. A. system15 adults, 30 children B. system30 adults; 22 children C. system22 adults; 30 children D. system30 adults, 15 children
Answers
Answer:
A
Step-by-step explanation:
45/2
A 240 horsepower automobile engine delivers only 210 horsepower to the driving wheels of the car. What is the efficiency of the transmission and drive mechanism
Answers
The efficiency of the transmission and drive mechanism is 87.5%
Given,
The power of the automobile engine = 240 horsepower
The power that the automobile engine delivers to the driving wheels of the car = 210 horsepower
We have to find the efficiency of the transmission and drive mechanism:
Efficiency of the transmission and drive mechanism = (power that delivers / power of engine) × 100
= (210 / 240) × 100 = 2100 / 24 = 700/8 = 87.5%
That is the efficiency of the transmission and drive mechanism is 87.5%
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Translate Pre Image coordinates using the rule (x + 18) and (y - 12).
Answers
We need to translate the points under the rule (x+18) and (y-12).
The points are given by the x-coordinate and y-coordinate following the form (x,y).
Now, let us use this rule for each point:
A.(-6,15)
Under the translation rule (-6+18,15-12) = (12,3)
So, A'=(12,3)
For B(-8,7)
Under the translation rule (-8+18,7-12)= (10,-5).
Then, B'=(10,-5)
For C(-11,12)
Under the translation rule (-11+18,12-12)=(7,0).
Then, C'(7.0)
Solve for xx and graph the solution on the number line below
-2 > -5+ x
Answers
Answer:
x< 3 this is for inequality and interval (inf,3)
Let M be the event that a randomly chosen person has a master's degree. Let B be the event that a randomly chosen person was a business major. Place the correct event in each response box below to show:
Given that the person has a master's degree, the probability that a randomly chosen person was a business major.
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The probability that the person has a business major is going to be represented by: p(B | M)
What is probability?This is the concept that is used in statistical and mathematical analysis to refer to the likelihood and the chances of something happening. That is the likelihood of an event occurring.
We have to define M as the event that the person that has been chosen randomly has a masters degree.
We have to define B as the event that the person that has being chosen randomly has a business major.
Given that the person has a master's degree, the probability that a randomly chosen person was a business major is given as p(B|M)
This would be the conditional probability that is written in the form of
p(B|M) = P(B and M) / P(M)
Where probability P(M) is the probability of having a masters degree, while the prbability P(B) is the probability of having a business degree.
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Sammy's teacher gives partial credit on quizzes if students show all of their work. Sammy earned the following points on his last quiz. Arrange the questions in order from least points earned to the greatest points earned.Questions- points1. 2 1/22. 1 2/53. 1 3/44. 2 2/35. 3 1/4
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First, express all the mixed numbers as decimals:
2 1/2 = (2x2+1)/2 = 5/2 = 2.5
1 2/5 = (5x1+2)/5 = 7/5 = 1.4
1 3/4 = (1x4+3)/4 = 7/4 = 1.75
2 2/3 = (2x3+2)/3 = 8/3 = 2.67
3 1/4 = (3x4+1)/4 = 13/4 = 3.25
Now, we have
1. 2.5
2. 1.4
3. 1.75
4. 2.67
5. 3.25
From least to greatest.
2. 1.4
3. 1.75
1. 2.5
4. 2.67
5. 3.25
Need help with part C. I have the first integral but cannot seem to get the second.
Answers
Answer:6_7
Step-by-step explanation:
A submarine is sitting still along the surface of the ocean as a part of a drill it does at a constant speed to a certain number of feet below the surface of the ocean
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The intervals in which the submarine is diving with a constant velocity is the intervals in which the graph is linear.
Velocity and positionThe velocity is given by the change in the position divided by the change in time, as follows:
Velocity = change position/change time.
It means that the velocity is the derivative of the position. Hence, if the velocity is constant, the position is represented by a linear graph, as the derivative of a line is a constant.
Hence, the submarine has a constant speed when the graph is linear, either constant, increasing or decreasing.
This problem is incomplete, hence I cannot give the exact intervals, as I can't see the graph, however you need to just check the graph and verify where it has linear behavior.
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3 c) and 10 d) - and 12 9draw a diagram for each pair of fractions. Which pairs are equivalent? Circle them
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Drawing the diagram of option D we have
Which means that 5/6 and 10/12 are equivalent fractions.
Looking back on your History class, you discovered something interesting. On your first test, you received a score of 65 points with no additional study time, other than doing your homework and attend lectures. On the second test, you decided to put in two additional hours of study time and receive a score of 85. After you have studied some mathematical modeling in math 49, you suspect that there is a relationship between your test score and the number of additional study time. Let S be your test score and T is your additional study time.
A. Assuming S and T have a linear relationship, find a formula for the linear function S=f(T).(12pts)
B. If you want a score of 98. How many hours of additional time of study would you have to put in? (3pts)
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Answer:
A. S = 65 + 10x
B. 3.3 hours
Step-by-step explanation:
A. S=f(T)
65 = f(0)
85 = f(2)
S₂ - S₁
85 - 65 = 20
T₂ - T₁
2 - 0 = 2
20 / 2 = 10
For every hour you study, you will score an additional 10 points with a baseline of 65 points.
S = 65 + 10x where x is the amount of time (in hours) that you studied for.
B. S = 65 + 10x
Since we want a specific score of 98, we plug it in for S and solve for x.
98 = 65 + 10x
33 = 10x
3.3 = x
If we wanted a score of 98, we would need to study for 3.3 hours.
14 socks in a drawer . Four of them are navy blue and 10 white What’s the probability that the second sock is navy blue if the first one was white
Answers
The Solution:
Given:
We are required to find the probability that the second sock is navy blue if the first one was a white sock.
Step 1:
The probability of the first sock being a white is:
[tex]P(first\text{ }W)=\frac{Number\text{ of white}}{Total\text{ number of socks}}=\frac{10}{14}=\frac{5}{7}[/tex]Step 2:
The probability of the second sock being a Navy blue is:
Note:
One sock has been taken out without replacement. So, the total number of socks is now 13.
[tex]P(second\text{ Navy Blue\rparen}=\frac{Number\text{ of navy blue socks}}{Current\text{ Total number of socks}}=\frac{4}{13}[/tex]Thus, the probability of the first being White and the second being Navy Blue is:
[tex]P(W\text{ NB})=P(W)\times P(NB)=\frac{5}{7}\times\frac{4}{13}=\frac{20}{91}=0.2198\approx0.22[/tex]Therefore, the correct answer is 20/91 or 0.22
The ratio of white roses to red roses in a garden is 8:7 . Check all statements that must be true based on the statement above. If none of the statements is true, check "None of the above".
A. There are exactly 8 white roses and exactly 7 red roses in the garden.
B. For every 7 white roses in the garden, there are 8 red roses.
C. Fer every 8 white roses in the garden, there are 7 red roses.
D. There are 8 white roses to every 7 roses in the garden.
E. None of the above.
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The true statement is for every 8 white roses in the garden, there are 7 red roses.
What is the true statement?
Ratio is used to compare two or more numbers together. It shows the relationship that exists between two or more numbers. In this question, for every 8 white roses, there would be 7 red roses.
This ratio does not mean that there are exactly 8 white roses and 7 red roses. It means that regardless of the number of white roses and red roses, when expressed in its simplest form the ratio would be 8 : 7. For example, there can be 56 : 49 white roses and red roses.
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g(n)=-2n-2
h (n)=4n-2
Find (goh) (-3)
Answers
Answer:
[tex](g \circ h)(-3)[/tex] = 26
Step-by-step explanation:
We are told that:
• [tex]g(n) = -2n - 2[/tex]
• [tex]h(n) = 4n - 2[/tex]
In order to calculate the value of [tex](g \circ h)(-3)[/tex], we need to first define [tex](g \circ h)[/tex].
[tex](g \circ h)[/tex] means that the input for the function [tex]g(n)[/tex] is the function [tex]h(n)[/tex]. Therefore, we have to replace the [tex]n[/tex] in the definition of [tex]g(n)[/tex] with the definition of [tex]h(n)[/tex]:
[tex](g \circ h)[/tex] = [tex]-2(4n - 2) - 2[/tex]
= [tex]-8n + 4 - 2[/tex]
= [tex]-8n + 2[/tex]
Now that we know the definition of [tex](g \circ h)[/tex], we can find the value of [tex](g \circ h)(-3)[/tex] by substituting -3 into the definition:
[tex](g \circ h)(-3)[/tex] = [tex]-8(-3) + 2[/tex]
= [tex]24 + 2[/tex]
= [tex]26[/tex]
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 34 liters per minute. There are 400 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added. Write an equation relating W to T. Then use this equation to find the total amount of water after 18 minutes.
Equation:
Total amount of water after 18 minutes:
Answers
Total amount of water after 18 minutes is 1365 Liters.
Given that
1) Owners of a recreation area are filling a small pond with water.
2) They are adding water at a rate of 35 liters per minute.
3) There are 700 liters in the pond to start.
4) Let W represent the total amount of water in the pond (in liters),
5) let T represent the total number of minutes that water has been added.
Now we have originally 700 litres i.e. when time =0 W =300
Next is rate of change of water per minutes = Positive 35
Thus the linear relationship between w and T has slope as 35 and y intercept as 300
Hence equation is
y = m x + c
W = 35T + 700
When T=19 minutes
W = 35(19) + 700
W = 1365 litres
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The equation relating W to T is W = 400 + 34T and total amount of water after 18 minutes is 1012 liters.
Equation will be formed by adding the amount of water already present with product of rate of water adding and amount of time in minutes. Representing this as equation -
W = 400 + 34T
Keep the value of T in the equation to find the total amount of water after 18 minutes.
W = 400 + 34×18
Performing multiplication on Right Hand Side of the equation
W = 400 + 612
Performing addition on Right Hand Side of the equation
W = 1012 liters
Therefore, the equation is W = 400 + 34T and amount of water is 1012 liters.
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Can you help me complete the proof and also correct any mistakes in my work.
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The given information is:
ABCD is a rhombus.
1 Statement: Rhombus ABCD
Reason: given
2. Statement: AB=AD
Reason: Definition of rhombus (all four sides are congruent)
3. Statement: AE=AE
Reason: Reflexive property
4. Statement: BE=DE
Reason: Diagonals bisect each other
5. Statement: Triangle ABE=Triangle ADE
Reason: SSS congruency (Side-Side-Side).
Rewrite the function by completing the square. g(x) = x^2 + 15x +54
g(x) = _ ( x + _ )^2 + _
Answers
7.5^2 = 56.25
g(x) = x^2 + 15x + (7.5)^2 - 2.25
g(x) = (x + 7.5)^2 + -2.25
y= -2/3x - 2 2x + y = 2 Find the solution of the systems of linear equation by graphing
Answers
x = 3, y = -4
Explanations:The given system of linear equations is:
[tex]\begin{gathered} y\text{ = }\frac{-2}{3}x\text{ - 2}\ldots\ldots\ldots\ldots.(1) \\ 2x\text{ + y = 2}\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The graph representing the equations is plotted below:
[tex]\begin{gathered} \text{The red line represents y = }\frac{-2}{3}x\text{ -2} \\ \text{The blue line represents 2x + y = 2} \end{gathered}[/tex]The point where both lines intersect is the solution to the system of equations.
The lines intersect at the point (3, -4), therefore, (3, -4) is the solution to the system of equations
There are 18 girls and 24 boys who want to play a game. They created the greatest number of teams possible.
How many boys will be on each team if each gender is split equally among the teams?
Answers
Answer:
your a bot
Step-by-step explanation:
please help this is for my study guide thanks! (no rounding)
Answers
Answer:
The volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]Explanation:
Given the figure in the attached image;
[tex]\begin{gathered} r=4\text{ in} \\ h=13\text{ in} \end{gathered}[/tex]Recall that the volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(4)^2\times13 \\ V=653.45\text{ }in^3 \end{gathered}[/tex]Therefore, the volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]graph the polygon and it’s image after a dilation centered C with scale factor k
Answers
We plot and join the given ordered pairs.
Graphing the image of the polygon after the dilationThe formula of dilation when it is not centred at the origin is:
[tex]\begin{gathered} (x,y)\rightarrow(k(x-a)+a,k(y-b)+b) \\ \text{ Where} \\ k\text{ is the scale factor} \\ (a,b)\text{ is the center of the dilation} \end{gathered}[/tex]Then, we can find the coordinates of the image:
[tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7-(-2))-2,\frac{2}{3}(1-4)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7+2)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(9)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(6-2,-2+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(4,2) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4-(-2))-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4+2)-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(6)-2,\frac{2}{3}(0)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(4-2,0+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(2,4) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1-(-2))-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1+2)-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(3)-2,\frac{2}{3}(9)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(2-2,6+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(0,10) \end{gathered}[/tex][tex][/tex]The cost of living last year went up 13%. fortunately, Alice Swanson got a 13% raise in her salary from last year. this year she is owning $22,570. How much did she make last year? Round to the nearest hundredth.
Answers
According to the information given in the problem, you know that Alice got got a 13% raise in her salary from last year, therefore, this year she is owning $22,570.
Let be "x" the amount of money in dollars Alice made last year.
Set up the following equation:
[tex]x+0.13x=22,570[/tex]So, to solve this equation, you must solve for the variable "x". The procedure for this is shown below:
[tex]\begin{gathered} 1.13x=22,570 \\ x=\frac{22,570}{1.13} \\ x=19,973.451 \end{gathered}[/tex]Rounded to the nearest hundredth:
- Look at the digit in the hundreths place. In this case it is 5.
- Look at the digitt to the right of the digit 5 (In this case is the digit 1, which is located in the thousandths place).
- Since the number in the thousandths place is less than 5, you must round down and just remove all the digits located after the digit 5.
Then:
[tex]x\approx19,973.45[/tex]She made about $19,973.45 last year.
10. Trapezoid PQRS is dilated about point P by a scale factor of 3 to form trapezoid P'Q'R'S'.-QTRPIsWhich statement is NOT true?The measure of angle P'is 3 times the measure of angle P.The perimeter of PQRS is one-third the perimeter of P'O'RS.The length of PQ'is 3 times the length of PO.QR and Q'R' are parallel.
Answers
Given:
Trapezoid PQRS is dilated about point P by a scale factor of 3 to form trapezoid P'Q'R'S'.
Required:
We need to find the dilation of Trapezoid PQRS by scale factor 3.
Explanation:
Recall that dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure.
Dilations preserve angle measure, betweenness of points and collinearity.
Let P be the perimeter of PQRS.
The dilation P'O'R'S' is enlarged by scale factor 3.
The perimeter of the P'O'R'S' is 3 times the perimeter of PQRS.
[tex]The\text{ perimeter of P'Q'R'S' =3p}[/tex][tex]\frac{1}{3}(The\text{ perimeter of P'Q'R'S' \rparen=p}[/tex]The perimeter of PQRS is one-third of the perimeter of P'O'RS is true.
The length of PQ' is 3 times the length of PQ is true since the scale factor is 3.
QR and Q'R' are parallel is true.
The measure of angle P' is 3 times the measure of angle P is not true.
Dilations preserve angle measure.
Final answer:
What’s the correct answer answer asap for brainlist
Answers
Answer: Maybe B
Step-by-step explanation: