To determine whether the point [tex](1,2)[/tex] is a solution of inequality [tex]3x - 2y - 6 > 0[/tex], we substitute the point in the inequality and if the result is True, then it will be the solution .
What is an Inequality ?
The Inequality is defined as a relationship between two expressions or values that are not equal to each other .
The inequality in the question is given as : [tex]3x - 2y - 6 > 0[/tex] ;
the point is ⇒ [tex](1,2)[/tex] ,
to check the solution , we substitute the values in the inequality as [tex]x=1[/tex]and [tex]y=2[/tex] ;
we get , [tex]3(1) -2(2) - 6 > 0[/tex]
= [tex]3-4-6 > 0[/tex]
= [tex]3-10 > 0[/tex]
= [tex]-7 > 0[/tex],
But we know that , [tex]-7 < 0[/tex] , So , the given point is not the solution of the given inequality .
The given question is incomplete , the complete question is
How do you determine if the given point (1,2) is a solution of each linear inequality 3x - 2y - 6 > 0 ?
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y=mx+b give the equation of the line in slope intercept form that runs through (-3,6) and (5,-2)
Answer:
y = -x +3
Step-by-step explanation:
You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-2 -6)/(5 -(-3)) = -8/8 = -1
InterceptThe y-intercept can be be found using the formula ...
b = y -mx
b = 6 -(-1)(-3) = 3
EquationThe equation in slope-intercept form is ...
y = mx +b
Using the found values, the equation is...
y = -x +3
<95141404393>
Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips. The maximum charge is $45. 00 per day plus $0. 40 per mile. Discounts apply when renting for longer periods of time or during off-peak seasons
A linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
What is linear inequality?
In mathematics, an inequality involving a linear function is referred to as a linear inequality. One of the inequality symbols is found in a linear inequality. In graph form, it displays the non-equal data.
Given:
Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips.
The maximum charge is $45. 00 per day plus $0. 40 per mile.
A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation, with the inequality sign replacing the equality sign.
According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.
So,
a linear inequality that models the total cost of the daily rental as a function of the total miles driven, m is:
c(m) ≤ 45 + 0.4m
Hence, a linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
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What is an unsolvable equation?
1. The Riemann Hypothesis Equation
5. The prices of packages of golf balls are
recorded in the table.
Packages of Golf Balls
1
2
3
4
Cost
$15
$30
$45
$60
A. Write a rule to find the cost of
n packages of golf balls.
B. How much do 7 packages of golf
balls cost?
The rule to find the cost and the cost of 7 packages can be given as 15n and $105 respectively.
What is Proportionality?When two quantities have some dependence in their values they can be said proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.
The table for the given case can be written as follows,
Packages of Golf Balls Cost
1 $15
2 $30
3 $45
4 $60
The relation for proportionality can be obtained as,
15/1 = 30/2 = 45/3 = 60/4 = 15
(A) Suppose n be the number of packages.
Then, the cost is given as 15n.
(B) The cost of 7 packages is as below,
⇒ 15 × 7 = $105
Hence, the answers to both part can be given as 15n and $105 respectively.
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A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents
the first bus stop. The location of the second bus stop is determined using the same relationships as
those between the coordinates of the bus station and the first bus stop.
City Bus Stops
North
Choose...
12
10-
City Blocks
6
8
4
2
N.
Bus Station
: increases by 2.
2
(7.6)
increases by 4, and the
(11,8)
4 6 8 10 12
City Blocks
Use the drop-down menus to describe the relationships between the coordinates of the first and second
bus stop.
The Choose...
East
Answer: The relationship between the x-coordinates of the first and second bus stop is that the x-coordinate of the second bus stop is 4 units greater than the x-coordinate of the first bus stop.
The relationship between the y-coordinates of the first and second bus stop is that the y-coordinate of the second bus stop is 2 units greater than the y-coordinate of the first bus stop.
Step-by-step explanation:
Let x represent the number of laptops. Let y represent the number of smartphones.
Sully earns $80 by selling a laptop and $60 by selling a smartphone. He wants to make a profit of at least $6,800. Write an inequality to model the amount Sully earns by selling laptops and smartphones
Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.
What is inequality?Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<
Here,
Let the quantity of sold laptops, x
y —- the quantity of sold smartphones
The fact that to solve this problem we use inequality help
The problem's underlying inequity is equal to
=> 80x + 60y ≥6800
Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.
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Mario wait table at a retaurant where he make money by earning tip. One night, two of hi regular cutomer dined at the retaurant. Cutomer A had a total bill of $430. 50 and tipped 20% of the bill. Cutomer B had a total bill of $184. 00 and tipped 25% of the bill. How much did Mario make from the tip of hi two regular cutomer
Mario make total $132.1 from the tip of his two customers.
The amount of tip obtained = total bill × percentage of the bill
Put the respective values in equation depending on the customer A or B
Tip from customer A
Tip = 430.50 × 20%
Now find percentage by multiplication and division on Right Hand Side of the equation
Tip = $86.1
Tip from customer B
Tip = 184 × 25%
Again perform multiplication and division on Right Hand Side of the equation
Tip = $46
Total tip earned = 86.1 + 46
Simply add the two numbers on Right Hand Side of the equation to find the total tip earned
Total tip earned = $132.1
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This year, there was 40% more snow than last year. The amount of snow this year is 140% of the amount of snow last year.
1. This year, there were 25% fewer sunny days than last year. The number of sunny days this year is (BLANK)% of the number of sunny days last year.
2. Compared to last month, there was a 50% increase in the number of houses sold this month. The number of houses sold this month is (BLANK)% of the number of houses sold last month.
3. The runner’s time to complete the marathon was 10% less than the time to complete the last marathon. The runner's time to complete the marathon was (BLANK)% of the time to complete the last marathon.
PLEASE FILL IN THE BLANKS. This is in fact the full question
Answer:
75%150%90%Step-by-step explanation:
You want the percentage multiplier associated with the following changes:
25% decrease50% increase10% decreaseMultiplierTo find the multiplier, add 1 to the change. When you want the multiplier in percent, then add 100% to the change expressed as a percent. (1 = 100%)
1. 25% fewer100% -25% = 75% . . . . of last year
2. 50% increase100% +50% = 150% . . . . of sales last month
3. 10% less100% -10% = 90% . . . . of last marathon's time
I’m not sure how to do this I’m trying to get my makeup work done! So I can start actually going to school and not be behind every week on somthing lol! Thank you so much to whoever helps!
Answer:
1)95
2)180
3)77
4)120
5)244
6)74
I think
can you help me please
Answer:
help u with what
Step-by-step explanation:
(i) change 234mm into m
(ii) change 876m^2 into square cm
Answer: (i) 0.234m
(ii) 8760000cm^2
Step-by-step explanation:
234÷1000=0.2234m
876x10^4=8760000cm^
Evaluate. 10+7⋅3+4 my answer are either 224,50,55,and,40
Answer:
55
Step-by-step explanation:
Find the measure of the given angle. Round to the nearest degree.
(O
6
?
13
15 degrees by eye i think
I just need help with number 9 in this picture if anyone could pls help!
What is the coefficient of y² in the expression 2x²y 10xy² 5y?
The coefficient of yA² for the three given expressions are 2, 10 and 5 respectively.
What is expression?
It is a mathematical statement that defines a mathematical concept as well as the system of a mathematical operation express in a symbolic form.
Mathematical expression is made up of at least two numerical terms along with a sign or at least two terms along with a sign. The expression having two or more numerical terms is called numerical expression.
As example 4 + 3 or 100÷4
The expression which has both variables and numbers is called algebraic expression.
As example X+6 or 25+5y
What is coefficient?
In an expression, the numbers which are accompanied by variables is called coefficient. As example, 24 + 3y, where 3 is the coefficient of y
but 24 is a constant number.
How can we determine the coefficient from the given expression?
We are given three expressions, these are 2xA²y, 10xyA² and 5yA²
for the 1st expression, 2 is the coefficient of A²y
for the 2nd expression, 10 is the coefficient
for the last 5 is the coefficient.
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HELP PLEASE! 100PTS!
You're playing a game of pool and it's your turn, but you have no direct shots. To make any shot, you will need to bank the cue ball (the white ball) off the side of the table before it hits your ball.
That means that you hit the cue ball so that it bounces off the side and then hits your colored ball, moving it in the direction of a pocket (hole). The angle that the ball hits the bumper is equal to the angle that it bounces off the bumper.
The cue ball is 18 inches from the top bumper (side of pool table) and 50 inches from the right bumper. The dimensions of the pool table are 96 inches in the horizontal direction by 46 inches in the vertical direction
By Solving this proportion will give you the value of the angle you need to aim your shot.
What is angle of elevation ?
angle elevation can be defined as the angle formed between line of sight and horizontal line.
Draw a diagram of the pool table, labeling the dimensions of the table and the position of the cue ball.
Since the cue ball is 18 inches from the top bumper and 50 inches from the right bumper, you can draw a right triangle with these side lengths.
The dimensions of the pool table can also be used to draw a right triangle, with the horizontal dimension (96 inches) as the base and the vertical dimension (46 inches) as the height.
These two triangles are similar because they are both right triangles and they share a right angle. Therefore, the ratios of their sides are equal.
You can use the ratios of the sides of these triangles to determine the angle at which you should aim your shot. To do this, you can set up a proportion using the corresponding sides of the two triangles. For example, you could use the ratio of the base to the height of the small triangle (18 inches to 50 inches) and set it equal to the ratio of the base to the height of the large triangle (96 inches to 46 inches).
Hence, by Solving this proportion will give you the value of the angle you need to aim your shot.
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The point (0, 5) lies on a circle with the center at (0, 0). What is the area of the circle?
Two radar stations 4.3 miles apart are tracking an airplane. The straight-line distance between
Station A and the plane is 9.6 miles. The straight-line distance between Station B and the plane is 8.6
miles. What is the angle of elevation from Station A to the plane? Round the distance to the nearest
degree.
9.6 ml
Ad
4.3 mi
8.6 mi
B
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
What is trigonometry?The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.
Here,
given :
An aircraft is being followed by two radar stations, which are 4.3 miles apart.
Station A is 9.6 miles away from the plane in a straight line.
Thus,
To find the angle of elevation from station A to plane :
Using Trigonometric ratios:
=> Sin A = 8.5 / 9.6
=> Sin A = 85/96
=> A = [tex]Sin^{-1}[/tex](85/96 )
=> A = 62.302840124651483 °
=> A = 62.3°
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
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A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
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Fatuma recently hired a roofer to do some necessary work. On the final bill, Fatuma was charged a total of $1449. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $63, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
The equation is
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.
Answer: The number of labor hours was
(A) The equation is:
$63[tex]x[/tex] = $1449 - $315
(B) The labor hours needed to complete the job was 18 hours.
STEPS TO FIND TIME OF THE COMPLETE JOBS(A) To find the number of labor hours needed to complete the job, we can set up an equation using the information given in the problem.
We know that the total bill was $1449, and $315 of that was for parts. So the remaining amount, $1449 - $315 = $1134, was for labor.We also know that the hourly rate for labor was $63. To find the number of hours needed for labor, we can divide the amount for labor by the hourly rate:$63[tex]x[/tex] = $1449 - $315
[tex]x[/tex] = ($1134 / $63)
Solving this equation gives us the number of hours needed for labor, which is 18 hours. We can check this by multiplying 18 hours by the hourly rate, which should give us the same amount for labor:[tex]x[/tex] = ($1134 / $63)
= 18 hours
Double check for:18 hours × $63 = $1134
This confirms that 18 hours is the correct number of labor hours needed to complete the job.
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A construction worker is tasked with tiling two square rooms, room A and room B. Room B has side lengths that are double the side lengths of room A. The construction worker uses one box of tiles to complete the flooring of room A.
How many boxes of tiles will they need to complete the flooring of room B? Assume the boxes of tiles are identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
Define Volume and Area.The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Since the side lengths of room B are double the side lengths of room A, the area of room B is four times the area of room A.
The number of tiles needed to cover a floor is equal to the area of the floor divided by the area of each tile.
Since the boxes of tiles are identical, the number of tiles in each box must also be identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
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What should be the value of a if the value of 2x² X − a 5 when x 0?
The value of a=0 in a given expression.
what are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
Define algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
If the value of 2x² - a*5 when x = 0 is 0, then we can substitute x = 0 into the equation and solve for a.
So,
[tex]2(0)² - a5 = 0[/tex]
[tex]-a5 = 0[/tex]
[tex]a = 0[/tex]
Therefore, the value of a should be 0.
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Solve for x in the equation 2^(2x-1)x[1/8]^(1-x)=4^(3x+1)
Answer: x=-6
Step-by-step explanation:
[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]
Answer:
Step-by-step explanation:
We have:
2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)
2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)
2^(2x-1) x 2^-3+3x = 2^6x+2
2^5x-4 = 2^6x+2
on comparing both sides we get :
5x-4 = 6x +2
x = -6
Y’all please help my mind isn’t working please
Answer:
Step-by-step explanation:
To find values of y we substitute values of x in the given expression so when x = 0
y = (0)^2 - 6(0) + 3
= 3.
x = 1, y = 1^2 - 6(1) + 3 = -2
x = 3, y = 3^2 - 6(2) + 3 = 0.
Use these values to draw the graph
(a) Read this from the graph
Coordinates of the minimum should be 3, -6)
(b) Equation of the line of symmetry is the vertical line through the minimum point ( x = 3).
(c) Read these from the graph.
(the points where the graph cut the x-axis).
(d) and e - read the values from your graph.
Before beginning a unit of frog anatomy, a seventh grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.
The following method for assigning the 24 students to two equal-sized groups allows for a statistical valid comparison of the two instructional programmes.
What is instructional program?An instructional programme is a course of study that requires the completion of a specified number of course credits from a prescribed group of courses and results in a formal award.
A) Each student will be given a unique random number generated by a random number generator on a calculator, statistical software, or a random number table. The assigned numbers will be listed in ascending order. Students with the lowest 12 numbers on the ordered list will be assigned to the instructional programme that requires physically dissecting frogs.
Students with the highest 12 numbers will receive an instructional programme that simulates frog dissection using computer software.
B) By not randomizing and allowing students to self-select, there is the possibility of changes in the differences between pre test and post test scores for a specific group due to the characteristics of students who choose a particular instructional method, rather than the instructional method itself.
For example, suppose frog-loving students already know a lot about frog anatomy; these students would be less likely to show a large difference between pre and post test scores. Assume that the frog-loving students prefer the computer simulation method (perhaps because they do not like the notion of dissecting the frogs they love).
The possible low change in pre- and post-test scores for the computer simulation group could then be attributed to the students' prior knowledge of frog anatomy, rather than to the instructional method itself. Because the students entering the frog dissection group have lower pre-test scores (less prior knowledge), they are more likely to show greater improvement between pre-test and post-test scores.
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1. Indicate whether the value of each expression is positive or negative.
-3(-6)
(-3)(6)
-(-3)(6)
2(3)(-6)
-2(-3)(-6)
2(-3)(-6)
So we know that if you multiply a negative number by a positive number, you get a negative number. We also know that if you multiply a negative number by a negative number you get a positive number! (Two negatives cancel each other out!)
So going down the list:
(-3)(-6) = positive (two negatives!)
(-3)(6) = negative (one negative, one positive!)
-(-3)(6) = positive (this is because you multiple left to right. because the negative is technically a -1 multiplying the -3, your -3 turns into a +3!)
(2)(3)(-6) = negative
(-2)(-3)(-6) = negative (remember, you multiply in the order of left to right! So multiplying the -2 and -3 gives you a positive. However, the -6 makes that positive number negative!)
(2)(-3)(-6) = positive
I hope this helps!
Find the distance between point k and point L
The distance between two points in a plane is the length of the line segment connecting them. The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.
What do you call the distance between points?The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.
The length of the line segment is the distance between two points. Congruent segments are those that share the same length. By using a ruler to draw a line, we may determine how far apart two points are.
x,y = (-8,0) (-8,0)
or
x/y = -8/0
If there was an association between L and K, we would use x,y = 8,0.
Since the query reads "between point K and point L," the x,y relationship becomes "-8,0."
Therefore, the answer is -8,0.
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A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.016 in., with a tolerance of 0.004 in.
0.016 in.
(a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate. (Use h for
the thickness.)
(b) Solve the inequality that you found in part (a). (Enter your answer using interval notation.)
An inequality involving absolute values that describes the range of possible thickness for the laminate.
|h - 0.016| <= 0.004The range of possible thickness for the laminate is given by the interval (0.012, 0.02).What is inequality?(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:
|h - 0.016| <= 0.004
(b) To solve the inequality, we need to consider two cases:
Case 1: h - 0.016 <= 0.004
h <= 0.02
Case 2: h - 0.016 >= -0.004
h >= 0.012
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helpppppp
math math math math
Answer: 35
Step-by-step explanation:
So first you plug 5 into the equation which is:
10(5)-15
which is 50-15
50-15 is 35
Answer:
35
Step-by-step explanation:
plug 5 in for x and u will get 35
solve the following equations for values of theta between 0 degrees and 360 degrees. 1. 2tan^2 theta - 7 sec theta + 8 = 0
The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.
How to solve a trigonometric equation
In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.
First, write the complete expression:
2 · tan² θ - 7 · sec θ + 8 = 0
Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:
2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0
2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0
2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0
6 · cos² θ - 7 · cos θ + 2 = 0
Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:
6 · u² - 7 · u + 2 = 0
u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]
u = - 7 / 12 ± (1 / 12) · 1
u = - 7 / 12 ± 1 / 12
There are two possibilities:
u₁ = - 2 / 3, u₂ = - 1 / 2
Fourth, find the angles associated to roots by inverse trigonometric functions:
u₁ = - 2 / 3
θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°
u₂ = - 1 / 2
θ₂₁ ≈ 120°, θ₂₂ ≈ 240°
To learn more on trigonometric equations: https://brainly.com/question/22624805
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