Angle x's cosine is doubled in 2cosx, which ranges from [-2, 2]. The cosine of the angle 2x, or two times the angle x, is called cos 2x, and it lies between [-1, 1].
What makes 2cosx and cos2x different from one another?Trigonometric function cos 2 x is a cosine of angle that is twice as large as angle, whereas trigonometric function 2 cos x is twice as large as angle.
What is the equivalent of 2sinxcosx?Due to the fact that they contain an angle that is twice as large as the angle in their formulas, the identities and formulas of sin 2x, cos 2x, tan 2x, cot 2x, sec 2x, and cosec 2x are referred to as double angle formulas. 2sinxcosx is the sin 2x formula.
2•cos²(x) + cos(x) - 1 = 0
Factoring gives;
(2•cos(x) - 1)•(cos(x) + 1) = 0
2•cos(x) - 1 = 0
cos(x) = 1/2
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if a function is not continuous at a point, then it is not defined at that point. True/False ?
False. Despite not being continuous at that point, a function can nevertheless be defined there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there.
False. Despite not being continuous at that point, a function can nevertheless be defined there. Functions that have a limit that is equal to their value at a particular point are said to be continuous functions. A function is said to be continuous at a particular location if it is. A function can, however, be defined at a location yet not be continuous there. For instance, even when a function is defined at a certain place, it may nevertheless have a finite jump there. This suggests that the function is not continuous at that point since the left-hand limit and the right-hand limit of the function at that point are not equal. So, even though a function is defined at a certain location, it may not be continuous there.
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a professor is deciding which classes to teach in the fall. she chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2. a. what's the probability that she chooses to teach both classes?
The probability that the student chooses both math and Spanish is 0.5.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that professor is deciding which classes to teach in the fall.
The chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2.
P(M) = 3/7
P(S) = 1/4
P (M' ∩ S') = 1/2
According to De-Morgans law
P (M ∩ S) = P(M) + P(S) - P (M' ∩ S')
P (M ∩ S) =1/2
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3/4 Divided by 6 2/3 as a fraction in simplest form
let's convert the mixed fractions to improper fractions first.
[tex]\stackrel{mixed}{6\frac{2}{3}}\implies \cfrac{6\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{20}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{4}\div \cfrac{20}{3}\implies \cfrac{3}{4}\cdot \cfrac{3}{20}\implies \cfrac{9}{80}[/tex]
9/80.
Step-by-step explanation:1. Write the expression.[tex]\frac{\frac{3}{4}}{(6+\frac{2}{3} )}[/tex]
2.Simplify the denominator.[tex]6+\frac{2}{3}=\\ \\\frac{18}{3}+\frac{2}{3} =\\ \\\frac{18+2}{3} =\\ \\\frac{20}{3}[/tex]
3. Rewrite the original expression.[tex]\frac{\frac{3}{4}}{(\frac{20}{3} )}[/tex]
4. Use the rules of fractions to rewrite the operation.Check the attached image.
[tex]\frac{3}{4} *\frac{3}{20}=\frac{3*3}{4*20} =\frac{9}{80}[/tex]
5. Express the final result.9/80.
ow many data points are plotted incorrectly on the scatter plot graph, if any?
Responses
A 00
B 11
C 22
D 3
The solution is Option A.
The number of data points that are incorrectly marked on the scatter plot is none
What is a Scatter Plot?Dots are used in a scatter plot to show the values of two different numerical variables. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.
The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from near the origin out to high y-values, the variables are said to have a positive correlation.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
Given data ,
Let the equation of graph be represented as A
Now , the value of A is
Let the values of x be = { 1 , 2 , 3 , 4 , 6 , 8 , 10 , 12 }
Let the values of y be = { 2.5 , 7.6 , 12.5 , 17.1 , 24.3 , 37.9 , 49.2 , 54.9 }
So , the points on the graph will be
A ( 1 , 2.5 ) , B ( 2 , 7.6 ) , C ( 3 , 12.5 ) , D ( 4 , 17.1 ) , E ( 6 , 24.3 ) , F ( 8 , 37.9 ) , G ( 10 , 49.2 ) , H ( 12 , 54.9 )
There are no points marked incorrectly on the scatter plot
Hence , the graph is plotted and there are no incorrect data points on the scatter plot
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The following dot plots show the number of hours of sleep employees got before a major sale at two stores. Each dot represents a different employee.
Complete the comparison of the typical hours of sleep.
In general, the employees at
got more sleep, with
of sleep per employee.
In general, the employees at Store 1 got more sleep, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.
The dot plots for the two stores show that Store 1 had employees who got between 5 and 10 hours of sleep, whereas Store 2 had employees who got between 4 and 8 hours of sleep. The median for Store 1 was 8.5 hours of sleep, and the median for Store 2 was 7.5 hours of sleep. This indicates that, in general, the employees at Store 1 got more sleep than the employees at Store 2. The dot plots also show that there were more employees at Store 1 with 8 hours of sleep than Store 2, and fewer employees at Store 1 with 6 hours of sleep than Store 2. This suggests that Store 1 had more employees getting 8 hours of sleep, and fewer employees getting 6 hours of sleep, than Store 2. This can be further seen by the fact that the average amount of sleep for employees at Store 1 was 8.5 hours, while the average amount of sleep for employees at Store 2 was 7.5 hours. Therefore, in general, the employees at Store 1 got more sleep than the employees at Store 2, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.
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The complete question is
The following dot plots show the number of hours of sleep employees got before a major sale at two stores. Each dot represents a different employee. Complete the comparison of the typical hours of sleep. In general, the employees at got more sleep, with of sleep per employee compared to Store 2's.
In a soccer game, 1/5 of the players on Team A and 1/11 of the players on Team B score a goal. A total of 5 players on Team A and 2 players on Team B score a goal. How many players are on each team?
Let's call the number of players on Team A as "A" and the number of players on Team B as "B".
We know that 1/5 of the players on Team A score a goal, so:
5 players / (1/5) = A players
5 * (1/5) = A
A = 25
We also know that 1/11 of the players on Team B score a goal, so:
2 players / (1/11) = B players
2 * (1/11) = B
B = 22
So there are 25 players on Team A and 22 players on Team B.
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Translate the equation 3(g+h)=12 into a sentence.
Answer:
The equation "3(g + h) = 12" can be translated into a sentence as: "Three times the sum of g and h equals 12."
Hope this helps.
Answer: 3 times g plus h equals 12
Step-by-step explanation:
3 times g + h = 3(g+h)
equals 12 = =12
Hope this helps!
suppose the chain has been running for a long time and we start watching the chain. what is the probability that the next three states will be 4,5,0 in that order
The probability is 1/144 which can be computed by product of Q-matrix probabilities of transition.
Consider the absorbing states 0 and 6 and utilize both the Q-matrix of transition probability from 1, 2, 3, 4, and 5 to itself, as well as the S matrix of probabilities from 1, 2, 3, 4, and 5 to 0, 6.
The probability of the next three states being 4, 5, 0 in that order depends on the transition probabilities from one state to the next. If we know the transition matrix, we can calculate the probability as the product of the transition probabilities from one state to the next.
Q = Image is uploaded.
S = Image is uploaded.
The (1,6) item in the matrix corresponds to the desired probability.
[tex](1-Q)^-1S[/tex] = Image is uploaded.
This matrix's rows are labelled 1,2,3,4,5, and its columns are 0,6, respectively. 1/144 is the necessary probability.
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Use the given triangle to fill in the blank.
tan X= ___
Answer:12/5
Step-by-step explanation:
tan(x)=opposite/adjacent
tan(x)=12/5
Answer:
2.4
Step-by-step explanation:
This is a right-angled triangle:
where:
Side XY = hypotenuse
= 13 units
With respect to Angle X:
Side YZ = opposite side
= 12 units
Side XZ = adjacent side
= 5 units
Trigonometric function:
Tan∅= [tex]\frac{opposite}{adjacent}[/tex]
∴TanX = [tex]\frac{SideYZ}{SideXZ}[/tex]
= [tex]\frac{12}{5}[/tex]
= 2.4
Please help me find the exponential function of the following graph, needed NOW!!! First to answer gets 10 points!
The exponential function is given as follows:
y = 64(0.5)^(x/5).
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^(x/n).
In which the parameters are given as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.Considering the initial value of 64, along with the fact that the amount halves each five days, the parameter values are given as follows:
a = 64, b = 0.5, n = 5.
Hence the function is defined as follows:
y = 64(0.5)^(x/5).
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list the elements of the sets (i) (Anb)'uc (ii) (Auc) 'n B (iii) (Aubuc)'
I. the elements of (Anb)'uc = {1,2,4,5,6,7}
Ii. The elements of (Auc) 'n B = { 5}
III. The elements of( Aubuc)' = { }
What is Venn diagram?A Venn diagram illustrates the relationships between two or more data sets. Venn diagrams are especially useful for highlighting similarities and differences and are commonly used to compare and contrast the characteristics of different data sets. In a Venn diagram, circles are used to represent each data set.
(Anb)' = {1,2,4,5,6,7}
(Anb)'uc = {1,2,4,5,6,7}
(Auc)' = {5,6}
(Auc) 'n B = { 5}
(Aubuc)' = { }. this means there is no elements for this.
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Megan tiled a rectangle with an area of 24 square centimeters. Which of these could not be Megan ‘s rectangle
Megan tiled a rectangle with an area of 24 square centimeters, the Megan ‘s rectangle is 2 centimeters by 12 centimeters.
Megan tiled a rectangle with an area of 24 square centimeters,
A = 24 square centimeters
Area of the rectangle = length x breadth
A = l x b
24 = 12 x 2
Therefore, length= 12cm and breadth is 2 cm.
The area occupied by the rectangle within its perimeter may be calculated using the formula for the area of a rectangle. A rectangle's area is calculated by multiplying its length by its width (breadth). As a result, the area of a rectangle whose length and breadth are "l" and "w," respectively, may be calculated using the following formula. L * W = the rectangle's area. Therefore, the area of a rectangle is equal to (length width).
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Complete question:
Megan drew a rectangle that has an area of 24 square centimeters. Which of the following could be the dimensions of her rectangle?
2 centimeters by 12 centimeters3 centimeters by 9 centimeters4 centimeters by 20 centimeters6 centimeters by 6 centimeters12 centimeters by 12 centimetersPLEASE HURRY! For which equation does it make the most sense to solve with the Zero Product Property?
x^2+9x+6=0
4x^2+16x=12
x^2+5x+6=0
x^3+7=0
Answer:
The equation that makes the most sense to solve with the Zero Product Property is x^2+9x+6=0.
Step-by-step explanation:
How much is 600 divide by 50 + 30 x 100 - 600 divide by 0 don’t use the calculator
Answer:
The result is 9000.
Step-by-step explanation:
The calculation is done as follows:
600 ÷ 50 = 12
12 + 30 x 100 = 3200
3200 - 600 ÷ 0 = 9000
However, dividing by 0 is undefined and results in an error.
Encuentre la solución general de la ecuación diferencial.
(Use C para la constante de integración.)
La solución de la ecuación diferencial dy / dx = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] es la ecuación y = - 3 · ㏑ |x³ - 4 · x + 4| + C.
¿Cómo resolver una ecuación diferencial con variables separables?
En este problema tenemos el caso de una ecuación diferencial ordinaria con variables separables, esto es, que las variables x, y pueden ser apartadas a cada lado de la identidad. A continuación, se presenta el procedimiento de la solución de la ecuación diferencial.
Primero, se escribe la ecuación diferencial y se separan las variables:
dy = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] dx
Segundo, se simplifica la expresión y se aplica la integral a ambos lados:
∫ dy = - 3 ∫ [(3 · x² - 4) / √(x³ - 4 · x + 4)] dx
Tercero, emplear la fórmula de sustitución algebraica u = x³ - 4 · x + 4:
du = 3 · x² - 4 dx
∫ dy = - 3 ∫ [du / u]
Cuarto, integral la expresión resultante:
y = - 3 · ㏑ |u| + C, donde C es la constante de integración.
Quinto, reversar la fórmula de sustitución algebraica:
y = - 3 · ㏑ |x³ - 4 · x + 4| + C
ObservaciónNo existen problemas verificados en español, de modo que se añade una pregunta en inglés.
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A student placed a straw into the water and blew bubbles into the water for 30 seconds. The pH of the glass of
tested again.
ater was
Use the pH scale below to determine the pH value of the water in this test. Record the value. Also, determine whether the
pH stayed the same, became more acidic, or became more alkaline compared to the first test.
Answer:
the water would most likely become more acidic.
Step-by-step explanation:
this is due to carbon dioxide being slightly acidic, it dissolves into the water inturn decreasing the pH.
I really need help on this cuz this is confusing
(also need help on doing the same thing but for the equation x^2=12y at point (6,3)
Using calculus,
For the parabola
.
.
Take the derivative of both sides
.
This is where the formula come from, you don't need to know where this came from.
The equation of the line
.
In this problem, we know that the coefficient of y is equal to 4p
So
.
.
.
.
.
For proof, let's graph this function
.
Now let's plug in the knowns to find the tangent line
If my work does not pop up, the answer is y=-x-3
The required equation of the tangent to the parabola at the given point y = -x - 3.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given expression,
x² = 12y
Comparing the above expression with the given expression,
P = 3
Now, we have p = 3 and (x₀, y₀) = (-6, 3)
So,
The equation of the tangent is given as,
y = -6/(2×3)x - 3
y = -x - 3
Thus, the required equation of the tangent to the parabola at the given point y = -x - 3.
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Question
How many data points are missing on the scatter plot graph, if any?
Responses
A 00
B 11
C 22
D 3
There is only one point missing on the scatter plot graph.
And the point is (10, 2.6).
What are the coordinates?Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.
The data for the gasoline purchases are given in the table.
From the diagram:
The missing point on the scatter plot graph is,
(10, 2.6)
Hence, the point is (10, 2.6).
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Determine the value of x.
X
12 cm
4 cm
Give your answer correct to 1 decimal place.
The value of the angle x is 18. 4°
How to determine the value of the variableit is important to note the six types of trigonometric identities, they are;
sinecosinetangentcotangentcosecantsecantsin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the diagram shown, we have the opposite and adjacent sides, then;
tan x = 4/12
Divide the values
tan x = 0. 3333
take the tangent inverse of the value
x = 18. 4°
Hence, the value is 18. 4°
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area can you pls help me
Answer:
6/5
Step-by-step explanation:
Answer:
6/5
Step-by-step explanation:
1/2×3/5×4
=12/10
divide by 2.
=6/5.
2) During a portage, the leader of a scout troop decided to save time by hiking around a
wooded area between the base camp and a lake. The troop reached the lake by walking for
30 minutes on a bearing of N60°E, then for 45 minutes on a bearing of N80°W. The leader
figured that they walked at an average speed of 3km/h. If they could have walked straight
through the forested area at 1km/h, did the troop save any time by going around? If so, how
much?
Answer:
could have walked straight
through the forested area at 1km/h, did the troop save any time by going around
A rectangular field is six times as long as it is wide. If the perimeter of the field is
770 feet, what are the dimensions of the field?
A) Write an equation you can
to answer the given question lot an be the width
Answer:
6W + W = 770
==> 7W = 770
W = 110 and L = 660 in case you are looking for the solution
Step-by-step explanation:
Let L -= length and W the width of the rectangular field
six times as long as it is wide translates to:
L = 6W
Perimeter of field = 2(L + W)
Given perimeter = 770 feet
2(L + W) = 770
L + W = 770/2 = 385
Since L = 6W, substitute for L in the above equation:
6W + W = 770
7W = 770
W = 770/7 = 110 feet
L = 6W = 6(110) = 660 feet
the width = 55 feet and the length = 330 feet
so basically we take the width as x and the length as 6x then since the perimeter of a rectangle = 2*width + 2*length we will form the equation 6x + 6x + x + x = 770
then we'll solve this equation
14x = 770
x = 55
then multiply x by 6 to get the length which is 330
9n^2=4+7n solve using quadratic formula
By using quadratic formula we solve 9n² = 4 + 7n, we get [tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]
What is Quadratic Formula?Quadratic formula is the simplest way to find the roots of a quadratic equation. There are certain quadratic equations that cannot be easily factorized, and here we can conveniently use this quadratic formula to find the roots in the quickest possible way. The roots of the quadratic equation further help to find the sum of the roots and the product of the roots of the quadratic equation. The two roots in the quadratic formula are presented as a single expression. The positive sign and the negative sign can be alternatively used to obtain the two distinct roots of the equation.
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Given:
The equation:
9n² = 4 + 7n
First rearrange the terms
9n² = 4 + 7n
9n² 7n + 4
9n² = 7n + 4
9n² - 7n - 4 = 0
By using quadratic formula, we get
a = 9, b = - 7, c = - 4
n = [tex]\frac{-(-7) \pm \sqrt{(-7)^2 - 4 .9.(-4)} }{2.9}[/tex]
[tex]n = \frac{7 \pm \sqrt{(-7)^2 - 4.9.(-4)} }{2.9}[/tex]
[tex]n = \frac{7 \pm \sqrt{49 - 4.9(-4)} }{18}[/tex]
[tex]n = \frac{7 \pm \sqrt{49 + 144} }{18}[/tex]
[tex]n = \frac{7 \pm \sqrt{193} }{18}[/tex]
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
[tex]n = \frac{7 + \sqrt{193} }{18}[/tex] or [tex]n = \frac{7 - \sqrt{193} }{18}[/tex]
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5/6+5/6 as a fraction
Answer:
10/6 or 1 4/6
Step-by-step explanation:
Just add the numerators together 10/6. If you need a simplified version it would be 1 4/6.
a club sells 40 tickets to a raffle. issac bought one ticket. the probability that he will win the raffle is
Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.
Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.
It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.
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steve is on a weight loss program. his goal weight is 195 pounds. he currently weighs 339 pounds and plans to lose three pounds each week. how long will it take him to reach his goal? let w represent the number of weeks to reach his goal.
The long will it take him to reach his goal is 48w.
To make it easier to solve the problem above, we change the sentence into a mathematical sentence.
Steven goal weight is 195 pounds. He currently weighs 339 pounds.
So that we know the amount of weight reduced:
= 339 - 195
= 144 pounds
He plans to lose three pounds each week. The long will it take him to reach his goal:
= 144 : 3
= 48 weeks
= 48w
So, the long will it take him to reach his goal is 48w.
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consider the nonlinear equation for population growth ax, where a > 0. a) does this equation exhibit over-, under- or exact compensation?b) does it have a non-trivial steady state?
For the given nonlinear equation for population growth ax where a>0, a0 the equation exhibits exact compensation whereas b) it has a non-trivial steady state.
The equation describes a population that grows at a rate that is proportional to its size. Specifically, the equation states that the population growth rate is equal to the product of a constant multiplier, a, and the size of the population, x. This means that when the population size increases, the rate of growth increases in proportion, causing the population to grow at a steady rate. the equation expresses a population growth rate that is proportional to the population size.
This means that when the population size is large enough, any further increases in the population size will be met with an equal increase in the population growth rate. This causes the population growth rate to remain constant, which is the definition of a non-trivial steady state
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in the graph is there any meaning to the width of the bars, the spacing between the bars, or the ordering of the bars? explain and include how this is different than a bar graph.
In a histogram, the width of the bars represents the range of values that fall into each specific category or bin. The spacing between the bars has no meaning in terms of the data being represented.
The ordering of the bars is based on the range of values within each bin, with the bars typically ordered from left to right in ascending order of value.
This is different from a bar graph, where the width and spacing of the bars can have meaning in terms of the comparison of the values being represented. For example, if the width of the bars in a bar graph represents the value of a data point, then a wider bar would indicate a higher value.
The spacing between the bars in a bar graph can also be used to show the relative difference between values. In a bar graph, the ordering of the bars may or may not have meaning, depending on the specific context and the purpose of the graph.
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Write it in the form (x+a)+b
Answer:
in form of what?and what's the question
how do i set up this problem
Therefore , the solution of the given problem of quadrilateral comes out to be x value is 8.13 .
A quadrilateral is what?A rectangle is a four-sided, four-cornered object in mathematics. Either the Latin quartet or creative portfolio are the terms' sources (meaning "side"). Four states, corners, and provincial assemblies make up the three divisions of a rectangle. Convex and curved surfaces can be broadly divided into two categories. Convex quadrilaterals also include parallelograms, triangles, rhombuses, rectangles, and trapezoids as subcategories.
Here,
Given :
=> 11x + 4 , 18x - 2 and 114 degree ,
Let m∠B is x:
So ,
According to angle sum property :
=> 11x + 4 + 18x - 2 + 114 + x = 360
=> 116 + 30x = 360
=> 30x = 360 - 116
=> 30x = 244
=> x = 244/30
=> x = 8.13
Therefore , the solution of the given problem of quadrilateral comes out to be x value is 8.13 .
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