The point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.
What is graph of equation?
Write the equation in the form y = mx + b to determine the slope m and y-intercept (0, b). 2) Next, determine the y-intercept. 3) Depending on whether the slope is positive or negative, go up or down and left or right from the y-intercept.
We are looking for the values of x and y that satisfy both equations simultaneously. We can do this by setting the right-hand sides of the two equations equal to each other:
y = x + 3 (equation 1)
y = 2x + 5 (equation 2)
Setting the right-hand sides equal to each other, we get:
x + 3 = 2x + 5
Simplifying this equation, we get:
x = -2
Now that we have the value of x, we can substitute it into either of the two equations to find the corresponding value of y. Let's use equation 1:
y = x + 3
y = -2 + 3
y = 1
So, the values of x and y that make both equations true are:
x = -2
y = 1
Therefore, the point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.
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where is the center of the face of the cube?
The center of the face of a cube is the midpoint of the face and lies along the line that runs between the opposite vertices of the face.
Where is the center of the face of a cube?This is the point of intersection of the two diagonals in a face. In other words, it is the point that is equidistant from all four corners of the face.
To visualize this, imagine dividing the face into four equal triangles by drawing lines from each corner to the center. The center of the face is at the intersection of these lines.
In three-dimensional space, the center of the face of a cube is also the center of the cube itself, as all faces of a cube are congruent (the same shape and size) and meet at the center of the cube.
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what is unit vector notation ?
Unit vector notation is a way of representing vectors in which magnitude of vector is equal to 1. A vector is mathematical object that has both magnitude (length) and direction, and can be represented as an arrow.
In unit vector notation, a vector is represented as a combination of a scalar (a numerical value) and a unit vector (a vector with a magnitude of 1 in the same direction).
The most common notation for unit vectors is to use a hat symbol (^) to indicate that a vector is a unit vector. For example, if we have a vector v, then its corresponding unit vector in the same direction would be represented as v. The unit vector in the x-direction is typically denoted as i, and the unit vector in the y-direction is denoted as j.
Unit vector notation is useful in many applications, including physics and engineering, where it is used to describe the direction of forces, velocities, and accelerations. It is also commonly used in computer graphics and game development, where it is used to represent the direction of movement or rotation of objects in a 3D space.
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of the
sat
5) The senior classes at High School A and High School B planned separate trips to New York City.
The senior class at High School A rented and filled 5 vans and 4 buses with 205 students. High
School B rented and filled 5 vans and 13 buses with 475 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students can a
bus carry?
The number of students the van carry is 17
the number of students the bus carry is 30
How to find the number of students can a bus carryLet's assume that a van can carry "v" students and a bus can carry "b" students.
From the information given, we can set up two equations:
5 vans + 4 buses = 205 students
5 vans + 13 buses = 475 students
We can write these equations as
5v + 4b = 205
5v + 13b = 475
solving simultaneously we have
v = 17 and b = 30
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What is an equation of the line that passes through the point (-4, -6) and is
perpendicular to the line 2x - y = 6?
Answer:
An equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x - y = 6 is y = -2x + 10.
Here is a grid of squares.write down the ratio of the number of unshaded to shaded squares
The ratio of the number of unshaded to shaded squares is 7 : 3.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
It is also defined as the fraction of one quantity with respect to other.
The ratio of a and b is denoted as a : b.
Given is a grid of squares which is given below.
Total number of squares = 10
Of that,
Number of shaded squares = 3
Number of unshaded squares = 7
We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.
Ratio of unshaded squares to shaded squares = 7 : 3
Hence 7 : 3 is the ratio of unshaded to shaded.
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how much 550 ml to cups
550 ml was found to be equivalent to approximately 2.324 cups using conversion factor method.
To convert 550 ml (milliliters) to cups, you can use the following conversion factor:
1 cup = 236.588 ml
Dividing 550 ml by 236.588 ml/cup, we get:
550 ml / 236.588 ml/cup = 2.324 cups (rounded to three decimal places)
Therefore, 550 ml is equivalent to approximately 2.324 cups
A conversion factor is a mathematical ratio used to convert a quantity from one unit of measurement to another. The conversion factor is usually derived from the relationship between the two units of measurement.
For example, if you want to convert a length measurement from feet to meters, you can use the conversion factor 1 ft = 0.3048 m.
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squirrel throws an acorn from the top of an 18 foot tall tree. The acorn reaches a height of 18.36 feet above
the ground after 0.2 seconds and a height of 7 feet above the ground after 1 second.Write a quadratic function to represent the situation.
Now we have the values of h0 and v, so we can write the quadratic function that represents the situation: h(t) = -16t^2 - 0.1125t + 18
What is Quadratic function ?
A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable. The term "quadratic" comes from the fact that the highest degree of the variable x in the function is 2, making it a second-degree polynomial.
Let's use the equation of motion for a free-falling object to model the acorn's motion:
h(t) = -16t^2 + vt + h0
where:
h(t) is the height of the acorn at time t
t is the time in seconds
v is the initial vertical velocity (upwards or downwards)
h0 is the initial height of the acorn
We know that the acorn is thrown from the top of an 18-foot tree, so its initial height is h0 = 18 feet. We also know that after 0.2 seconds, the acorn reaches a height of 18.36 feet above the ground, so:
h(0.2) = 18.36
-16(0.2)^2 + v(0.2) + 18 = 18.36
Simplifying the equation, we get:
-3.2v + 18 = 18.36
-3.2v = 0.36
v = -0.1125
Therefore, the initial vertical velocity of the acorn is v = -0.1125 feet/second (negative because it is moving downwards).
Now we need to find the height of the acorn after 1 second. Using the same equation of motion:
h(1) = -16(1)^2 + v(1) + 18
We know that the height of the acorn after 1 second is 7 feet above the ground, so:
-16 + v + 18 = 7
v = -5
the initial vertical velocity of the acorn is v = -5 feet/second (negative because it is moving downwards).
This is the quadratic function that models the height of the acorn at any time t in seconds, where h(t) is in feet.
Therefore, Now we have the values of h0 and v, so we can write the quadratic function that represents the situation h(t) = -16t^2 - 0.1125t + 18
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HELP ASAP !!!!!!!PLEASE
The both are exponential functions from the fact that the both are raised to a give power. The constant and rate of both functions are different.
What is a function?A function is a block of code that performs a specific task. In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
We can see that the two functions that we here are all such that we can be able to see that they are exponential in nature as shown in the image that depicts the question that has been asked.
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Simplify: –3|–2|+ 4|–5|
You want to solve the following system of equations by addition. What should
you do first, so that one variable is eliminated when you add the equations?
-2x+4y= 10
3x-2y=-7
OA. Multiply the top equation by 2 and the bottom equation by 3.
B. Multiply the top equation by 3 and the bottom equation by-2.
C. Multiply the bottom equation by 2.
D. Multiply the top equation by -3.
SUBMIT
Answer: C
Step-by-step explanation:
The two variables need to be eliminated. You can do this by multiplication or subtraction.
Multiply by -3 to the top equation will eliminate the x variable in the system
-3(2x - 4y = 5)
6x - 3y = 10
==> -6x + 12y = -15
6x - 3y = 10
adding a top with a bottom will eliminate the x
==> -6x + 6x = 0, 12y + (-3y) = 9y, -15 + 10 = -5
How do you draw a horizontal line in Matlab?
The "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function,
So the "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function, which creates a line object. You must supply the x-coordinates of the starting and ending points of the line as well as the line's y-coordinate in order to draw a horizontal line. To draw a horizontal line in MATLAB, use the following syntax: CSS Copy Code: x = [x min x max]; percentage of the x-coordinates of the line's beginning and finish points, y = [y value y value]; line(x, y percentage )'s y-coordinate; % Create a horizontal line
The starting and stopping positions of the line are indicated by the x-coordinates "x min" and "x max," respectively, while the line's y-coordinate is shown by "y value." is the "line".
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A coffee shop sells its coffee for $2.50 per cup.
In April they had total sales of $31,250.
In May they sold 10,150 cups of coffee.
Their total sales in June was the average of what they sold in April and May.
How many cups of coffee were sold in April?
What was the total sales ($$$) for May?
How many cups of coffee were sold and what was the total dollars in sales for the month of June?
Answer:
Step-by-step explanation:
Let's call the number of cups sold in April "x".
The total sales in April were $31,250, so we can set up an equation to find x:
2.50 * x = 31,250
Dividing both sides by 2.50, we get:
x = 12,500
So in April, 12,500 cups of coffee were sold.
The total sales in May were 10,150 cups * $2.50 per cup = $25,375.
The average of the sales in April and May was $31,250 + $25,375 / 2 = $28,312.50.
So in June, they sold $28,312.50 / $2.50 per cup = 11,250 cups of coffee.
Answer: There were 12,500 cups sold in April. In May they made $25,375. They sold 11,325 cups and made $28,312.50 in June.
Step-by-step explanation:
To find the cups of coffee sold in April, we will divide the total sales by price per cup.
$31,250 / $2.50 = 12,500 cups
To find the total sales for May, we will multiply the cups sold by the price per cup.
10,150 * $2.50 = $25,375
If they sold the average of April and May in June, we will find the average of April and May.
12,500 cups in April + 10,150 cups in May = 22,650
22,650 / 2 = 11,325 cups sold in June
Then, to find the dollar sales, we will multiply by the price per cup again.
11,325 * $2.50 = $28,312.50
How long is a 500 word essay in pages?
Answer:2
Step-by-step explanation:
A contest was held in which checkout clerks from two stores had to scan a given number of items as fast as they could. Their times were measured to the nearest second, as summarized in the table.
Choose the true statements about the situation that compares the differences in the centers of the data sets.
The correct statements regarding the data-set are given as follows:
The clerks from Store A were more consistent than the clerks from Store B.According to the median, the clerks from Store A were faster than the clerks from Store B.How to interpret the data-set?The consistency of the data-set is obtained by the IQR of each data-set, subtracting Q3 by Q1, hence:
Store A: 85.5 - 76.5 = 9.Store B: 86 - 73 = 13.Due to the lower IQR, the clerks from store A were more consistent.
For mean/median, the lower the mean and median, the faster they were.
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At a wedding there were 40 people from gromms side and 56 people from bride's family at the wedding
find the ratio of the groom's family to the bride's family at the wedding
Answer:
5 : 7
Step-by-step explanation:
groom's side: 40
bride's side: 56
ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7
Answer: 5 : 7
Six miners divide 15 ounces of gold dust equally. How
many ounces of gold dust does each miner receive?
Answer:
Each miner receive 2.5 ounces of gold dust.
Step-by-step explanation:
15/6= 2.5 ounces
If AC=82 and AE=2x+11 find the value of x
Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. The value of x = 40.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It might imply "declare the value of something," as in "a $200 award," or it can mean "hold something in high regard," as in "I cherish our friendship."Draw the above diagram and add the angles that are missing.
To determine the value of x, use the information provided in the accompanying diagram.
Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. (say).
Observe the illustration.
[tex]$& \Rightarrow \angle \mathrm{EAD}=70 \\[/tex]
[tex]$& \Rightarrow \angle \mathrm{EAD}+\angle \mathrm{DAB}=180 \\[/tex]
[tex]$& \Rightarrow \angle \mathrm{DAB}=180-70=110[\because E A B \text { is a straight line and } \mathrm{AD} \text { stands on it. }] \\[/tex]
Apply the total of internal angles in step two.
We are aware that a quadrilateral's inner angle total is 360.
[tex]& \Rightarrow \angle \mathrm{DAB}+\angle \mathrm{ADC}+\angle \mathrm{DCB}+\angle \mathrm{CBA}=360 \\[/tex]
[tex]$& \Rightarrow 110+80+56+3 \mathrm{x}-6=360 \\[/tex]
[tex]& 0 \quad 0 \quad 0 \quad 0 \quad 0 \\[/tex]
[tex]$& \Rightarrow 3 \mathrm{x}-6=360-110-80-56[/tex]
[tex]\Rightarrow 3 x-6=114 \\0 \\[/tex]
[tex]\Rightarrow x=120 \\[/tex]
[tex]\Rightarrow x=40 \\[/tex]
0
Therefore the value of x = 40. Hence, option A is correct.
The complete question is:
Use the information given in the following figure to find the value of x.
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Please help! Im givin 20 points! Please!
The y-coordinate for the solution to the system of equations is 6.
What is equation?Equation is a physical and mathematical statement the describing physical phenomenon the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.
The y-coordinate for the solution to the system of equations is 6. This is calculated by substituting the given y-value (2/3) into the equation -x+3y=9 and solving for x. Specifically, -x+3(2/3) = 9, which reduces to -x = 3. Therefore, x = -3 and substituting this value into the first equation yields 3y = 9, which simplifies to y = 3. Therefore, the y-coordinate for the solution to the system of equations is 6.
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Yasmine is buying a new dresser to put in her bedroom she wants the dresser to be as large as possible but she only has 3 3/4 feet of space against the wall to put in. this means she cannot buy a dresser wider than this. the widths of the dressers at the store are 3 2/5 feet 3 1/3 and 3 5/6 feet. Which dresser should she buy ?
Answer:
3 2/5 feet
Step-by-step explanation:
It's smaller than 3 3/4 feet, but it's the largest option, besides 3 5/6 feet which is larger than 3 3/4.
pls help asap I need to get this done by tmw
The interest that Marisol will earn in a period of 5 years is C. $ 1, 437. 50
The number of years that Marisol kept the account open, given the amount she receives when she closes her account is 12 years .
How to find the interest ?The simple interest on the account per year is :
= 5, 000 x 5. 75 %
= $ 287. 50
In 5 years, this is:
= 287. 50 x 5
= $ 1, 437. 50
The number of years that Marisol left the account open was :
= ( 8, 450 - 5, 000 ) / 287.50 per year
= 12 years
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The first part of the question is :
Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
4 of 5
Part 1: The function c (m) = 60 + 10m gives the monthly cost "C" of visiting a gym as a
function of the number of visits "m."
What would the inverse function tell us?
O The minimum number of visitis
O The visits for a cost of $60
O The cost in terms of visits "m"
O The number of visits made for a costs of "C"
Option (4): The inverse of the function tells us the number of visits m that can be made for a cost of c.
What is meant by the inverse of a function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."
Given a function,
c(m) = 60 + 10m
where c = cost of visiting the gym
m = number of visits
Then the Inverse function is:
c(m) - 60 = 10m
m = (c(m) - 60) / 10
Therefore the inverse of the function tells us the number of visits m that can be made for a cost of c.
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Find the missing side lengths. Show your work.
The missing lengths are 12 unit and 6 unit.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
we can use the property similar triangle which states the the ratio of corresponding sides of similar triangle are in proportion
Using proportion
x / 20 + x = 9 / 24
24x = 180x + 9x
24x -9x = 180
15x = 180
x= 12
Again, Using proportion
y/ y+9 = 4/ 10
10y = 4y + 36
6y = 36
y= 6
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PLS HURRY! Swimming pool A started with a depth of 30 inches of water. Pool A was being filled at a rate of 2 inches per minute.
The depth of swimming pool B, as it was being filled, is shown in the table.
(in the attached image)
Write a linear equation in slope-intercept form for both swimming pools, and then determine how many minutes it took for each pool to be filled to a depth of 71 inches.
Answer:
Equations:
A: y = 2x + 30
B: y = 3x + 6
Time to fill to 71 inches:
A: 20.5 minutes
B: 25.5 minutes
Step-by-step explanation:
Pool A: starts at 30 inches, fills at 2 inches/minute
Equation: y = 2x + 30
Pool B: starts at 20 inches, fills at 3 inches/minute
Pool B slope = filling rate = (26 - 20)/(2 - 0) = 6/2 = 3
Equation: y = 3x + 20
Pool A: y = 71
71 = 2x + 30
2x = 41
x = 20.5
Pool B: y = 71
71 = 3x + 20
3x = 51
x = 25.5
Question 6 of 25
What are the solutions to the system of equations graphed below?
The solutions to the system of equations are given as follows:
(0, -4) and (2,0).
How to obtain the number of solutions of the system of equations?The number of solutions of the system of equations is given by the number of times which the two functions intersect.
The two intersection points are given as follows for this problem:
(0, -4) and (2,0).
Which are the solutions to the system of equations.
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find average the rate of change of the function on the interval specified:
y=1/x on [1,3]
Answer: The average rate of change of a function over an interval is given by the slope of the secant line connecting the endpoints of the interval. To find this, we need to find the difference in y values (the rise) divided by the difference in x values (the run) between the two points (1,1/1) and (3,1/3).
The rise is 1/3 - 1/1 = 1/3 - 1 = -2/3
The run is 3 - 1 = 2
So the average rate of change over the interval [1,3] is -2/3 ÷ 2 = -1/3.
Step-by-step explanation:
can someone help me with this geometry question
According to the figure of the rhombus ∠ UTV = 36 degrees
How to find angle UTVAngle UTV is solved learning some property of rhombus
The opposite angles are equal.
∠ TWV = ∠ TUV and ∠ UTW = ∠ UVWThe diagonals divide the angles.
∠ UTV = ∠ UTW / 2
Assuming ∠ UTW = ∠ UVW = x
Given: ∠ TWV = ∠ TUV = 108
2x + 2(108) = 360 sum of angles of a rhombus
x + 108 = 180
x = 180 - 108
x = 72
∠ UTV = 72/2
∠ UTV = 36 degrees
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What is a variable interval in psychology?
In psychology, a variable interval refers to a type of schedule of reinforcement, which is a pattern of delivering rewards or punishments following a specific behavior.
A variable interval schedule is one in which reinforcement is provided after a variable amount of time has elapsed following a behavior. This means that the amount of time between the behavior and the reinforcement varies from one instance to the next, and is determined by a predetermined average or range.
For example, in an experiment, a rat might receive a food reward for pressing a lever, but the amount of time between each reward might be unpredictable, with the average time between rewards being, say, 3 minutes. So, the rat might press the lever and receive a reward after 30 seconds, then have to wait 4 minutes before pressing the lever again and receiving another reward.
Variable interval schedules tend to be more effective than fixed interval schedules at maintaining behaviors over time, as they prevent the subject from anticipating exactly when the next reinforcement will occur and thus reduce the likelihood of extinction of the behavior. They are also associated with more consistent and stable responding, as the subject knows that the behavior will be reinforced eventually, but doesn't know exactly when.
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set up the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.y=x2/3+3,y=3,x=6
About the line y=16.
[tex]\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx[/tex] is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.
A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.
This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").
As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.
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The accompanying table shows the number of bacteria present in a
certain culture over a 5 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the number of bacteria present after 14 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0 1353
1 1584
2 2037
3 2248
4 2630
5 3146
Answer:
Step-by-step explanation:
To find an exponential regression equation for this set of data, we can use a calculator or spreadsheet software with built-in regression functions. Using a calculator, we can input the data points into lists and use the exponential regression function to find the equation:
x y
0 1353
1 1584
2 2037
3 2248
4 2630
5 3146
Using exponential regression, we get the equation y = 1323.119e^(0.216x).
To determine the number of bacteria present after 14 hours, we can plug in x = 14 into the equation:
y = 1323.119e^(0.216 * 14) ≈ 35433
Therefore, the number of bacteria present after 14 hours is approximately 35,433 (rounded to the nearest whole number).
If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
csc Θ = undefined
The exact roots csc Θ = undefined in 0° ≤ Θ≤ 360° are x = 0°, 180°.
Explain undefined value in trigonometric function?A trigonometric function's undefined value indicates that division by zero was required to calculate the ratio for that particular function. The values of the quadrantal angle functions are listed in the table below.By the definition:
csc Θ = 1/ sin Θ
Hence, for those values of where sin θ = 0, csc θ is undefined.
The answer to this equation is:
x = kx ; k ∈ Z
Written in the intervals:
x = 0, π
In degrees.
x = 0°, 180°
Thus, the exact roots csc Θ = undefined in 0° ≤ Θ≤ 360° are x = 0°, 180°.
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The correct question is-
What are the exact roots for csc Θ = undefined in 0° ≤ Θ≤ 360°.