The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.
According to the statement
we have to explain the characteristics of the Geometric Sequence.
So, For this purpose
We know that the
A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
From its definition it is clear that the
There is a common ratio between the terms.
And this point represent the characteristics of the Geometric Sequence not all other points.
Now, The option A is the correct rather than the other options.
So, The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Which statements describe characteristics of a geometric sequence? Check all that apply.
a.There is a common difference between terms
b.Each term is multiplied by the same number to arrive at the next term.
c.The sequence increases or decreases in a linear pattern
d.There is a common ratio between terms
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(2x+1)/(x²-3) simplified
The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
How to simplify the expression?The expression is given as:
(2x+1)/(x²-3)
The above expression is a fraction and the numerator has 2 terms
For a fraction
A + B)/x
The fraction can be split as
A/x + B/x
Using the above as a guide, we have:
(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)
Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
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A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
Answer:
someone please help me check my page
someone please help me check my pageStep-by-step explanation:
What is the difference between the smallest 7-digit number and the largest 6-digit number?
Answer:
the greatest 7 digit no.is = 999,99,99 the smallest 6 digit no.is= 1,00,000
Step-by-step explanation:
Sorry if I'm wrong I tried.
You start at (-4, 0). You move left 1 unit and down 5 units. Where do you end?
Answer: (-5, -5)
Step-by-step explanation:
(-4, 0)
Here, -4 is our x value and 0 is our y value
The x value moves horizontal (left and right) while the y value moves vertical (up and down)
If we move 1 unit left, we change x by -1 so, -4 -1 = -5
If we move 5 units down, we change y by -5 so, 0 -5 = -5
Therefore,
our new endpoint is: (-5, -5)
1. Find the length of a.
Answer:
Step-by-step explanation:
[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]
==> 84.57
What is the solution for x in the equation?
10x − 4.5 + 3x = 12x − 1.1
x =
Answer: x= 3.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 3.4
Step-by-step explanation:
[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]
Select the correct answer from the drop-down menu. consider the equations y = |x − 1| and y = 3x 2. the approximate solution of this system of equations is .
The approximate solution of this system of equations is
(x,y)=(-0.25,1.25)
What is an equation?Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account.
Given that,
y = |x − 1| and y = 3x+2
y = |x − 1|
= (x-1) , for (x-1)>0 or x>1
and
y = -(x-1) , for(x-1)<0 or x<1
y = -x+1
Now, For x>1
y = x-1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = x-1
→ 3x-x = -1-2
→ 2x = -3
→ x = -3/2
→ x = -1.5 which is <1.
For x<1
y = -x+1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = -x+1
→ 3x+x = 1-2
→ 4x = -1
→ x = -1/4
→ x= -0.25 which is <1.
substitute the value of x = -0.25 in equation 1 for x<1.
y = -x+1
= -(-0.25)+1
y = 1.25
Hence, The approximate solution of this system of equations is
(x,y)=(-1/4,5/4)=(-0.25,1.25).
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Rewrite 2x = 128 as a logarithmic equation.
Ologx128=2
O log2x = 128
O log₂128 = x
Olog128x = 2
The logarithmic equation is:
log₂128 = x
So the correct option is the third one
How to rewrite this as a logarithmic equation?
Here we have the expression.
2ˣ = 128
Now, if we apply the natural logarithm to both sides, we can get:
ln(2ˣ) = ln(128)
Because of the property of natural logarithms, we can write the left side as:
ln(2ˣ) = x*ln(2) = ln(128)
Now, if we isolate x, we get:
x = ln(128)/ln(2)
And remember that:
ln(k)/ln(n) = logₙ(k)
Then we can rewrite the logarithmic equation as:
x = log₂(128)
Which is the third option.
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please help 14 points ASAP
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median: Upper quartile:
Maximum:
Interquartile range:
The desired measures for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74.Maximum: 80.IQR: 20How to find the five number summary and interquartile range of the data-set?The five number summary is composed by the measures explained below, except the IQR.
The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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Using the following table determine the probability a person tests positive who does not actually have Tuberculosis.
Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:
c. 49/148.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:
p = 98/296 = 49/148.
Which means that option c is correct.
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The probability a person tests positive who does not actually have Tuberculosis is 1/100
How to determine the probability a person tests positive who does not actually have Tuberculosis?The probability is given as:
The probability a person tests positive who does not actually have Tuberculosis.
This is a conditional probability, and it can be calculated using
P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)
Using the given table of values, we have:
P = 98/9800
Evaluate the quotient
P = 1/100
Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100
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What is the smallest positive integer having eactly 5 different positive integer divisors?
The smallest positive integer having exactly 5 different positive integer divisors is 60.
What are positive integers?Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers. Positive integers can be used for addition, subtraction, multiplication, and division operations.To find the smallest positive integer having exactly 5 different positive integer divisors:
Take out the LCM of 1,2,3,4, and 5.The LCM of 1,2,3,4, and 5 is 60.Therefore, the smallest positive integer having exactly 5 different positive integer divisors is 60.
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guys please help me
Answer:
-1 and 1
Step-by-step explanation:
Reflecting D over the y-axis maps it onto (1,2).
This is supposed to map onto F(0,3), so this is a shift 1 unit left and 1 unit up.
So, the blanks are -1 and 1, respectively.
Answer: (x + [-1], y + [1])
Step-by-step explanation:
See attached. We can draw, or picture it in our heads, what the reflection would look like. Then we can pick one (or multiple to test) points and see the translation.
We can also test with a set of points. B', (2, 4) becomes G in the transformation. G is at (1, 5)
(1 - 2, 5 - 4) -> (-1, 1)
Después de 15 meses de haber prestado un capital al 5% de rédito, tengo que pagar de interés Q468.75. ¿Qué capital se ha prestado?
The capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The principal P, amount borrowed, at a certain rate of interest R%, for a time of T years, giving an interest of I, can be calculated using the formula:
P = (I * 100)/(R * T).
In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.
Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.
Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).
P = (468.75*100)/(5*1.25),
or, P = 46875/6.25,
or, P = 7500.
Thus, the capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The provided question is in Spanish. The question in English is:
"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"
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Find the total surface area. A. 78 B. 98 C. 69 D. 92
The total surface area of the figure is 92 m².
How to find the surface area of a figure?The surface area of a figure is the sum of the whole sides of the figure.
Therefore,
surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 + 1 / 2 (2 + 6)3.5
Hence,
surface area = 16 + 16 + 24 + 8 + 14 + 14
Therefore,
surface area = 32 + 24 + 8 + 28
surface area = 56 + 8 + 28
surface area = 92 m²
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What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangle u v w. side u v is labeled as 35 meters. side v w is labeled as 30 meters. side u w is labeled as 30 meters.
Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
SineSince the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
Law of cosinesThe law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
In quadrilateral qrst, angle r s t measures (5x 15)°. angle tqr measures (4x 3)°. circle p is inscribed with quadrilateral q r s t. what is the measure of angle rst?
The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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K
Consider a study conducted in 2018 to estimate the percentage of people from a certain region who do not use the
Internet. Complete parts (a) through (c) below.
a. If a 99% confidence level is used, how many people should be included in the survey if the researchers wanted to
have a margin of error of 7%?
There should be people included in the survey.
(Round up to the nearest person as needed.)
rred
The number of people who must be included in the survey, that is, the sample size should be 340.
We assume the sample size to be n.
The confidence interval required is 99%.
The Z-score corresponding to the 99% confidence interval is (Z) 2.58.
The true proportion (p) of the sample is not given, so we assume it to be 50% or 0.5.
The margin of error for the sample (E) is given to be 7% or 0.07.
By the formula of margin of error, we know that:
E = Z√[{p(1 - p)}/n].
Putting in the values, we have, we get:
0.07 = 2.58√[{0.5*0.5}/n],
or, (0.07/2.58)² = 0.25/n,
or, n = 0.25/{(0.07/2.58)²} = 339.6122449 ≈ 340.
Thus, the number of people who must be included in the survey, that is, the sample size should be 340.
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PLEASE ANSWER THIS IT'S 30 POINTS
Answer:
Step-by-step explanation:
since we know that the 50 degrees is one side of the line then the angle that is strait opposite from this angle is 50 degrees, so 50+60=110degrees and 180-110=70, so x=70 degrees
Please help me asap due at 5:00
Answer:
11/18.
Dan is 8.
Step-by-step explanation:
The initial fraction is
x / 2x-4
Adding 3/3 we have
x+3 / 2x-1 = 2/3
Cross multiply:
3(x+3) = 2(2x-1)
3x + 9 = 4x - 2
9 + 2 = 4x - 3x
11 = x,
So the original fraction was 11 / 2(11) - 4
= 11/18.
If Dans age is d then Lois's age = 4d.
So 4d + d = 40
5d = 40
d = 8.
So Dan is 8 years old.
Find the length of the function over the given interval. y = 3x from x = 0 to x = 2
The length of the function y = 3x over the given interval [0, 2] is 3.2 units
For given question,
We have been given a function y = 3x
We need to find the length of the function on the interval x = 0 to x = 2.
Let f(x) = 3x where f(x) = y
We have f'(x) = 3, so [f'(x)]² = 9.
Then the arc length is given by,
[tex]\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2[/tex]
This means, the arc length is 3.2 units.
Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units
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For a given rabbit population, the relationship between the number of adult female rabbits, F, and the number of offspring, R, that survive to maturity, is given by this equation: R=3+(350F/F+625)
Considering the given function in the problem, it is found that:
a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.
b. At least 18 female rabbits are required for there to be 13 offspring.
What is the given function in this problem?The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:
[tex]R = 3 + \frac{350F}{F + 625}[/tex]
When there are 12 female rabbits, we have that F = 12, hence:
[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]
9.6 offspring survive to maturity when there are 12 female rabbits in the population.
For at least 13 offspring, we have that the number of rabbits needed is given as follows:
[tex]R \geq 13[/tex]
[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]
[tex]\frac{350F}{F + 625} \geq 10[/tex]
[tex]350F \geq 10F + 6250[/tex]
[tex]F \geq \frac{6250}{340}[/tex]
[tex]F \geq 18[/tex]
At least 18 female rabbits are required for there to be 13 offspring.
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Graph f(x) = 2x - 3 on a coordinate plane.
Can you explain what you are going to do in order to graph this equation?
What do you expect the graph to look like?
Answer:
Create a table.
Plug values into the equation to complete the table.
Use the table to plot points on the graph.
Draw lines through the points on your graph.
The graph should look linear because there is an x that doesn't have a power greater than or less than 1.
Shandra drove 220 miles in 5 hours. if she continued at the same rate, how long would it take to travel 352 miles?
Answer:
8 Hours
Step-by-step explanation:
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
[tex]\frac{220}{5}x=352[/tex]
Multiply both sides by 5
[tex]220x=1760[/tex]
Divide both sides by 220
[tex]x=8[/tex]
Therefore it would take 8 hours.
8 Hours long would it take to travel 352 miles,
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
Multiply both sides by 5
Divide both sides by 220
Hence, it would take 8 hours.
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Add 77 -10 with its additive inverse.
Answer: 77 - 10 = 67, and the additive inverse of 77 - 10 is 77 + 10. 77 + 10 = 87.
Hope this helps! This question was kind of confusing for me, because I didn’t understand why you said to add 77 - 10… is this is the incorrect answer sorry your question was worded weird
HELP: If you multiply both sides of an inequality by a negative number when should you reverse the inequality symbol?
A. Sometimes
B. Always
C. Never
D. Depends on if the number is a fraction of not
Based on the task content; If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always. Option B
Multiplication of inequalityBased on the rule of inequality, whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
For instance,
-4x > 12
divide both sides by -4
x < 12/-4
x < -3
If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always.
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Evaluate the expression w2 - v+ 1 for W = -2 and v = -8.
A. -11
B. 5
C. 13
D. -3
Answer:
13
Step-by-step explanation:
w^2 = -2^2 = 4
-v = -1*-8 = 8
Put it together: w^2-v+1 --> 4+8+1 = 13
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the
translation?
(x + 5, y-3)
(x + 5, y + 3)
(x, y)(x-3, y + 5)
(x, y) (x + 3, y + 5)
(x, y)
O(x, y)
Mark this and return
Save and Exit
lext
Submit
Answer:
(x+5, y-3)
Step-by-step explanation:
I would say this because when a plane is translated up it would be positive and when it's translated to the left it would be negative,
Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9
The vertical asymptote of f(x) is (A) x = 0, –9.
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.To find the vertical asymptote of f(x):
The vertical asymptotes of a function are the zeroes of the denominator of a rational function
The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]
Set the denominator to 0:
[tex]x^{3} -81x=0[/tex]Factor out x:
[tex]x(x^{2} -81)=0[/tex]Express 81 as 9^2:
[tex]x(x^{2} -9^{2} )=0[/tex]Express the difference between the two squares:
[tex]x(x-9)(x+9)[/tex]Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].
Solve for x:
[tex]x=0\\[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.
(See attachment for the graph of f(x))
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The complete question is given below:
Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).
A) x = 0, –9
B) x = –9
C) x = 0, 9
D) x = 9
1
2. Rotate Rectangle ABCD 90° counterclockwise.
Then, translate it along the vector (3,4).
A
D
B
C
-4 -2
4
2
АУ
O
-2.
-4
2
4
X
A'(
B'(
C'(
D'(
A"(
B"(
C"(
D"(
)
)
)
)
HELP ME PLS
Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]
[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]
Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]
[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]
