Answer:
D. 9
Step-by-step explanation:
Let
abc=100a+10b+c
bca=100b+10c+a
cab=100c+10a+b
abc + bca + cab=(100a+10b+c) + (100b+10c+a) + (100c+10a+b)
=100a + 10b + c + 100b + 10c + a + 100c + 10a + b
Collect like terms
=100a + a + 10a + 10b + 100b + b + c + 10c + 100c
=111a + 111b + 111 c
Factorise
=111(a+b+c)
abc + bca + cab = 111(a+b+c)
Factors of 111(a+b+c)= 1, 3, 37, 111, and (a+b+c)
abc + bca + cab is divisible by a+b+c because it is a factor of 111(a+b+c)
abc + bca + cab is divisible by 3 because 3 is a factor of 111(a+b+c)
abc + bca + cab is divisible by 37 because 37 is a factor of 111(a+b+c)
abc + bca + cab is not divisible by 9 because 9 is not a factor of 111(a+b+c)
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Answer:
y = -x +2
Step-by-step explanation:
y =x has a slope of 1
Perpendicular lines have slopes that multiply to -1
m* 1 = -1
The slope of the perpendicular line is -1
We have a slope and a point
y = mx+b
y= -1x+b
Substitute the point into the equation
-3 = -1(5) +b
-3 =-5 +b
Add 5 to each side
-3+5 = b
2 =b
y = -x +2
I NEED YOUR HELP PLS
Answer:
For question 1 you can try dividing each of the value
For instance, you can divide 9 by 25 and see if you get a nice number
e.g. 1/8=0.125, numbers like these
For the second question, you can find the fraction by dividing 1000 starting with the decimal points
e.g 0.650, you would be plotting 650/1000 and you would simplify the fraction to the lowest value any value above the decimal point you can multiply by the denominator and add the nominator value to get your final answer.
Step-by-step explanation:
Answer:
Write the denominator in its prime factors. If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
example: 9/25
25 = 5*5, so it will be terminating
example: 7/12
12 = 3*2*2, which contains a 3, so it will be repeating.
. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
what is the sum of the interior angles of a regular hexagon
Answer:
see below
Step-by-step explanation:
The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.
Answer:
The sum of the interior angles of a regular hexagon is 720°
Step-by-step explanation:
As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
Find the missing probability. P(A)=1120,P(B|A)=1320,P(A∩B)=?
Explanation:
Assuming you meant to say
P(A) = 11/20
P(B|A) = 13/20
then,
P(A∩B) = P(A)*P(B|A)
P(A∩B) = (11/20)*(13/20)
P(A∩B) = (11*13)/(20*20)
P(A∩B) = 143/400
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100 100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 8 88 finishers in the final round of the 2012 20122012 Olympics. The lower dot plot shows the times of the same 8 88 swimmers, but in the semifinal round. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.) Choose all answers that apply: Choose all answers that apply:
Answer:
The center of the semifinal round distribution is greater than the center of final round distribution.
The variability in the semifinal round distribution is less than variability in the final round distribution.
Step-by-step explanation:
The mean value of each distribution set is not calculates as the center of semifinal round distribution is greater than the final round distribution. MAD Mean Absolute Deviation is calculated from the dotted graph plot, the distribution of semifinal round is less spread out than the final round distribution.
Answer:
correct answer is None of the above i understood nothing the other person was trying to say...
Step-by-step explanation:
mark me brainliest please...
A.) Pinky bought 1. 1/2 kg of apples and 5. 1/4 kg of mangoes 1. 1/2 kg of oranges. Find the total weight of fruits B.) if her family eats 3/4 kg of apples and 2. 1/2 kg of mangoes and 1/2 kg of oranges. Find the weight of fruits left (Please say the answer with explanation who says the answer first I will mark them as the brainliest)
Answer:
A. Total weight of the fruits is 2.25 kg
B. There are no more fruits left.
Step-by-step explanation:
A.
To get the total weight of the fruits, we will first of all have to sort out the fruits and multiply the weight of the fruits by the number available.
Weight of apples:
we have one 1apple weighing 1/2 kg. The weight will be 1 |X 1/2 = 1/2 kg
Weight of mangoes:
We have five mangoes weighing 1/4 kg. Total weight will be 5 X 1/4 = 5/4 kg
Weight of oranges:
We have one orange weighing 1/2 kg. Total weight will be 1X 1/2 = 1/2 kg
Total weight of the fruits will be total weight of Mangoes + oranges + apples
= 1/2 + 5/4 + 1/2 = 2.25kg
B.
If her family begins to eat off some portions of the fruits, we will have to calculate the sum total of all the weights of fruits eaten
The portion eaten will be 3/4 + (2 X 1/2) + 1/2 = 2.25kg
If this happens the family would have eaten all of the fruits because
the original weight present is only 2.25kg of fruits to start with
|3x–1|=8 please help!!!!!
Answer: -3
Add 1 to both sides
[tex]3x-1+1=8+1[/tex]
[tex]3x=9[/tex]
Divide both sides by 3
[tex]3x/3=9/3\\x=3[/tex]
solve for x and y plz 12x - 5y = -20 x + 4 = y
Answer:
(0,4)
Step-by-step explanation:
System of Equations:
[tex]\left \{ {{12x-5y=-20} \atop {x+4=y}} \right.[/tex]
x= y-4 .... Change format so you can substitute to first equation
12(y-4)-5y=-20 .... Plug in x= y-4 to first equation
12y - 48 -5y = -20 ..... Distributed
7y -48 =-20 .... Added like terms
7y=28 .... Added 48 to both sides
y=4
.... Plug y into the second equation to find x
x + 4=y
x +4 = 4 .... Plugged in y
x = 4-4 .... Subtracted 4 from both sides
x=0
Your answer is (0,4)
Hope this helps:)
31. Each day, Talisa exercises by first
stretching and then swimming
some laps, as shown in the table.
Make a scatter plot of the total
time she exercises as a function
of the number of laps she swims.
Draw a trend line.
Answer:
Step-by-step explanation:
Given the following :
Laps - - - - - - - - 5 - - - 6 - - - 7 - - - 8 - - - 9
Total time - - - 25 - - 28 - - 29 - - 30 - - 32
Using online graphing tool:
The y - axis named dependent variable represents the total time taken.
The x-axis, represents the number of laps.
The equation of the trend line attached to the plot is in the form :
y = mx + c
y = 1.6x + 17.6
Where y = total time taken
x = number of laps
m = 1.6 = gradient of the line (change in y / change in x)
C = 17.6 = intercept (whee the trndline intersects the y-axis).
LCM of x<sup>2</sup>+5x+6 and x<sup>2</sup>-x-6 is ………………………
Answer:
[tex] (x^2 - 9)(x + 2) [/tex]
Step-by-step explanation:
Given:
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 - x - 6 [/tex]
Required:
LCM of the polynomials
SOLUTION:
Step 1: Factorise each polynomial
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 + 3x + 2x + 6 [/tex]
[tex] (x^2 + 3x) + (2x + 6) [/tex]
[tex] x(x + 3) + 2(x + 3) [/tex]
[tex] (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 [/tex]
[tex] x^2 - 3x +2x - 6 [/tex]
[tex] x(x - 3) + 2(x - 3) [/tex]
[tex] (x + 2)(x - 3) [/tex]
Step 2: find the product of each factor that is common in both polynomials.
We have the following,
[tex] x^2 + 5x + 6 = (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 = (x + 2)(x - 3) [/tex]
The common factors would be: =>
[tex] (x + 2) [/tex] (this is common in both polynomials, so we would take just one of them as a factor.
[tex] (x + 3) [/tex] and,
[tex] (x - 3) [/tex]
Their product = [tex] (x - 3)(x + 3)(x +2) = (x^2 - 9)(x + 2) [/tex]
What is 12.5% of 72
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf of \ refers \ to \ multiplication.[/tex]
[tex]12.5\% \times 72[/tex]
[tex]\frac{12.5}{100} \times 72[/tex]
[tex]\sf Multiply.[/tex]
[tex]\frac{900}{100} =9[/tex]
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 | 20
3 | 10
5 | 0
7 | -10
A. Initial value: 20, rate of change: 10
B. Initial value: 30, rate of change: 10
C. Initial value: 25, rate of change: -5
D. Initial value: 20, rate of change: -10
Answer:
C, at 0/25, 1/20, 2/15, 3/10,...
Answer:
C
Step-by-step explanation:
20 squared (+5) divided by 100
The answer is 4.05
Step-by-step explanation:
20^2 is 20•20 which is 400 || +5=405 || /100=4.05
4x
5.
If 7:5 = (x + 2y): (x - y), find the value of
5y
Answer:
5/2 OR 2.5
Step-by-step explanation:
( x + 2y ) = 7 , ( x - 2y ) = 5
x = 7 - 2y , x = 5 + 2y
substitute the two eqns together:
7 - 2y = 5 + 2y
7 - 5 = 2y + 2y
2 = 4y
y = 1/2
when y = 1/2 ,
5y = 5(1/2)
= 5/2 OR 2.5
1: The best statement for reason 6 of this proof is -∠A ≅ ∠C
-∠B ≅ ∠D
-∠B and ∠D are supplements
-∠B ≅ ∠B
2.The best reason for statements 3.5. and 7 in this proof is
- Alternate interior angles are congruent.
-Corresponding angles are congruent.
-Alternate exterior angles are congruent.
-Interior angles on the same sides of a transversal are supplements.
3. The best statement for reason 8 of this proof is
-∠B ≅ ∠B -∠A and ∠C are supplements.
-∠B ≅ ∠D
-∠A ≅ ∠C
Answer:
1) -∠B ≅ ∠D
2) -Interior angles on the same side of a transversal are supplementary
3) -∠A ≅ ∠C
Step-by-step explanation:
1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D
2) Given that ABCD is a parallelogram, therefore ∠A and ∠B, ∠A and ∠D and ∠B and ∠C are interior angles on the same side of a transversal and are therefore supplementary
3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.
I answered all my work correctly but I don’t understand this one.
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answer:
[tex]AC=20[/tex]
Step-by-step explanation:
The line segment AC is the entire length of the line. Within this segment, point B is found.
Point B, in a way, splits the segment into two, creating the segments AB and BC.
To find the length of AC, add the lengths of the lines AB and BC together:
[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]
The length of AC is 20.
:Done
Answer:
20 units.
Step-by-step explanation:
Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.
If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.
Hope this helps!
4.
Aliyah, Brenda and Candy share a sum of money in the ratio of 3:5:6. After
Candy gives $100 to Aliyah and $50 to Brenda, the ratio becomes 2 : 3:3.
(a) Suppose Aliyah has $3x at the start, express Candy's initial sum of money in
terms of x.
(b) Find the value of x.
(c) Hence, how much money does Brenda have in the end?
Answer:
(a) Candy's initial sum as a terms of x is $6x
(b) x = $60
(c) $350
Step-by-step explanation:
The given parameters are;
The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6
The amount Candy later gives Aliyah = $100
The amount Candy later gives Brenda = $50
The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3
(a) Whereby Aliyah has $3x at the start, we have;
Total sum of mony = Y
Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14
Therefore, Y×3/14 = $3x
x = Y×3/14 ÷ 3 = Y/14
Amount of Candy's initial share = Y × 6/14
Therefore Candy's initial sum as a terms of x = $6x
(b) Given that Aliyah's and Candy's initial sum as a function of x are $3x and $6x, therefore, in the ratio 3:5:6, Brenda's initial sum as a function of x = $5x
Which gives;
Total amount of money = $14x
With
6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3
Therefore, we have;
14·x × 2/(2 + 3 + 3) = (6·x - 150)
14·x × 2/(8) = (6·x - 150)
14·x × 1/4 = (6·x - 150)
7·x/2 = (6·x - 150)
12·x - 300 = 7·x
12·x - 7·x = 300
5·x = 300
x = $60
(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350
The final amount of money with Brenda = $350.
find the multiplicative inverse of 3 by 4 minus 5 by 7
Answer:
28
Step-by-step explanation:
[tex]\frac{3}{4}-\frac{5}{7}[/tex]
Least Common Denominator of 4 & 7 is 4 * 7 = 28
[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]
Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]
Complete the following two-way frequency table.
Answer:
Step-by-step explanation:
Number of candies with Forest = 12
Candies containing coconut and chocolate both = Number common in coconut and the chocolate = 3
Candies which do not contain coconut but contain the chocolate = 6
Candies which contain the coconut but do not contain the chocolate = 1
Candies which neither contain the chocolate nor coconut = 2
From the given Venn diagram,
Contain coconut Do not contain coconut
Contain chocolate 3 6
Do not contain chocolate 1 2
Please solve (will make brainiest)
Answer:
1a) 1/64
1b) 1/169
1c) 1/9
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Question A,
[tex] {4}^{ - 3} = \frac{1}{ {4}^{3} } = \frac{1}{64} [/tex]
Question B,
[tex] {13}^{ - 2} = \frac{1}{ {13}^{2} } = \frac{1}{169} [/tex]
Question C,
[tex] {( - 3)}^{ - 2} = {( - \frac{1}{3}) }^{2} = \frac{1}{9} [/tex]
Remember, a percent is a fractional part
of 100. In a bag of candy, 15 of the 50
pieces are red. What percentage of the
candy is red?
mex
B 50%.
C 3006
D 659
Answer:
Step-by-step explanation:
B
Answer:
The answer would be 30% (although I don't see that as an answer).
Step-by-step explanation:
This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.
15/50 = (15*2)/(50*2) = 30/100 = 30%
There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
5 buses is the answer pls mark me brainliest
Least number of bus require for trip = 5 buses
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Now,
Total number of student = 9 × 25
= 225
Number of chaperones = 4 × 2
= 8
Total people = 225 + 8 + 4
= 237
Least number of bus require for trip = Total people / Bus hold
= 237 / 45
= 5.266
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answer:
$52.2Step-by-step explanation:
Given her total cost of ride tickets modeled by the equation c = 3.5t where c is the total cost of tickets and t is the number of tickets, If Stacy bought 15 tickets, to know the amount she would spend on 15 tickets, we will substitute t = 15 into the modeled equation as shown;
[tex]c = 3.5t\\when t = 15\\\\c = 3.5(15)\\\\c = \frac{35}{10} * 15\\ \\c = \frac{5*7}{5*2} * 15\\\\[/tex]
[tex]c = \frac{7}{2} * 15\\ \\c = \frac{105}{2}\\ \\c = \ 52.2[/tex]
Hence Stacy would spend $52.2 on 15 tickets
Answer:
I hope this helps!
Step-by-step explanation:
1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?
Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
[tex]v_1 = 60\ mph[/tex]
Sheyna drives back from the lake with average speed of 36 mph
[tex]v_2 = 36\ mph[/tex]
It took 2 hours less time to get there than it did to get back.
Let [tex]t_1[/tex] be the time taken to drive to lake.
Let [tex]t_2[/tex] be the time taken to drive back from lake.
[tex]t_2-t_1 = 2[/tex] hrs ..... (1)
To find:
Total time taken = ?
[tex]t_1+t_2 = ?[/tex]
Solution:
Let D be the distance to lake.
Formula for time is given as:
[tex]Time =\dfrac{Distance}{Speed }[/tex]
[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]
[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]
Putting in equation (1):
[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]
So,
[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]
[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]
So, the answer is:
[tex]t_1+t_2 = \bold{8\ hrs}[/tex]
A personal trainer keep track of the number of minutes each of his 20 clients exercise on the treadmill and the number of calories each client burned during that time removing. which TWO of these data points will cause the correlation coefficient to decrease the most?
A). Data point A
B). Data point B
C). Data point C
D). Data point D
Answer:
Data Point B and Data point E
Step-by-step explanation:
Data point B and data point E are the farthest and are more distant away from the best line of fit compared to other data points. The more clustered data points are, the more the correlation that exists between the variables in question.
Therefore, data point B and data point E, will cause the correlation coefficient to decrease the most.
The pepper plant has 2/3 as many fruits on it as the tomato plant has. The tomato plant has 9 fruits on it. How many fruits does the pepper plant have on it?
Answer:
The pepper plant has 15 fruits on it.
Step-by-step explanation:
Let the tomato plant have x plants. Let the pepper plant have y plants. Since the pepper plant has 2/3 more fruits on it than the tomato plant, we have that y - x = 2x/3
collecting like terms,
y = 2x/3 + x
The above is the number of plants the pepper plant has.
y = 2x/3 + x
y = (2x + 3x)/3
y = 5x/3
Since x = number of fruits on tomato plant = 9, then
y = 5x/3
y = 5(9)/3
y = 5 × 3
y = 15
Since y = number of fruits on pepper plant = 15
So, the pepper plant has 15 fruits on it.
Can someone please tell me how to solve this problem??!! I literally have to go back in math if I don’t pass this HELP!!
Answer:
D. 270° < φ < 360°Step-by-step explanation:
Imagine coordinate system
I quarter is where x>0 and y>0 {right top} and it is (0°,90°)
II quarter is where x<0 and y>0 {left top} and it is (90°,180°)
III quarter is where x<0 and y<0 {left bottom} and it is (180°,270°)
IV quarter is where x>0 and y<0 {right bottom} and it is (270°,360°)
Now, we have an angle wich vertex is point (0,0) and one of its sides is X-axis and the second lay at one of the quarters.
For the trig functons of an angle created by this second side always are true:
In first quarter all functions are >0
in second one only sine
in third one: tangent and cotangent
and in fourth one: cosine
{You can check this by selecting any point on the second side of angle and put it's coordinates to formulas of these functions:
[tex]\sin \phi=\dfrac y{\sqrt{x^2+y^2}}\,,\quad \cos \phi=\dfrac x{\sqrt{x^2+y^2}}\,,\quad \tan\phi=\dfrac yx\,,\quad \cot\phi=\dfrac xy[/tex] }
So:
sinφ<0 ⇒ III or IV quarter
tanφ<0 ⇒ I or IV quarter
IV quarter ⇒ φ ∈ (270°, 360°)
