The recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75
Recursive functionsThe general recursive function is expressed as:
an+1 = d + an
where
r is the common difference
Given the sequence below
1.5, 2.25, 3.0, 3.75, ...
Common difference = 2.25 - 1.5 = 0.75
Substitute
f(n + 1) = f(n) + d
f(n + 1) = f(n) + 0.75
Hence the recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75
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Abc co issues a zero coupon bond with 5 years to maturity. investor's required rate of return is 3.25%, what is the price of the zero coupon bond issued?
Based on the number of years till maturity and the required rate of return, the price of the zero-coupon bond is $852.22.
what price is the zero coupon bond selling at?When a bond's par value is not given, assume it is $1,000.
the price of a zero coupon bond is:
= par value / (1 + rate) ^ number of years till maturity
solving gives:
= 1,000 / (1 + 3.25%)⁵
= 1,000 / 1.17341139582939453125
= $852.22
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PLEASE HELP IM STUXK
The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work and be sure to give final responses in complete sentence form in context of the problem, and explain your reasoning.
a. Mean is 70.8, median is 70, and mode is 60
b. Mean describes the data best
c. Mean can be a misleading central measure in case of outliers
Calculating Mean, Median and Mode
Mean = Total sum of pries / Total number of sunglasses
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median = (n/2 + 1)th term
Here, n is the number of sunglasses.
Median = (25/2 + 1)th term
Median =13th term
Median = 70
Mode = Most occurring data
Mode = 70
Why is mean the best central measure to describe the data?
When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilize. Thus, mean describes the average price of the sunglasses here
Mean Being Misleading
In case there are outliers, the mean of the data gets highly affected. Hence, it can be misleading for analyzing average price of the data.
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A region in the first quadrant is bounded by the graph y equals two thirds times x, the y-axis, and the horizontal line y
By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.
How to calculate the area of the region by definite integrals
Integrals can be used to determine the area of regions bounded by curves set on Cartesian plane. The upper limit of the integral of the question is initially found:
(2 / 3) · x = 7
x = 21 / 2
The area can be defined as an rectangle in the first quadrant minus the area below the linear equation:
[tex]A = \left(\frac{21}{2} \right) \cdot (7) - \frac{2}{3} \int\limits^{\frac{21}{2} }_{0} {x} \, dx[/tex]
[tex]A = \frac{147}{2} - \frac{1}{3} \cdot \left[\left(\frac{21}{2} \right)^{2}-0^{2}\right][/tex]
A = 147/4
By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.
Remark
The statement is poorly formatted and incomplete. Correct form is shown below:
A region in the first quadrant is bounded by the line y = (2/3) · x, the y-axis and the horizontal line y = 7. Determine the area of the region.
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please help me im in a rush
Answer:
a. 25 seniors are randomly selected; 14 plan to go to a 4 year college
b. 420 students
Step-by-step explanation:
a. the less they have in common, the better
b. 14/25 is only between 25 students. make the denominator the same (750) and multiply the same to the numerator
750/25 = 30
14/25 x 30 = 420/750
PLEASE HELP ASAP
I think it’s supposed to be an arithmetic series or sequence.
Kaydence is saving for an RRSP. She saved $100 the first year, $200 the second year, $300 the third year, and so on. If she put $100 away on January 1, 2014, $200 away on January 1, 2015, and continued to put money away on the first of each year, how much money would Kaydence have saved by the end of the day on January 1, 2050?
Answer:
$70,300
Step-by-step explanation:
The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.
Sum of an arithmetic seriesThe formula for the sum of n terms of an arithmetic series is ...
Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d
ApplicationThe number of terms being added is ...
2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits
The formula with a1=100, d=100, and n=37 is ...
[tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]
Kaydence would have saved $70,300 by the end of Jan 1, 2050.
Evaluate the function when x=5
F(5)=?
Step-by-step explanation:
When evaluating piecewise function, make sure the x value satisfies the function we use.
since 5>3, we use the second equations
That function is a constant function, this means at any x>3, exclusive, we will have a y value of -1.
So
[tex]f(5) = - 1[/tex]
The lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B. Cone A radius is r and height h - Cylinder B radius is r and height h. True or false?
The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)
What is the ratio of lateral area of cone to the lateral area of the cylinder?In accordance with space geometry, the lateral areas of the cone and cylinder are described by the following equations:
Cone
[tex]A_{l} = \pi \cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex] (1)
Cylinder
[tex]A_{l} = 2\pi\cdot r\cdot h[/tex] (2)
If we divide (2) by (1), then we have the following ratio:
[tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]
The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)
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Determine whether the relationship is an inverse variation or not. Explain.
The relationship is not an inverse variation because the product xy is not a constant.
What is Inverse variation?Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.
In this type of variation the product of the two quantities is constant.
Analysis:
if x is one quantity and y is the other,
Mathematically, x = [tex]\frac{k}{y}[/tex]
Where, k is a constant,
it means k = xy
from the table, when, x =2, y = 409, xy = 2 x 409 = 818
Also, x = 3, y = 240, xy = 3 x 240 = 720
Therefore, 720 not equal to 818.
In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.
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Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
Which equations are correct? select three options. n = 10 n = 7 cf = 59 fe = 42 cd = 30
Based on the calculations on this parallelogram, the correct equations are:
n = 10CF = 59FE = 42The properties of a parallelogram.Based on the image of the parallelogram shown in the image attached below, we can logically deduce that the opposite sides of this parallelogram are all equal. Thus, we have:
Side DE = Side CF
6n - 1 = 5n + 9
6n - 5n = 9 + 1
n = 10.
From Side CF, we have:
CF = 5n + 9
CF = 5(10) + 9
CF = 59.
For the measure of side FE, we have
FE = 4n + 2
FE = 4(10) + 2
FE = 42.
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Complete Question:
Figure CDEF is a parallelogram.
Parallelogram C D E F is shown. The length of F C is 6 n minus 1, the length of C D is 4 n + 2, and the length of D E is 5 n + 9.
Which equations are correct? Select three options.
n = 10
n = 7
CF = 59
FE = 42
CD = 30
Answer:
A,C,D
Step-by-step explanation:
On an exam you get two points for every question answered correctly, zero points for each question left blank and lose one-half point for each question answered incorrectly. what is your total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly?
Using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.
According to the question,
For each correct question, you get 2 points, and there are 22 correct questions, so multiply 22 by 2
22 * 2 = 44 points.
For each question left blank, you get 0 points, and there are 7 questions left blank, so multiply 7 by 0
7 * 0 = 0 points
For each incorrect question, you get -1 point, and there are 5 incorrect questions, so multiply 5 by -1
5 * (-1) = -5 points.
The total number of score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points.
Hence, using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.
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Jonathan bought a new computer for $1,716 using the electronic store's finance plan. he will pay $143 a month for 12 months. which equation can jonathan use to find out how much money he still owes after each month of the plan?
By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
According to the statement
Jonathan bought a new computer for $1,716
He will pay $143 a month for 12 months.
Total amount he will for 12 months is 143(`12)
Now,
y = the money he still owes
x = the number of months (from x = 0 to x = 12)
y = 1,716 - 112x
So, By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.
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The first three terms of a sequence are
given. Round to the nearest thousandth (if
necessary).
3, 6, 12, ...
Find the 9th term.
Answer: 768
Step-by-step explanation:
3, 6 ,12 ,24, 48, 96, 192, 384, 768
12 x 2 = 48
48 x 2 = 96
96 x 2 = 192
192 x 2 = 384
384 x 2 = 768
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the HL Theorm.
Question 2
1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
URGENT!!
Given the following table with selected values of f (x) and g(x), evaluate f (g(4)).
x –6 –4 1 3 4
f (x) 4 –1 –6 1 3
g(x) 1 4 3 –4 –6
–4
–1
1
4
Answer:
f[g(4)] = 4
Step-by-step explanation:
Given table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]
f[g(4)] is a composite function.
When calculating composite functions, always work from inside the brackets out.
Begin with g(4): g(4) is the value of function g(x) when x = 4.
From inspection of the given table, g(4) = -6
Therefore, f[g(4)] = f(-6)
f(-6) is the value of function f(x) when x = -6.
From inspection of the given table, f(-6) = 4
Therefore, f[g(4)] = 4
As we can see
g(4)=-6So
f(g(4))f(-6)4Which phrase describes an unknown or changeable quantity?
Answer:
That is a variable.
Step-by-step explanation:
- opposed to a constant which is known and does not change.
Divide. Reduce the answer to lowest terms.
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
To find the answer we will use KCF (Keep, Change, Flip) apply it to the following question and then complete by multiplying and reducing. If needed of course.
[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
Apply KCF:
[tex]\frac{1}{5} \div\frac{3}{4}=\frac{1}{5} \times\frac{4}{3}[/tex]
[tex]\frac{1}{5} \times\frac{4}{3}[/tex]
Solve:
[tex]1\times4=4[/tex]
[tex]5\times3=15[/tex]
[tex]=\frac{4}{15}[/tex]
Answer is in simplest terms.
Which means your answer is the first option or "4/15."
Hope this helps.
Can someone help me with these problems having trouble and show work please !
Answer:
1.x=0, –10
2.x=3, 4
Step-by-step explanation:
1.
x(x+10)=0===> x=0, –10
2.
x²–3x–4x+12===> x²–7x+12=0
(x–3)(x‐4)=0====> x=3, 4
I need help in this !! Thank you !!
(a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
Cumulative frequency curve (OGIVE)From the question, we are to determine the median mark
The median mark for a cumulative frequency curve corresponds to the second quartile (Q₂)
Q₂ = 1/2(n+1)th mark
Where n is the total frequency
In the graph,
n = 160
∴ Q₂ = 1/2(160+1)th mark
Q₂ = 80.5th mark
The 80.5th mark is 44
∴ The median mark is 44
(b)
The number of students who scored 54 marks or less = 120 - 0
The number of students who scored 54 marks or less = 120
(c)
The number of students who scored 60 marks or more = 160 - 140
The number of students who scored 60 marks or more = 20
Hence, (a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
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5.a.A tourist buys 5 pieces of Nepali cap at Rs 452 per piece including 13% VAT. How much will he recive while leaving Nepal?
Step-by-step explanation:
vat of a cap=13/100*452
=58.76
price after vat=58.76+452=510.76
price after vat of 5 cap = 510.76*5=2553.8
Could y’all help me
Answer:
16. C
17. C
Step-by-step explanation:
16.
this is just a multiplication of the 2 functions.
that means we multiply the functional expressions, and the result is the new functional expression of the multiplied functions.
2(3x - 5) × (-2x + 1) = (6x - 10) × (-2x + 1) =
= 6x×-2x + 6x×1 + -10×-2x + -10×1 =
= -12x² + 6x + 20x - 10 = -12x² + 26x - 10
17.
the domain of a function is the interval or set of all valid x values (or input values).
the range is the interval or set of all valid y or functional result values.
so, for the domain we need to see what values x may have for a 4th root.
for this we can imagine that a 4th root is the square root of the square root of x.
this is directly related to x⁴ being the square of the square of x.
the valid input values for a square root are all positive numbers (incl. 0). the result will be again a positive number (incl. 0), which is again a valid input number for the second square root.
therefore, the valid values of x for a 4th root are also the valid values for a square root. and vice versa.
and that is
0 <= x < infinity
FYI : we can never say x = infinity, because infinity is not a number, just a generation concept. so, infinity can never be included in any interval, it can only be listed as an excluded limit concept.
A basketball league’s average score is 58 points per game. Coach McGee tracks a team’s average for five weeks and compares it to the league’s average. The table shows the variances in scores for five weeks.
Points Above/Below Average
Week 1
Week 2
Week 3
Week 4
Week 5
2 and StartFraction 1 Over 8 EndFraction
1.6
Negative 2 and StartFraction 1 Over 8 EndFraction
–1.8
Negative 1 and StartFraction 4 Over 5 EndFraction
Which comparison is true? Use the number line to help you.
A number line going from negative 5 to positive 3 in increments of 1.
Week 1 = Week 3
Week 4 = Week 5
Week 2 < Week 4
Week 5 < Week 3
The correct option for the inequality is
Week 4 = Week 5. Option B. This is further explained below.
What is inequality?Generally, the relationship between two expressions that do not have the same value is denoted by a sign such as, which means "not equal to," >, which means "greater than," or, which means "less than."
In conclusion, When converted to decimal form, Week 5's score comes out to -1.8, which is the same as Week 4's score.
Week 4 = Week 5
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Answer:
The Answer Is B
Step-by-step explanation:
Week 4 = Week 5
which is most likely to be the first step in solving a system of nonlinear equations by substitution
The correct option is C. Isolating a variable in one of the equations.
The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.
What is system of nonlinear equations?A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.
The method to solve a system of nonlinear equations by substitution is-
Figure out each equation's graph.One of the equations should be solved for either variable.Fill in the other equation using the expression from step 2.Put the resultant equation to use.The importance of systems of nonlinear equations are-
They aid in a lot of our everyday predictions. In addition, nonlinear equations need not involve numbers. Sometimes you have to deal with the numbers, but more often than not you are only dealing with the graph's shape, and in such case it pays to be aware of the characteristics of certain shapes.To know more about the system of equations, here
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The complete question is-
Which is most likely the first step in solving a system of nonlinear equations by substitution?
A. Substituting a number for one of the variables
B. Substituting one equation into the other equation
C. Isolating a variable in one of the equations
D. Taking the square root of both sides of one of the equations
Answer:
Isolating a variable in one of the equations.
Step-by-step explanation:
What is the domain of f(x)=
F(X). 4)*
?
A. x>0
B. All real numbers
C. y> 0
D. x<0
Answer: All real numbers
Step-by-step explanation:
The domain is the set of inputs.
what is the solution to the equation 35-2x=23
Answer:
x = 6
Step-by-step explanation:
35 - 2x = 23
35 - 23 - 2x = 0
35 - 23 = 2x
12 = 2x
x = 6
35- 2x = 23
Subtract 35 from both sides.
-2x = 23 - 35Subtract 35 from 23 to get −12.
-2x = -12Divide both sides by −2.
x = -12 / - 2Divide −12 by −2 to get 6.
x = 6 ===> AnswerThe area of a rectangular cocktail table is x²-18x +32. If the width is x-16, what is it's length?
Answer:
x-2
Step-by-step explanation:
The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is [tex]x^{2} -18x +32[/tex]
So we know that when x-2 is multiplied with x-16, it gives off [tex]x^{2} -18x +32[/tex]
As an oak tree grows taller, it also grows wider. In other
words, the diameter of its trunk increases. Imagine that a
tree's height is about 8 times its diameter. Assume this
relationship will not change, and that the tree trunk is a
rather cylindrical shape. Write a function for the volume of
wood in the tree's trunk as it grows
The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]
The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where
'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given:
Height(h) = 8 x diameter = 16 x radius (r) (diameter = 2 x radius )
∴ h = 16r.
V= [tex]\pi r^2h[/tex]
Substituting h = 16r in the volume formula we get
V = [tex]\pi r^2(16r)[/tex] = [tex]16\pi r^3[/tex]
Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].
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what is the potential energy of a rock that weighs 100 newtons that sits on a hill 300 meters high
Answer:
30000J or 30 KJ
Step-by-step explanation:
Formula for finding Gravitiational Potential Energy or GPE = mgh (or Wh since W = mg)
Given
W = 100N
h = 300m,
GPE = Wh = 100 x 300 = 30000J or 30 KJ
The vertices of a rectangle are Q (2, -3), R (2,4), S (5,4), and T (5, -3).
4. Translate rectangle QRST 3 units left and 3 units down to produce rectangle Q'R'S'T'. Find the area of QRST and the area of rectangle Q'R'S'T'.
5. Compare the areas. Make a conjecture about the areas of a preimage and its image after a
translation.
6. The vector PQ=(4,1) describes the translation of A (-1, w) onto A' (2x+1, 4) and B (8y-1,
1) onto B' (3,32). Find the values of w, x, y, and z.
4) [tex]A_{QRST} = A_{Q'R'S'T'} = 9[/tex].
5) The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.
6) x = 1, w = 3, y = - 1/4, z = 1/3
How to analyze and apply rigid transformations
Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. In this question we have applications of translations, a kind of rigid transformation.
Exercise 4
In this part we must determine the areas of rectangles QRST and Q'R'S'T':
Rectangle QRST
A = RS · QT
A = 3 · 3
A = 9
Rectangle Q'R'S'T'
Q'(x, y) = (2, - 3) + (- 3, - 3)
Q'(x, y) = (- 1, - 6)
R'(x, y) = (2, 4) + (- 3, - 3)
R'(x, y) = (- 1, 1)
S'(x, y) = (5, 4) + (- 3, - 3)
S'(x, y) = (2, 1)
T'(x, y) = (5, - 3) + (- 3, - 3)
T'(x, y) = (2, - 6)
A = R'S' · Q'T'
A = 3 · 3
A = 9
The rectangles QRST and Q'R'S'T' have both an area of 9 square units.
Exercise 5
The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.
Exercise 6
In this case, we must solve the following equations:
PQ = A'(x, y) - A(x, y)
(4, 1) = (2 · x + 1, 4) - (- 1, w)
(4, 1) = (2 · x + 2, 4 - w)
(4, 1) = (2 · x, - w) + (2, 4)
(2, - 3) = (2 · x, - w)
(x, w) = (1, 3)
PQ = B'(x, y) - B(x, y)
(4, 1) = (3, 3 · z) - (8 · y - 1, 1)
(4, 1) = (2 - 8 · y, 3 · z)
(4, 1) = (- 8 · y, 3 · z) + (2, 0)
(2, 1) = (- 8 · y, 3 · z)
(y, z) = (- 1/4, 1/3)
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