T(-1, 7)
→
T′(-1, -7)
U(-1, 8)
→
U′(-1, -8)
V(9, 6)
→
V′(9, -6)
Alicia took a friend for a birthday dinner. The total bill for dinner was $44.79 (including tax and a tip). If Alicia paid a 21.6% tip, what was her bill before adding the tip?
(Round your answer to the nearest cent.)
Answer: 27.33
Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze
5. Find the area of the kite.
18 m
-21 m-
Answer: 189 m^2
Step-by-step explanation:
Area = (Diagonal 1 x Diagonal 2) ÷ 2
Please help me l don’t understand new topic
Answer:
(x-3)(x+4)
Step-by-step explanation:
This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49
χ1,2=-1+-7^2=3
=-4
Please help confused thank you
Answer:
Step-by-step explanation:
Typically you see f(x)=something like you do up in the original equation.
that is your function/graph.
a) f(0) means plug in 0 for x
f(0) = (-0)³-0²-0+13
f(0) = 13
b) f(2) =(-2)³-2²-2+13 >simplify the exponenents first
(-2)³ = (-2)(-2)(-2)= -8
f(2) = -8-4-2+13 >simplify work from left to right
f(2) = -12-2+13
f(2) = -14+13
f(2) = -1
c) f(-2) = [-(-2)]³-(-2)²-(-2)+13 >multiply - and - for (-(-2))³
f(-2) = (2)³-(-2)²-(-2)+13 >simplify exponents
f(-2) = 8-4-(-2)+13
f(-2) = 4-(-2)+13
f(-2) = 6+13
f(-2) = 18
d) means add f(1) and f(-1)
f(1) +f(-1) = (-1)³-1²-1+13 +[-(-1)]³-(-1)²-(-1)+13
f(1) +f(-1) = -1-1-1+13 +[1]³-1-(-1)+13
f(1) +f(-1) = -1-1-1+13 +1-1+1+13
f(1) +f(-1) = -2-1+13 +1-1+1+13
f(1) +f(-1) = -3 +13 +1-1+1+13
f(1) +f(-1) = 10+1-1+1+13
f(1) +f(-1) = 11 -1+1+13
f(1) +f(-1) = 10 +1 +13
f(1) +f(-1) = 24
. When completed, the Crazy Horse Monument in South Dakota will be 563 ft high. The monument is based on a 16-foot-tall scale model of the structure. What is the scale used in the construction?
Based on the information, we identified that the scale used in the construction is approximately 1:35.2.
How to find the scale?To find the scale used in the construction of the Crazy Horse Monument, we need to divide the height of the actual monument by the height of the model. Let's use the following formula to calculate the scale:
scale = (height of actual monument) / (height of scale model)The height of the actual monument is 563 feet and the height of the scale model is 16 feet. Substituting these values in the formula, we get:
scale = 563 feet / 16 feetSimplifying the fraction, we get:
scale = 35.1875Therefore, the scale used in the construction of the Crazy Horse Monument is approximately 1:35.2.
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bacteria in a culture is given by function n(t)=920e^0.35t
A) The continuous rate of growth of this bacterium population = 0.35
B) The initial population of the culture = 920
C) The number of bacteria at time t=5 are 5294
Here, the function [tex]n(t)=920\times e^{(0.35\times t)}[/tex] represents the number of bacteria in a culture at time t
A) We know that in exponential function f(x) = [tex]ae^{kx}[/tex], k is the rate of growth
Here, in this function n(t) = [tex]920\times e^{(0.35\times t)}[/tex], the continuous rate of growth is 0.35
B) To find the initial population of the culture
Substitute t = 0, in n(t)
n(0) = [tex]920\times e^{(0.35 \times 0 )}[/tex]
n(0) = 920 × e⁰
n(0) = 920
This is the initial population.
C) Now we find the number of bacteria at time t=5
[tex]n(t)=920\times e^{(0.35\times t)}[/tex]
Substitute t = 5 in above equation.
n(5) =[tex]920 \times e^{(0.35 \times 5)}[/tex]
n(5) = 5294.23
n(5) ≈ 5294
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The number of bacteria in a culture is given by the function
n(t) =920e^0.35t Where t is measured in hours
A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent
B) what is the initial population of the culture (at t=0) your answer is __
C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria
what is the answer? compute the following integral.
The integral for this problem has the result given as follows:
[tex]\int_2^5 -8f(x) dx = 168[/tex]
How to solve the integral?The integral over the largest region for this problem is given as follows:
[tex]\int_2^9 f(x) dx = -14[/tex]
The integral can be divided into two smaller regions, as follows:
[tex]\int_2^9 f(x) dx = \int_2^5 f(x) dx + \int_5^9 f(x) dx[/tex]
Hence the integral from x = 5 to x = 9 is given as follows:
[tex]-14 = \int_2^5 f(x) dx + 7[/tex]
[tex]\int_2^5 f(x) dx = -21[/tex]
Multiplying -21 by -8, the result of the integral is given as follows:
[tex]\int_2^5 -8f(x) dx = 168[/tex]
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algebra hw I will give brainlyest
The other value of x where g(x) = 15 is 16 in the absolute value function
Finding the value of xSince the vertex of the absolute value function is at (10,0), the equation for the function can be written as:
g(x) = a|x - 10|
To find the value of a, we can use the fact that the function passes through the point (4,15):
15 = a|4 - 10|
15 = 6a
a = 2.5
So the equation for the absolute value function is:
g(x) = 2.5|x - 10|
To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:
2.5|x - 10| = 15
|x - 10| = 6
x - 10 = 6 or x - 10 = -6
x = 16 or x = 4
Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.
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Help please i would appreciated it
here is the picture is about Row Ops
The matrix operation add -4(row 1) to row 3 is[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
Evaluating the matrix expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right][/tex]
From the question, we understand that
We are to add -4(row 1) to row 3
This means that
row 3 = row 3 - 4 * row 1
When these values are evaluated, we have
4: 4 - 4 * 1 = 0
-1: -1 - 4 * 2 = -9
6: 6 - 4 * 1 = 2
-8: -8 - 4 * -5 = 12
This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
Hence, the result of the matrix expression is [tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]
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Find the area and central angle of the polygons given the apothem or side length. Thank you.
The missing parameters of the regular polygons are listed below:
Case 1: θ = 45°, a = 10.864 cm
Case 2: θ = 72°, s = 5.812 cm
How to compute parameters of regular polygons
In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:
Central angle
θ = 360 / n
Relationship between apothema and side length
a = s / [2 · tan (180 / n)]
Where:
n - Number of sidesa - Apothemas - Side lengthNow we proceed to find missing parameters:
Case 1: s = 9 cm, n = 8
θ = 360 / 8
θ = 45°
a = (9 cm) / [2 · tan (180 / 8)]
a = 10.864 cm
Case 2: a = 8 cm, n = 5
θ = 360 / 5
θ = 72°
s = 2 · a · tan (180 / n)
s = 2 · (8 cm) · tan (180 / 5)
s = 5.812 cm
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Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost?
The vertices that produces the circuit of lowest cost is A and D. So, the correct answer is A) and D).
To apply the repeated nearest neighbor algorithm, we need to start at a vertex and repeatedly choose the nearest neighbor until all vertices have been visited. Then, we return to the starting vertex to complete the circuit.
Starting at vertex A, we can follow the path A-DE-BE-C-AD-BC-E-A. The total cost of this circuit is 3 + 1 + 13 + 7 + 6 + 5 + 3 = 38. Starting at vertex B, we can follow the path B-E-DE-BC-AD-C-A-B. The total cost of this circuit is 1 + 3 + 7 + 6 + 5 + 15 + 10 = 47.
Starting at vertex C, we can follow the path C-BC-AD-DE-E-B-CA-C. The total cost of this circuit is 5 + 6 + 1 + 13 + 3 + 15 = 43. Starting at vertex D, we can follow the path D-AD-BC-C-E-DE-BD-DA. The total cost of this circuit is 6 + 5 + 7 + 3 + 10 + 11 = 42.
Starting at vertex E, we can follow the path E-DE-BE-C-BC-AD-CA-E. The total cost of this circuit is 1 + 13 + 7 + 5 + 6 + 15 = 47. Therefore, the circuits with the lowest cost are those starting at vertex A and vertex D, both with a total cost of 38 and 42 respectively. So, the correct option is A) and D).
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help nowwwwwwww PLSSSS
Answer: y = -|x + 1| + 1
Step-by-step explanation:
This is a "V" shaped graph, so we know it uses the absolute value function. This is the parent function:
y = |x|
This represents the possible transformations:
➜ a is amplitude
➜ h is horizontal shift
➜ k is vertical shift
f(x) = a | x - h | + k
Next, we see it is shifted one unit upwards.
y = |x| + 1
Then, we see it is also shifted one unit left.
➜ Note that this shift is -h units, so we will use positive for moving left.
y = |x + 1| + 1
Lastly, we see this graph is flipped and has a negative slope, or amplitude.
y = -|x + 1| + 1
please help me with this question thank you
The difference between the adjustable-rate mortgage (ARM) and the fixed-rate mortgage is $176,494.80.
How to find the difference ?First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )
= $ 1, 172, 971. 20
Then we can find the total payment for the fixed - rate mortgage :
= Monthly payment x Number of years
= 2, 767. 99 x 30 years x 12 months
= $ 996, 476. 40
The difference is:
= 1, 172, 971.20 - 996, 476. 40
= $ 176,494. 80.
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In a chess tournament, there are six rounds of matches.
In each match, there are two players: the winner goes through to the next
round, and the loser leaves the tournament.
How many players were there at the start of the tournament?
There were 64 players at the start of the tournament.
To determine the number of players at the start of the tournament
We need to work backwards from the final round to the first round.
In the final round, there will be only two players remaining since the winner of that match will be declared the overall champion.
In the penultimate (fifth) round, there will be four players remaining.
These four players must have come from the previous round, where there were eight players.
Continuing this pattern, in the fourth round, there will be eight players, and in the third round, there will be 16 players.
In the second round, there will be 32 players, and in the first (initial) round, there will be 64 players.
Therefore, there were 64 players at the start of the tournament.
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The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor between a square of dimensions 7 by 7 and a scaled copy of dimensions 21/2 by 21/2 is 3/2 or 1.5.
We know that the dimensions of the square on the left are 7 by 7, and the dimensions of the square on the right are 21/2 by 21/2.
To find the scale factor, we can divide the dimensions of the square on the right by the dimensions of the square on the left
scale factor = (21/2) / 7
We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 7
scale factor = (21/2) / 7 = (21/2) * (1/7) = 3/2
Therefore, the scale factor is 3/2, or 1.5.
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In the quadratic formula, the number for a is filled in with the coefficient of x
In the quadratic formula, the number for "a" is filled in with the coefficient of x².
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For instance, given the quadratic equation 2x² - 3x - 1 = 0, we have:
a = 2
b = -3
c = -1
[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 + 8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]
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Find the amount that results from the given investment.
$700 invested at 4% compounded daily after a period of 4 years
After 4 years, the investment results in $.
(Round to the nearest cent as needed.)
C
After 4 years, the investment of $700 at 4% compounded daily results in a future value of $821.45.
How is the future value determined:The future value represents the present value or investment compounded at an interest rate periodically for a certain number of years.
The future value can be determined using the FV formula or an online finance calculator.
N (# of periods) = 1,460 days (4 years x 365)
I/Y (Interest per year) = 4%
PV (Present Value) = $700
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $821.45
Total Interest = $121.45
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Trundle wheels are used to measure distances along the ground.
The radius of the trundle wheel is 30 cm.
Jim wants to work out the distance between two junctions on a road.
He rolls the trundle wheel between the two junctions.
The trundle wheel rotates exactly 48 times.
Work out the distance between the two junctions.
Give your answer in metres correct to the nearest metre.
The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)
:: No. of rotations = 48
:: Circumference of a circle = ( 2 x π x r )
where, r is radius of the circle
So, as,
Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]
Therefore,
Distance = (2 x π x 0.3) x (48)
Distance = 2 x (3.14) x 0.3 x 48
Distance = 90.432 meters
When rounded off to the nearest meter,
Distance = 90 meters.
So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
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I know I asked this before but i need help asap
Answer:
15h-6k+12m
Step-by-step explanation:
The perimeter of the triangle is the sum of all of its side lengths
P=a+b+c
If a=5h-4k
b=10h+7m
c=5m-2k
Then the formula would be
P=(5h-4k)+(10h+7m)+(5m-2k)
P=15h-6k+12m
Hope this helps!
Michelle has 3 kg of strawberries that she divided equally into small bags with 15 kg in each bag.
a. How many bags of strawberries did she make?
In a case whereby Michelle has 3 kg of strawberries that she divided equally into small bags with 1/5 kg in each bag the number of bags of strawberries she make is 15bags of strawberries.
How can the number of the bags of strawberries be calculated?We should note that 1kg = 1000g
3kg = 1000g
Since each of the bag is 1/5 kg = 1000/5 g = 200g
The needed bag will now be =3000/200= 15
Therefore, we can see that she made 15bags of strawberries the conversion were made so that it can be calculated easily since ythe kg are very small.
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Pythagorean theorem - Missing sides
Pls help me I need your help to my homework
If you help me, I help you too I promise
What is 0 + 0? Please help I wont pass kinder garden :(
Answer:
Step-by-step explanation: 0+0=0
Answer:
0
Step-by-step explanation:
0+0= nothing that why.
A triangle is translated by using the rule (x,y) → (x-4.y+1). Which describes how the figure is moved?
O four units left and one unit down
O four units left and one unit up
O one unit right and four units down
O one unit right and four units up
Mark this and return
Save and Exit
Next
Submit
Answer:
Four units left and one unit up
Step-by-step explanation:
Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.
Need help with these!!
The decimal used to figure the price of their clothing is 2.1
The improvement in Larry's test score written as a decimal is 1.52
How to write in decimals?Markup = 210%
= 210/100
= 21/10
= 2.1
Larry's increased test score percentage = 152%
= 152/100
= 1.52
In conclusion, the price of clothing and Larry's test score in decimals is 2.1 and 1.52 respectively.
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A population of rabbits is increasing at a rate of 1.5% per month. If there are 60 rabbits today, how many will there be after 10 months? Round to the nearest whole.
If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.
To solve this problem, we need to use the formula for exponential growth:
A = P(1 + r)ᵗ
where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.
Plugging these values into the formula, we get:
A = 60(1 + 0.015)¹⁰
A ≈ 71
t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.
Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.
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Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.
Julian sets the simulated biker to a speed of
20
km
h
20
h
km
20, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. After he rides his bike for
15
1515 minutes, Julian's app reports a position of
−
2
1
4
km
−2
4
1
km minus, 2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text.
What has Julian's average speed been so far?
To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.
We can use the formula for average speed:
Average speed = total distance / total time
To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.
Displacement = final position - initial position
Displacement = (-214 km) - (-d) = d - 214 km
The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.
Total distance = |d - 214 km|
To find the total time, we need to convert 15 minutes to hours:
Total time = 15 minutes / 60 minutes/hour = 0.25 hours
Now we can substitute the values into the formula for average speed:
Average speed = total distance / total time
Average speed = |d - 214 km| / 0.25 hours
Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:
Average speed = (20 km/h) x t / 0.25 hours
where t is the time Julian biked in hours.
Setting the two expressions for average speed equal to each other, we can solve for t:
|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours
|d - 214 km| = 20 km/h x t
Solving for t:
t = |d - 214 km| / 20 km/h
Now we can substitute this expression for t into either expression for average speed:
Average speed = (20 km/h) x t / 0.25 hours
Average speed = |d - 214 km| / 0.25 hours
Substituting the expression for t:
Average speed = |d - 214 km| x 4 / |d - 214 km|
Simplifying:
Average speed = 80 km/h
Therefore, Julian's average speed so far has been 80 km/h.
If mZRST = 70, mZQST = 2x, and mZQSR = 3x - 10, what is the mZQSR
16
48
32
38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
Explain about the adjacent angles:If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.
We may infer from our criteria and the aforementioned instances that any pair of neighbouring angles has a shared vertex and a common side. They really aren't adjacent if one of these elements is absent. By searching for these two characteristics, we can categorise pairs of angles as neighbouring or not adjacent.There are numerous unique connections between angles in pairs. You can recognise other angle connections, such as supplementary and complementary angles, by recognising nearby angles.Given data:
m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10From the figure:
m∠RST = m∠QST + m∠QSR
Put the values
70 = 2x + 3x - 10
5x = 80
x = 16
Thus,
m∠QSR = 3x - 10 = 3(16) - 10
m∠QSR = 38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
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Complete question:
If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.
The figure is attached:
16
48
32
38
Overview
Question Progress
1/3 Marks
11
12
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Homework Progress
27/30 Marks
At a school there are five lessons in a day.
In total, the five lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
+ Answer:
b) In fact, the first lesson of the day is shorter than the other lessons.
The other lessons last the same amount of time.
What does this tell you about the length of the final lesson?
A It is shorter than the answer to part a)
B It is the same as the answer to part a)
C It is longer than the answer to part a)
minutes
Submit Answering
Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.
Given that;
The time to finish five lessons = 4 hours
Then one lesson takes = 4/5 hours to finish
(a) Since each lesson takes equal amount of time
Therefore,
The time taken by final lesson in minutes = (4/5)x60
= 48 minutes
(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.
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If cos(x) = -5/6, x in quadrant II, then find exact values (without finding x):
sin(2x)= ?
cos(2x)=?
tan (2x)=?
If cos(x) = -5/6, and x lies in quadrant"II", then exact values are:
sin(2x) = (-5√11)/(18);
cos(2x) = 7/18;
tan (2x) = -5√11/7.
We know that, Cos(x) = -5/6 and "x" is in quadrant II, so, we can use the Pythagorean identity to find sin(x):
sin(x) = √(1 - cos²(x)) = √(1 - (-5/6)²) = √(1 - 25/36) = √(11/36) = √11/6
Using the double angle trigonometry identities for sine and cosine, we find sin(2x) and cos(2x):
Substituting the value of Sin(x) and Cos(x),
We get,
sin(2x) = 2sin(x)cos(x) = 2(√11/6)(-5/6) = (-5√11)/(18);
cos(2x) = cos²(x) - sin²(x) = (-5/6)² - (11/6) = 25/36 - 11/36 = 14/36 = 7/18;
Finally, we find tan(2x) by using the identity:
tan(2x) = sin(2x)/cos(2x) = (-5√11/18) / (7/18) = -5√11/7.
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The graph of line T passes throug the points listed beow.
(a,-b)and (-C,d) Line s is parallel to linet. What is the slope of line s?
Therefore, the slope of line s is equal to (d + b) / (a - c).
What is slope?In mathematics, the slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those same two points. In other words, the slope is the change in the y-coordinate divided by the change in the x-coordinate. If the slope is positive, the line is increasing from left to right and has an upward direction. If the slope is negative, the line is decreasing from left to right and has a downward direction. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical. The concept of slope is important in various fields of mathematics, science, and engineering, as it helps to describe the relationship between two variables and make predictions based on that relationship. It is also used in calculus to find the rate of change of a function, and in geometry to find the equation of a line or the angle between two lines.
Here,
Since line s is parallel to line t, it has the same slope as line t. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the points on line t are (a, -b) and (-c, d), so the slope of line t is:
slope of t = (d - (-b)) / (-c - a)
slope of t = (d + b) / (a - c)
Since line s is parallel to line t, it has the same slope as line t:
slope of s = (d + b) / (a - c)
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