7. [0/1 Points] DETAILS PREVIOUS ANSWERS Calculate the iterated integral. 5 15 Tex + 3y dx dy 60% 60.-e15 15 - 45+1 e e 7. X 3 Need Help? Read It
Answers
The iterated integral of 5x + 3y over the given region is 131.25.
To calculate the iterated integral of 5x + 3y over the region given by x = 0 to x = 3 and y = 0 to y = 7, we can use the
following formula:
∫∫R f(x,y) dA =\(∫a^b ∫c^d f(x,y) dy dx\)
Substituting the given values, we get:
∫0^3 ∫0^7 (5x + 3y) dy dx
Evaluating the inner integral first, we get:
\(∫0^3 (5x ×y + 3y^2/2)|0^7 dx\)
= ∫\(0^3 [(5x × 7 + 3(7^2)/2) - (5x ×0 + 3(0^2)/2)] dx\)
=\(∫0^3 (35x + 73.5) dx\)
= \([35x^2/2 + 73.5x]|0^3\)
= (157.5 + 105)/2
= 131.25
Therefore, the iterated integral of 5x + 3y over the given region is 131.25.
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Related Questions
Jeris nonlabor income is V-398 per week and her lotal time avalabie in the wek is T=110 houn. Her marginal waty of leisure is MUL = 451 L0.1, and her marginal valify of consumption is UU 4C
0.5
. What is her reservation wage? (please keep 1 decimal poirt) Qutstion 2 QUESTION3 nalion, (keep one decimal place) QUESTON 4 h sat rice to obain ensa points tse conplebing the atignmest on time? Thue faie Jen's nonlabor income is Visg9 per week and her total time avalable in the week is T=110 hours. Her marginal utility of leisure is MU
L
=452L
0.1
, and her marginal utility of consumption is MU C
C
=4C
0.5
. What is her reservation wage? (please keep 1 decimal point) QUESTION 2 Jack's marginal utity of consumption is MU
C
=L−49, and the marginat utily of leisure is MU
L
=C−162, Jack does not have any nonlabor income, Le. V=0. Jack faces a $46 an hour wage rate. Jack's total number of hours available per week is 168 . What is Jack's optimal choice of hours of leisure? (calculate to 2 decimal places) QUESTION 3 Based on BLS websile, the total number of employed males in the ovilian labor force in the U.S. in 2020 is milion (keep one cecimal place)
Answers
Jeri's reservation wage is $39.8 per week. Jack's optimal choice of hours of leisure is 66.42 hours per week.
For Jeri's reservation wage, we need to find the wage rate at which she would be indifferent between working and not working. Her marginal utility of leisure is given as MUL = 451L^0.1, and her marginal utility of consumption is UU = 4C^0.5. To find the reservation wage, we equate the marginal utility of leisure to the marginal utility of consumption and solve for the wage rate.
Similarly, for Jack's optimal choice of hours of leisure, we need to maximize his utility by choosing the right balance between leisure and work. His marginal utility of consumption is given as MU C = L - 49, and his marginal utility of leisure is MU L = C - 162. We can set up a utility maximization problem by equating the marginal utilities of leisure and consumption and solve for the optimal hours of leisure.
The total number of employed males in the civilian labor force in the U.S. in 2020 can be obtained from the Bureau of Labor Statistics (BLS) website. Without the specific data available, we cannot provide an accurate answer to the number of employed males in 2020. It is recommended to refer to the BLS website or their published reports for the most up-to-date and accurate information.
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How do I write a midpoint formula and distance formula?
Answers
Answer:
Step-by-step explanation:
Midpoint formula: x= x_1 + x_2 / 2 I believe
Answer:
midpoint formula: (sorry image is flipped)
distance formula:
\(d = \sqrt{(x2 - x1)^{2} (y2 - y1)^{2} } \)
The graphed line shown below is y = negative 2 x minus 8.
On a coordinate plane, a line goes through (negative 4, 0) and (negative 2, negative 4).
Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?
y = negative (2 x + 8)
y = negative 2 (x minus 8)
y = negative 2 (x minus 4)
y = negative (negative 2 x + 8)
Answers
Answer:
A
Step-by-step explanation:
Our given equation is: y = -2x - 8
In order to have an equation with infinitely many solutions, it needs to be the same as the given equation.
Look at the answer choices:
A) y = -(2x + 8) = -2x - 8
This is the exact same equation, which means that any solutions for the given will also be solutions for this one. That means there will be infinitely many solutions.
B) y = -2(x - 8) = -2x + 16
We can tell this is definitely not the same as the given, so eliminate.
C) y = -2(x - 4) = -2x + 8
Again, this has a +8 instead of -8, so it's not the same and wrong.
D) y = -(-2x + 8) = 2x - 8
Here, we have positive 2 as the slope instead of -2, so it's not the same and wrong.
Thus, the answer is A.
Hope this helps!
A
Our given equation is: y = -2x - 8
In order to have an equation with infinitely many solutions, it needs to be the same as the given equation.
Look at the answer choices:
A) y = -(2x + 8) = -2x - 8
This is the same equation, which means that any solutions for the given will also be solutions for this one. That means there will be infinitely many solutions.
B) y = -2(x - 8) = -2x + 16
We can tell this is definitely not the same as the given, so eliminate.
C) y = -2(x - 4) = -2x + 8
Again, this has a +8 instead of -8, so it's not the same and wrong.
D) y = -(-2x + 8) = 2x - 8
the answer is A.
Question 6(Multiple Choice Worth 2 points)
(Line of Fit MC)
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test
Answers
The y-intercept of the line of fit is 80, which means that a student who studies for 0 hours is predicted to earn 80% on the test.
This means that even if a student does not study at all, they are predicted to earn a grade of 80% on the test based on the relationship between the amount of time spent studying and the grades earned on the test. This y-intercept value is also the predicted grade if the student did not study at all.
However, it is important to note that this prediction is based solely on the linear relationship observed in the given data and may not necessarily hold true for all cases or situations.
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solve for m
k=1/2mv^2
Answers
The kinetic energy solved for the mass m is:
m = 2*K/v²
How to solve the kinetic energy for m?
The equation for the kinetic energy is:
K = (1/2)*m*v²
We want to solve this for m, this means that we need to isolate the variable m which is the mass.
If we multiply both sides by 2, we will get:
2*K = 2*(1/2)*m*v²
2*K = m*v²
Now dividing both sides by v² we will get:
2*K/v² = m*v²/v²
2*K/v² = m
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5. (27:21) Harry says there are 5 families gone on
one block alone. If there are 12 families on that
block, how many families might you expect to be
gone on a street with 60 families?
Answers
Based on the number of families that left and the number in total on that block, the expected number of families gone on the other block is 25 families.
On the first block, the proportion of families that is gone is:
= Number of families gone / Total number of families on block
= 5 / 12
If there are 60 families on a block, the number gone would be:
= Proportion of families gone x Total number of families
= 5/12 x 60
= 25 families
In conclusion, 25 families would be gone
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in each of problems 9 through 16 determine the taylor series about the point x0 for the given function. also determine the radius of convergence of the series. sin x, x0 = 0
Answers
The radius of convergence of the series is infinity, which means that the series converges for all values of x.
The Taylor series for sin(x) about \(\begin{equation}x_0 = 0\end{equation}\) is:
sin(x) = x - (x³)/3! + (x⁵)/5! - (x⁷)/7! + …
The Taylor series is a way to represent a function as an infinite sum of terms. The series is built around a point x0 and includes terms that depend on the derivatives of the function evaluated at x0. The general formula for the Taylor series of a function f(x) around x0 is:
\(f(x) = f(x_0) + \frac{f'(x_0)}{1!}(x - x_0) + \frac{f''(x_0)}{2!}(x - x_0)^2 + \frac{f'''(x_0)}{3!}(x - x_0)^3 + \ldots\)
where f'(x0) is the first derivative of f(x) evaluated at x0, f''(x0) is the second derivative of f(x) evaluated at x0, and so on.
In general, the Taylor series for a function f(x) about x0 is:
\(f(x) = f(x_0) + \frac{f'(x_0)}{1!}(x-x_0) + \frac{f''(x_0)}{2!}(x-x_0)^2 + \frac{f'''(x_0)}{3!}(x-x_0)^3 + \cdots\)
The radius of convergence of the series is infinity, which means that the series converges for all values of x.
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A firm with $600,000 in sales, cash on hand of $750,000, liabilities of $200,000, and total assets of $1 million has a total asset turnover of
Answers
the firm has a total asset turnover of 0.6, which means that for every $1 of total assets, the firm generates $0.6 in sales. This ratio indicates the firm's efficiency in utilizing its assets to generate revenue
Total asset turnover is a financial ratio that measures a company's efficiency in generating sales from its total assets. It is calculated by dividing the total sales by the average total assets. In this case, the firm has $600,000 in sales and total assets of $1 million.
Total Asset Turnover = Total Sales / Average Total Assets
To calculate the average total assets, we sum the beginning and ending total assets and divide by 2:
Average Total Assets = (Beginning Total Assets + Ending Total Assets) / 2
Given that the firm's total assets are $1 million, the average total assets would also be $1 million.
Plugging in the values into the total asset turnover formula:
Total Asset Turnover = $600,000 / $1,000,000 = 0.6
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TB The number is 27% of the pupils in a school are in Primary Six. There are 540 Primary Six pupils How many pupils are there in the school? % % There are 20 pupils in the school. 27%-> 1% →>> 100%->
Answers
In linear equation, 2000 pupils are there in the school.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
= 540/27%
= 54000/27
= 2000
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what is the sum of the interior angles of the polgon
Answers
Step-by-step explanation:
all regular polygons have (n-2)*180 this formula can use here. n= no of sides
Answer:
M = (n-2)*180 degrees for polygons with n sides.
Step-by-step explanation:
As already noted, there is no description of the polygon in question. However, the formula for the sum of the measure of the interior angles of a regular polygon is M = (n-2)•180 where n is the number of sides. A triangle has 3 sides, so M = (3-2)*180 = 180 degrees.
A hexagon has 6 sides, so M = (6-2)*180 = 720.
Please help me!
The Farmer's Ranch House
9. The farmer's house is shown in the diagram below. He wants to build a screened-in patio on the back of his house.
Use the figure to answer the questions. (6 points)
a The area of the patio is planned to be (x + 10x - 200) square feet. What will the length be?
Patio
Patio
**10) - 0-10)
Original
House
b.
What is the area of the original house in simplest form?
Terigth
c
The farmer decides to extend the width of the patio. The area of the patio with the extension is now (x2 + 12x-160) square feet. By how
many feet will the patio be extended from what you found in part a?
Answers
Answer:
The answer is below
Step-by-step explanation:
a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:
\(Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20\)
b) Area of original house = length of house * breadth of house
The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:
Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200
Area of original house = x² + 30x + 200
c) If the width is extended, hence:
\(Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet\)
How to convert polar coordinates to rectangular coordinates.
Answers
the rectangular coordinates corresponding to the polar coordinates (5, π/6) are approximately (4.33, 2.5).
To convert polar coordinates to rectangular coordinates, you can use the following formulas:
Given polar coordinates (r, θ), where r represents the distance from the origin (or pole) to the point, and θ represents the angle between the positive x-axis and the line connecting the origin to the point:
Rectangular coordinate x = r * cos(θ)
Rectangular coordinate y = r * sin(θ)
Here's a step-by-step process for converting polar coordinates to rectangular coordinates:
1. Identify the given polar coordinates (r, θ).
2. Use the formula x = r * cos(θ) to calculate the rectangular coordinate x.
3. Use the formula y = r * sin(θ) to calculate the rectangular coordinate y.
4. The rectangular coordinates (x, y) represent the equivalent representation of the given polar coordinates.
For example, let's say we have polar coordinates (r, θ) = (5, π/6). To convert these to rectangular coordinates:
x = 5 * cos(π/6) = 5 * (√3/2) = 5√3/2 ≈ 4.33
y = 5 * sin(π/6) = 5 * (1/2) = 5/2 = 2.5
So, the rectangular coordinates corresponding to the polar coordinates (5, π/6) are approximately (4.33, 2.5).
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when compared to quantitative and qualitative research respectively mixed methods research tends to be more complex or easier
Answers
Mixed methods research tends to be more complex when compared to quantitative and qualitative research respectively. This is because mixed methods research combines both quantitative and qualitative research methods in a single study.
Quantitative research involves the collection and analysis of numerical data, while qualitative research involves the collection and analysis of non-numerical data, such as words, images, and sounds.
Mixed methods research, on the other hand, involves the collection and analysis of both types of data. This requires the researcher to have a deeper understanding of both quantitative and qualitative research methods, as well as the ability to integrate the two types of data in a meaningful way.
Furthermore, mixed methods research often involves the use of multiple data sources, multiple research methods, and multiple levels of analysis. This adds an additional layer of complexity to the research process.
As a result, mixed methods research tends to be more complex than either quantitative or qualitative research alone.
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Suppose the vectors \( \bar{i}, \bar{j}, \bar{p} \) and \( \bar{q} \) are all unit vectors and the angle \( \theta=222^{\circ} \). Find the cartesian vector form of \( \bar{F}=(-31 \bar{i}+102 \bar{j}
Answers
The cartesian vector form of \(F\) is \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\). We call x + yi the Cartesian form for a complex number.
Given that \(i,j,p\) and \(q\) are unit vectors and the angle \(\alpha = 222\)°, we can express the cartesian vector form of \(F\) as \(F = (-31cos(\alpha )i + 102sin(\alpha )j)\).
To calculate the components of \(F\) , we use the trigonometric functions \(cos(\alpha )\) and \(sin(\alpha )\) with the given angle \(\alpha = 222\)°.
\(cos(222) = -0.766\\sin(222) = -0.643\)
Substituting these values into the cartesian vector form, we have:
\(F = (-31cos(222)i + 102sin(222)j)\\F = (-31 * -0.766i + 102*-0.643j)\\F = (23.746i - 65.586j)\)
Therefore, the cartesian vector form of \(F\) is \(F = (23.746i - 65.586j)\).
The cartesian vector form of \(F = (23.746i - 65.586j)\)
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What is the range of the function?
Answers
Answer:
B. 2, 6, 8
Step-by-step explanation:
I just learned this
Jennifer made these measurements on ABC,BC must be-?
Answers
Answer:
between 10 and 12
Step-by-step explanation:
Given the measure of angles:
m∠B = 70°
m∠C = 60°
m∠A = 50°
We know m∠B = 70° because the sum of interior angles in a triangle is equal to 180°.Following this information, since the side lengths are directly proportional to the angle measure they see:
Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.
Angle C is the smallest angle, so the side AB is the shortest side.
Therefore, side BC must be between 10 and 12 inches.
X^3-5x-39 find x it lies between 3 and 4
Answers
The equation actually has 3 solutions, 2 complex and one real.
The real solution is \(3.8797\).
17. Who am I? ___ Collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.
a) template
b) array
c) structure
d) local variables
Answers
You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.
A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.
The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.
The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.
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Find the H.C.F of 144,180,240,300
Answers
GCF = 12
for the values 144, 180, 240, 300
Solution by Factorization:
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The factors of 240 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The factors of 300 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Then the greatest common factor is 12.
Answer:
12
Step-by-step explanation:
We are looking for the highest common factor
Breaking each term into primes
144 = 12*12 = 4*3 * 4*3 = 2*2*3*3
180 = 20 *9 = 4*5*3*3 = 2*2*3*3*5
240 = 24*10 = 4*6*2*5 = 2*2*2*3*2*5 = 2*2*2*2*3*5
300 = 30*10 = 5*6*2*5 = 5*2*3*2*5 = 2*2*3*5*5
Look for the common factor
2*2*3 = 12
3,203 ÷ 15
The quotient is
and the remainder is
Answers
Answer:
213 r8
Step-by-step explanation:
Answer:
213 remainder 8
Step-by-step explanation:
213*15=3195+8=3203
What is the length of one leg of the triangle? 11 units 11 startroot 2 endroot units 22 units 22 startroot 2 endroot units
Answers
Considering the given triangle is a right-angled triangle. Therefore, one side of the triangle is \(11\sqrt{2}\) and the other side of the triangle is \(22\sqrt{2}\). Since we have to find one of the legs of the triangle, we can assume \(22\sqrt{2}\) is the length of the hypotenuse and \(11\sqrt{2}\) the length of one of the sides of the right-angled triangle.
Therefore, by Pythagoras' theorem,
\(\sqrt{ (22\sqrt{2}) ^{2} - (11\sqrt{2} )^{2} } =\) length of one leg of the triangle = 26.95 units
Therefore, The length of one leg of the triangle is 26.95 units.
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Answer:
b…22
Step-by-step explanation:
how to do a math equation for derivative
Answers
Answer:
So in general, a derivative is given by y′=limΔx→0ΔyΔx. To recall the form of the limit, we sometimes say instead that dydx=limΔx→0ΔyΔx.
Step-by-step explanation:
Answer:
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Step-by-step explanation:
Drag each tile to the correct location on the algebraic problem. Not all tiles will be used.
Fill in the missing steps and justifications used to solve the given equation.
Answers
6x-7+7=12+7 = addition property of equality
6x-7-12=-12+7 = subtraction property of equality
X= 19/6 = simplification
What is addition property of equality?The addition property of equality states that adding the same quantity on both sides of an equation produces equivalent results.
An example = 6x-7+7=12+7. This is because, 7 is added to both sides of the equation.
The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality.
For example, 12 is subtracted from both sides of the equation as follows: 6x-7-12=-12+7
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Y=5x
A proportional relationship
Answers
Yes, the equation y = 5x represents a proportional relationship
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is y=5x.
In a proportional relationship, the ratio of y to x is constant.
In the given equation the variable x and y has a proportional relationship.
The equation is in the form of y=mx+b
the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.
Hence, Yes, the equation y = 5x represents a proportional relationship
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help please. how do I combine them to like terms
Answers
Answer:
2x^2+2y+xy
Explanation:
x^2+x^2=2x^2
y+y=2y
A school volleyball team consists of 7 male and 8 female players. Only 12 of the players are to be selected to attend the tournament in Vancouver next weekend. Determine the probability to the nearest hundredth that equal numbers of males and females are selected to go to Vancouver.
Answers
The probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.
To determine the probability that equal numbers of males and females are selected to go to Vancouver, we need to calculate the number of ways to select 6 males and 6 females from the total pool of 7 males and 8 females.
The number of ways to select 6 males out of 7 is given by the combination formula:
C(7, 6) = 7! / (6!(7-6)!) = 7
Similarly, the number of ways to select 6 females out of 8 is:
C(8, 6) = 8! / (6!(8-6)!) = 28
Since we need to select equal numbers of males and females, we multiply the number of ways to select males and females together:
Total number of favorable outcomes = C(7, 6) * C(8, 6) = 7 * 28 = 196
Now, we need to calculate the total number of ways to select any 12 players from the total pool of 15 (7 males + 8 females):
Total number of possible outcomes = C(15, 12) = 15! / (12!(15-12)!) = 455
Finally, we can calculate the probability of selecting equal numbers of males and females by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 196 / 455 ≈ 0.431
Therefore, the probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.
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if you are sexually active, what are the odds of you contracting an sti by the time you are 25 years old?
Answers
The odds of you contracting an sti by the time you are 25 years old is 50%.
Even if a person has only had one physical relationship, that partner could be infected. Of course, the risks of contracting STDs (also known as sexually transmitted illnesses, or STIs) increase if a person has unprotected intercourse with a variety of partners.
Many persons with STDs have no evident indications or symptoms. As a result, individuals may assume they are "clean" and inform partners they don't need to use a protection.
But that's not a good idea. For example, almost six out of ten young people infected with HIV are unaware of their status. As a result, they risk infecting others with the AIDS virus.
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A company that manufactures SIM cards for cell phones, estimates that 30% of all SIM cards are defective before being used. In a recent shipment of SIM cards to Bell Mobility, determine the expected number of "good" SIM cards that will be sold before the first defective one is sold.
Answers
In a shipment of SIM cards where 30% are estimated to be defective, the expected number of "good" SIM cards that will be sold before the first defective one is approximately 1 or 2.
To calculate the expected number of "good" SIM cards that will be sold before the first defective one, we can use the concept of geometric distribution. The probability of selling a "good" SIM card before selling the first defective one is equal to the complement of the probability of selling a defective card first.
Since the estimated defect rate is 30%, the probability of selling a defective card first is 0.3. Therefore, the probability of selling a "good" card first is 1 - 0.3 = 0.7. The expected number of "good" SIM cards sold before the first defective one can be calculated as 1 divided by the probability of selling a "good" card first, which is 1 / 0.7 = 1.43. So, we can expect approximately 1 or 2 "good" SIM cards to be sold before the first defective one.
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CAN SOMEONE HELP ME PLEASE
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Guys can you please help. I dont understand. Thank you. :))))
Lines AB and CD intersect at E. If the measure of angle AEC=5x-20 and the measure of angle BED=x+50, find, in degrees, the measure of angle CEB.
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Answer: 112.5
Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.