The area of the ellipse [tex]E[/tex] is given by
[tex]\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy[/tex]
To use Green's theorem, which says
[tex]\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
([tex]\partial E[/tex] denotes the boundary of [tex]E[/tex]), we want to find [tex]M(x,y)[/tex] and [tex]L(x,y)[/tex] such that
[tex]\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]
and then we would simply compute the line integral. As the hint suggests, we can pick
[tex]\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]
The line integral is then
[tex]\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy[/tex]
We parameterize the boundary by
[tex]\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the integral is
[tex]\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt[/tex]
[tex]=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi[/tex]
###
Notice that [tex]x^{2/3}+y^{2/3}=4^{2/3}[/tex] kind of resembles the equation for a circle with radius 4, [tex]x^2+y^2=4^2[/tex]. We can change coordinates to what you might call "pseudo-polar":
[tex]\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}[/tex]
which gives
[tex]x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}[/tex]
as needed. Then with [tex]0\le t\le2\pi[/tex], we compute the area via Green's theorem using the same setup as before:
[tex]\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt[/tex]
[tex]=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt[/tex]
[tex]=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt[/tex]
[tex]=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt[/tex]
[tex]=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt[/tex]
[tex]=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi[/tex]
The areas of the ellipse and curve interior can be calculated using Green's Theorem and the respective parametrizations, x(t) = 5cos(t) and x(t) = 4cos3(t), followed by integrating.
Explanation:To compute the area inside the ellipse using Green's Theorem, we use the fact that the area can be written as ∬ dxdy = 1/2 ∫ d(−y dx+x dy). Using the hint, x(t) = 5cos(t), we parametrize the ellipse and integrate over the boundary to compute the area.
Similarly, for the parametrization of the curve x2/3 + y2/3 = 42/3, we could use the hint x(t) = 4cos3(t), which is a cube root form representation. After this, compute the area of the interior using the proper integration methods.
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A 190-pound man and a 130-pound woman went to Burger King for lunch. The man had a BK Big Fish sandwich (750 Cal), medium french fries (400 Cal), and a large Coke (225 Cal). The woman had a basic hamburger (370 Cal), medium french fries (400 Cal), and a diet Coke (0 Cal). After lunch, they start shoveling snow and burn calories at a rate of 420 Cal/h for the woman and 610 Cal/h for the man. Determine how long each one of them needs to shovel snow to burn off the lunch calories. The metabolizable energy contents of different foods are as given in the problem statement. Shoveling snow burns calories at a rate of 420 Cal/h for the woman and 610 Cal/h for the man.
Answer:
2.25 hours for the man and 1.83 hours for the woman.
Step-by-step explanation:
We first find the number of calories consumed by both the man and the woman.
The man's calories are:
750+400+225 = 1375
The woman's calories are:
370+400+0 = 770
The man burns 610 calories per hour. This means to find the number of hours, we divide the number of calories by the rate burned per hour:
1375/610 = 2.25 hours
The woman burns 770 calories per hour. This means to find the number of hours, we divide the number of calories by the rate burned per hour:
770/420 = 1.83 hours
A 190-pound man needs to shovel snow for approximately 2.25 hours, and a 130-pound woman needs to shovel for approximately 1.83 hours to burn off the calories from their Burger King meal.
The question involves calculating the time it takes for a 190-pound man and a 130-pound woman to burn off the calories consumed from a meal at Burger King through the physical activity of shoveling snow. The man consumed a total of 1375 Calories (750 Cal for BK Big Fish sandwich, 400 Cal for medium french fries, and 225 Cal for a large Coke). The woman consumed a total of 770 Calories (370 Cal for a basic hamburger, 400 Cal for medium french fries, and 0 Cal for a diet Coke).
To find out how long each person needs to shovel snow to burn off the lunch calories, we divide the total number of calories consumed by the rate at which they burn calories while shoveling snow.
For the man: 1375 Calories / 610 Cal/h = approximately 2.25 hours.
For the woman: 770 Calories / 420 Cal/h = approximately 1.83 hours.
Change from General Conic Form to Standard Form: 137+64y=-y^2-x^2-24x
Answer:
(x + 12)² + (y + 32)² = 1031
Step-by-step explanation:
137 + 64y = -y² - x² - 24x
Arrange the terms in descending powers of x and y.
x² + 24x + y² + 64y = -137
Complete the squares for x and y
(x² + 24x + 144) + (y² + 64y + 1024) = -137 + 144 + 1024
Write the equation as the squares of binomials of x and y
(x + 12)² + (y + 32)² = 1031
This is the equation of a circle with centre at (-12, -32) and radius r = √1031.
I need help with question 9
let's not forget that a function and its inverse have a domain <-> range relationship, namely, if the original function has a point of say (3 , 7 ), then its inverse function will have a point of (7 , 3 ), the same pair just flipped sideways.
[tex]\bf (g\circ f^{-1})(x)\implies g(~~~f^{-1}(x)~~~) \\\\\\ (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~) \\\\[-0.35em] ~\dotfill\\\\ \textit{so let's firstly find out what is }f^{-1}(2)[/tex]
we don't have an f⁻¹(x), darn!! but but but, we do have an f(x) on the left-hand-side graph, and it has a pair where y = 2, namely ([ ] , 2), so then, f⁻¹(x) will have the same pair but sideways, let's inspect f(x).
hmmmmmm when y = 2, x = 0, notice the y-intercept on the graph, ( 0, 2 ).
so then, that means that f⁻¹(x) has a pair sideways of that, namely ( 2, 0), or f⁻¹(2) = 0.
so then, g( f⁻¹(2) ), is really the same as looking for g( 0 ), well then, what is "y" when x = 0 on g(x)? let's inspect the right-hand-side graph.
hmmmmmmmmmmm notice, the point is at ( 0 , 2 ), namely when x = 0, y = 2.
[tex]\bf (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~)\implies g(0)\implies 2[/tex]
Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.
3x+2y≥14
-8x+3y≤10
f(x,y)=8x+8y
Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function [tex]f(x, y) = 8x + 8y[/tex]
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
[tex]3x+2y=14\\-5x +5y=10[/tex]
-------------------
[tex]x = 2\\y = 4[/tex]
[tex]-8x + 3y = -29\\3x + 2y = 14[/tex]
---------------------
[tex]x = 4\\y = 1[/tex]
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of [tex]f(x, y)[/tex]
[tex]f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48[/tex]
Then the value that minimizes f(x, y) is (4,1).
Option b
A zoo had 12 large aquariums with fish. The number of fish in each aquarium is shown 37, 58, 62,36,42,71,56,58,69,66,47,68 what is the range in the number of fish
Answer:
35
Step-by-step explanation:
First, we will define range.
The difference between the highest and lowest values in a data is called range. To find the range, first the highest and lowest values are found from data, then the lowest value is subtracted from the highest value.
In the above data,
Highest Value=71
Lowest Value=36
Range=Highest value-lowest value
=71-36
=35
The range in the number of fish across the 12 large aquariums is 35, calculated by subtracting the minimum number of fish, 36, from the maximum number, 71.
The question asks us to calculate the range in the number of fish across 12 large aquariums at a zoo. To find the range, we need to identify the largest and smallest numbers in the given data set and then subtract the smallest from the largest.
Here is the list of the numbers of fish in each aquarium: 37, 58, 62, 36, 42, 71, 56, 58, 69, 66, 47, 68.
First, we find the maximum and minimum values:
Maximum (the largest number of fish in an aquarium): 71
Minimum (the smallest number of fish in an aquarium): 36
Next, we calculate the range by subtracting the minimum value from the maximum value:
Range = Maximum - Minimum
Range = 71 - 36
Range = 35
Therefore, the range in the number of fish across the 12 aquariums is 35.
In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic in this process and known to follow a normal distribution. Two different etching solutions have been compared, using two random samples of 10 wafers for each solution. Assume the variances are equal. The etch rates are as follows (in mils per minute): Solution 1 Solution 2 9.7 10.6 10.5 10.3 9.4 10.3 10.6 10.2 9.3 10.0 10.7 10.7 9.6 10.3 10.4 10.4 10.2 10.1 10.5 10.3 Calculate sample means of solution 1 and solution 2
Answer:
Sample mean for solution 1: 19.27; sample mean for solution 2: 10.32
Step-by-step explanation:
To find the sample mean, find the sum of the data values and divide by the sample size.
For solution 1, the sum is given by:
9.7+10.5+9.4+10.6+9.3+10.7+9.6+10.4+10.2+10.5 = 192.7
The sample size is 10; this gives us
192.7/10 = 19.27
For solution 2, the sum is given by:
10.6+10.3+10.3+10.2+10.0+10.7+10.3+10.4+10.1+10.3 = 103.2
The sample size is 10, this gives us
103.2/10 = 10.32
The sample mean for Solution 1 is 10.05 mils per minute, while the sample mean for Solution 2 is 10.32 mils per minute. These figures represent the average etch rates of each solution in the semiconductor manufacturing process. So here the sample mean should be calculated.
Explanation:To calculate the sample means of Solution 1 and Solution 2, we first sum up the etch rates of each solution, and then divide by the number of samples in each solution.
For Solution 1, the etch rates sum up to 100.5 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.05 mils per minute.
For Solution 2, the etch rates sum up to 103.2 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.32 mils per minute.
So, the sample means for Solution 1 and Solution 2 are 10.05 and 10.32 mils per minute respectively. These means are useful to compare the average efficiency of these two solutions as a part of normal distribution analysis in the semiconductor manufacturing process.
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Find the angle of elevation, to the nearest degree, of the sun if a 54 foot flagpole casts a shadow 74 feet long.
Answer:
If the angle is in degrees, when taking the tangent, make sure your calculator is in Degree mode.
I hope this helps.
A scale drawing of the side view of a house is shown at the right. Find the total area (in square inches) of the side of the house in the drawing PLEASE HELP!!
Answer:
The total area of the side of the house in the drawing is [tex]1.4\ in^{2}[/tex]
Step-by-step explanation:
step 1
Convert the actual dimensions of the side view of a house to the dimensions of the drawing
The scale of the drawing is [tex]\frac{1}{20}\frac{in}{ft}[/tex]
so
[tex]20\ ft=20/20=1\ in[/tex]
[tex]24\ ft=24/20=1.2\ in[/tex]
[tex]8\ ft=8/20=0.4\ in[/tex]
The total area is equal to the area of rectangle plus the area of triangle
so
[tex]A=(1)(1.2)+\frac{1}{2}(1)(0.4)=1.4\ in^{2}[/tex]
Match the function with its graph.
Answer:
The answer is 1D , 2A , 3C , 4B ⇒ answer (c)
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
* Lets explain each function
∵ y = tan(x)
∵ y = -tan(x - π/2)
# (x - π/2) means the graph translated horizontally to
the right π/2 units
# -tan(x - π/2) means the graph reflected across the x-axis
∴ The graph is (D)
* 1) y = -tan(x - π/2) ⇒ (D)
∵ y = tan(x + π/2)
# (x + π/2) means the graph translated horizontally to
the left π/2 units
∴ The graph is (A)
* 2) y = -tan(x - π/2) ⇒ (A)
∵ y = -cot(x - π/2)
# (x - π/2) means the graph translated horizontally to
the right π/2 units
# -cot(x - π/2) means the graph reflected across the x-axis
∴ The graph is (C)
* 3) y = -cot(x - π/2) ⇒ (C)
∵ y = cot(x + π/2)
# (x + π/2) means the graph translated horizontally to
the left π/2 units
∴ The graph is (B)
* 4) y = -tan(x - π/2) ⇒ (B)
∴ The answer is 1D , 2A , 3C , 4B answer (c)
What transformations of the parent function f(x) = x| should be made to graph, f(x) = - |x| + 5
Reflection over the x-axis, shift down 5 units
Reflection over the x-axis, shift up 5 units
Reflection over the y-axis, shift down 5 units
Reflection over the y-axis, shift up 5 units
Reflection over x-axis, shift down 5 units.
Answer:
Option B is correct.
Step-by-step explanation:
Given Parent Function, f(x) = |x|
Transformed function, f(x) = - |x| + 5
In transformed function, f(x) = -|x|
Represent that parents function is first reflected ove x - axis.
then in transformed function, f(x) = -|x| + 5
represent that after reflection function is shifted 5 unit in upward direction.
Therefore, Option B is correct.
A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will win or lose for each outcome is v1, v2, and v3, respectively. What is the expression p1v1 + p2v2 + p3v3 equal to?
The total amount you will win (or lose) in the long run.
The average amount you will win (or lose) per game in the long run.
The exact amount you will win (or lose) per game.
The amount that you will win (or lose) for 3 games.
That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".
Answer:
Step-by-step explanation:
Given that a game has 3 possible outcomes, with probabilities p1, p2, and p3
The amount win or lose for each outcome is v1, v2, and v3, respectively.
If X is the amount of win or lose then x has the following prob distribution
[tex]X v_1 v_2 v_3\\Pr. p_1 p_2 p_3\\[/tex]
Hence Expected value of x = average of x
=[tex]p1v1 + p2v2 + p3v3[/tex]
Thus answer is
Option b) The average amount you will win (or lose) per game in the long run.
A right rectangle prism is 6 cm by 14 cm by 5 cm what is the surface area of the right prism
Answer:
[tex]\large\boxed{S.A.=368\ cm^2}[/tex]
Step-by-step explanation:
The formula of a surface area of a rectagular prism:
[tex]S.A.=2(lw+lh+wh)[/tex]
l - length
w - width
h - height
We have the dimensions 6cm × 14cm × 5cm. Substitute:
[tex]S.A.=2(6\cdot14+6\cdot5+14\cdot5)=2(84+30+70)=2(184)=368\ cm^2[/tex]
The surface area of the rectangular prism is 368 cm²
To calculate the surface area of the prism, we use the formula below.
Formula:
As = 2(lw+lh+wh).............. Equation 1Where:
As = Surface area of the prisml = Lenght of the prismh = height of the prismw = width of the prism.From the question,
Given:
l = 6 cmw = 14 cmh = 5 cmSubstitute these values into equation 1
As = 2[(6×14)+(14×5)+(6×5)]As = 2(84+70+30)As = 2(184)As = 368 cm²Hence, The surface area of the rectangular prism is 368 cm².
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rational exponents: product rule
simplify
v^3/4 multiply v^5/7
Answer:
[tex]v\sqrt[28]{v^{13}}[/tex]
Step-by-step explanation:
The exponent rules that apply are ...
[tex](a^b)(a^c)=a^{b+c}\\\\a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]
Using these rules for your product, we have ...
[tex]v^{\frac{3}{4}}\times v^{\frac{5}{7}}=v^{\frac{3}{4}+\frac{5}{7}}\\\\=v^{\frac{41}{28}}=v\cdot v^{\frac{13}{28}}=v\sqrt[28]{v^{13}}[/tex]
(p+q)* (p-q) can you answer this question cause i cant and can you show the process also
Answer:
Step-by-step explanation:
a cake has a circumference of 25 1/7 what is the area of the cake .use 22/7 to approximate π round to the nearest hundredth
Answer:
A = 50.29 units²
Step-by-step explanation:
See attached photo
The Dittany family's vegetable garden is shaped like a scalene triangle. Two of the sides measure 6 feet and 10 feet. Which could be the length of the third side, in feet?
Question 2 options:
18
16
9
6
Answer:
The length of the third side could be 9 ft
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
In this problem
Let
c-----> the length of the third side, in feet
Applying the Triangle Inequality Theorem
1) [tex]6+10>c[/tex] -------> [tex]c<16\ ft[/tex]
2) [tex]c+6>10[/tex] -----> [tex]c>4\ ft[/tex]
so
The length of the third side must be greater than 4 ft and less than 16 ft
Remember that
The scalene triangle has three different sides
therefore
The length of the third side could be 9 ft
For the geometric series given by 1+2+4+ which of the following statements is FALSE?
S600>a600
S600>S599
S1=a1
None of the other 3 statements here are false
The false statement among the options given is 'None of the other 3 statements here are false', because all the other three statements about the geometric series are actually true.
Explanation:The question presents a geometric series: 1, 2, 4, ... Each term is double the previous term, which means that for this series, the common ratio (r) is 2. Now let us analyze the statements given:
S600 > a600: The sum of the first 600 terms of the series will be greater than the 600th term.
This is true, since the sum of a geometric series to n terms is given by the formula Sn = a1(1 - rn)/(1 - r) for r > 1, where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio.
Since the sum involves multiple terms and all terms are positive, it will be bigger than the last term.
S600 > S599: The sum of the first 600 terms will be greater than the sum of the first 599 terms.
This is also true, since each term added to the series is positive, so the sum will increase.
S1 = a1: The sum of the first term equals the first term itself.
This is true because the first term of the series is 1, and the sum of just one term (i.e., the first term) is the term itself.
Therefore, the false statement is 'None of the other 3 statements here are false' because actually, none of the other three statements provided are false.
Final answer:
The presented geometric series has a common ratio greater than 1, so the sum of the first 600 terms is greater than the 600th term; similarly, the sum of 600 terms is greater than the sum of 599 terms. Since all provided statements are true, the answer is that 'None of the other 3 statements here are false'.
Explanation:
The question presents a geometric series with the first term 1 and a common ratio of 2. This series is 1+2+4+8+... and so on. We are asked to identify which of the given statements is false regarding the series.
S600 > a600: This statement says that the sum of the first 600 terms is greater than the 600th term. In a geometric series where the common ratio is greater than 1, the sum of the first n terms is indeed greater than the nth term, so this statement is true.S600 > S599: This statement indicates that the sum of the first 600 terms is greater than the sum of the first 599 terms. Since each term in the series is positive, adding another term will always increase the sum, thus this statement is also true.
S1 = a1: This statement equates the sum of the first term to the first term itself. Since there's only one term involved, they are the same. Therefore, this statement is true.
By process of elimination, since the other statements are true, the correct answer would be 'None of the other 3 statements here are false'.
Madison enjoys the game of golf. He knows that he will one-putt a green 15% of the time, two-putt 20% of the time, three-putt 35% of the time, and four-putt 30% of the time. Find the expected value for the number of putts Madison will need on any given green. Make sure to write down the entire equation that you used to solve this problem.
Answer:
2.8 putts in average on any given green
Step-by-step explanation:
To calculate how many putts Madison will need on any given green, we need to calculate the weighted average of his putts.
We use a global sample of 100 puts and factor in the fact he had a one-putt performance 15% of the time, two-putts 20% of the time and so on.
So, the calculation goes like this:
[tex]\frac{1 * 15 + 2 * 20 + 3 * 35 + 4 * 30}{100} = \frac{280}{100} = 2.8[/tex]
So, he'll need an average of 2.8 putts in average on any given green.
Which makes sense since 65% of the time, he needs 3 putts or more on the green.
The expected number of putts Madison will need for any given green is 2.85. This is calculated by multiplying each possible outcome by its probability and then summing these values.
Explanation:The subject of this question is the calculation of an expected value in the context of a game of golf. The expected value is a weighted average, taking into account the probability of each event. Expected value calculations are common in probability and statistics.
In Madison's case, the expected number of putts can be calculated with the following formula:
E(X) = Σ [x * P(X = x)], where x is the outcome (number of putts) and P(X = x) is the probability of that outcome.
Applying the probabilities and outcomes given: E(X) = 1(0.15) + 2(0.20) + 3(0.35) + 4(0.30) = 2.85
So, the expected value of the number of putts Madison will need for any given green is 2.85.
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Jeremy and Robin like to collect nickels. Jeremy has n nickels, and Robin has 55 nickels. Together they have a total of 100 nickels.
Answer:
Jeremy has 45 nickels.
Step-by-step explanation:
I'm guessing the question is how many nickels does Jeremy have.
n + 55 = 100
n = 45
Answer:
45 nickels.
Step-by-step explanation:
We have been given that Jeremy and Robin like to collect nickels. Jeremy has n nickels, and Robin has 55 nickels. Together they have a total of 100 nickels.
We can represent our given information in an equation as:
[tex]n+55=100[/tex]
[tex]n+55-55=100-55[/tex]
[tex]n=45[/tex]
Therefore, Jeremy has 45 nickels.
The isosceles trapezoid ABDE is part of an isosceles triangle ACE. Find the measure of the vertex angle of ACE. (See attachment)
A. 130 degrees
B. 60 degrees
C. 65 degrees
D. 50 degrees
I really need an explanation along with the answer, thank you!!
Answer:
We know that [tex]\triangle ACE[/tex] is isosceles, that means [tex]\angle A \cong \angle E[/tex], by definition.
Also, [tex]\angle BDC \cong \angle DBC[/tex], because [tex]BD \parallel AE[/tex].
Then, we have [tex]115\° + \angle BDC = 180\°[/tex], by sumpplementary angles.
[tex]\angle BDC = 180 -115 = 65\° = \angle DBC[/tex]
Which means,
[tex]\angle C= 180 - 65 - 65[/tex], by definition.
[tex]\angle C= 50[/tex]
Then,
[tex]\angle A + \angle E + 50 = 180\\2\angle A = 180 - 50\\\angle A= \frac{130}{2}=65 = \angle E[/tex]
Therefore, the measures of vertex angles are 65 for the base angles of triangle and 50 for the different angle.
What is the distance between the 2 points? Round to the nearest tenths place.
Check the picture below.
Answer:
[tex]10.8 units[/tex]
Step-by-step explanation:
To find the answer, we need to use the distance formula.
[tex]d=\sqrt{(x-x)^2 +(y-y)^2}[/tex]
Let us look at our points. We have:
[tex](-2, 5)[/tex] and [tex](-6, -5)[/tex]
Now, let's identify our x's and y's:
x₁ = -2
y₁ = 5
x₂ = -6
y₂ = -5
Plug it in to the distance formula and simplify:
[tex]d=\sqrt{(-6+2)^2+(-5-5)^2}[/tex]
[tex]d=\sqrt{(-4)^2+(-10)^2}\\d=\sqrt{16 +100} \\d=\sqrt{116}\\[/tex]
[tex]d=2\sqrt{29}[/tex] OR [tex]10.77032961...[/tex]
The measure of the angle formed by two intersecting perpendicular lines is 90°.
A. true
B. false
Answer: True, the measure of the angle formed by two intersecting perpendicular lines should be 90 degrees.
Answer:
True.
Step-by-step explanation:
You can see it with the cartesian plane. The cartesian plane are two intersecting perpendicular lines. The intersection point is the (0,0) and each cuadrant is 90°. 90°(4 cuadrants) = 360° .
simplify the radical expression the square root of 63x to the 15th power y to the 9th power divided by 7xy^11
Answer:
The analysis of your expresson is given in the images below.
Please see attached pictures.
Look at the line plot, explain how you found the mean, median, and range. Compare the two line plots, is there an overlap and what degree of overlap? What is the Mean?What is the Median? *What is the Range. What is the degree of overlap.
We kinda need the graph
HELP PLEASE!! As John walks 16 ft towards a chimney, the angle of elevation from his eye to the top of the chimney changes from 30° to 45°. Identify the height of the chimney from John's eye level to the top of the chimney rounded to the nearest foot.
Answer: 22 feet.
Step-by-step explanation:
Note that there are two right triangles in the figure attached: ACD and BCD. Where "h" is the height of the chimeney from John's eye level to the top of the chimney.
You need to use the trigonometric identity [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] for this exercise.
For the triangle BCD:[tex]tan(45\°)=\frac{h}{x}[/tex]
Solve for h:
[tex]h=xtan(45\°)\\h=x[/tex]
For the triangle ACD:
[tex]tan(30\°)=\frac{h}{x+16}[/tex]
Substitute [tex]h=x[/tex] and solve for h:
[tex]tan(30\°)=\frac{h}{h+16}\\\\(h+16)(tan(30\°))=h\\\\0.577h+9.237=h\\\\9.237=h-0.577h\\\\9.237=0.423h\\\\h=\frac{9.237}{0.423}\\\\h=21.836ft[/tex]
Rounded to the nearest foot:
[tex]h=22ft[/tex]
If a bag contains 12 apples , 4 bananas , and 8 oranges , what part to whole ratio bananas to all fruit
Answer:
4 : 24 or 1 : 6
Step-by-step explanation:
There are 4 bananas and 24 fruits so we just make that a ratio of 4 : 24.
We can then simplify that ratio to 1 : 6.
Answer:
the answer is 1:3
i did the test
Step-by-step explanation:
If a working was originally $25 and it is on sale for $18 what is the percent of discount
First we must subtract 25 in 18 because we are doing percentages.
So we do [tex]25 - 18 = 7[/tex]
So we get 7.
Now we need to do [tex]7/25 * 100% = 28%[/tex]
We would get a total of 18% of on the discount.
The temperature of a chemical solution is originally 21, degree, C. A chemist heats the solution at a constant rate, and the temperature of the solution is 75, degree, C after 12 minutes of heating.
Assuming the question is "at what rate did the chemist heat the solution," the answer is the chemist heated the solution at +4.5 degrees Celsius per minute.
75-21=54
54/12=4.5
Yi is told that the item that she wants to buy is still available at a store that is 3/4 inch on a map from her current location. If the scale of the map is 1 inch= 12 miles, how far away is yi from the store?
Answer:
9 miles.
Step-by-step explanation:
We have been given that Yi is told that the item that she wants to buy is still available at a store that is 3/4 inch on a map from her current location. The scale of the map is 1 inch= 12 miles.
To find the actual distance between Yi and store we will multiply 3/4 by 12 as:
[tex]\text{The distance between Yi and store}=\frac{3}{4}\text{ inch}\times \frac{\text{12 miles}}{\text{inch}}[/tex]
[tex]\text{The distance between Yi and store}=\frac{3}{4}\times \text{12 miles}[/tex]
[tex]\text{The distance between Yi and store}=3\times \text{3 miles}[/tex]
[tex]\text{The distance between Yi and store}=9\text{ miles}[/tex]
Therefore, Yi is 9 miles away from the store.
A rectangle has a length that is 2 meters more than the width. The area of the rectangle is 288 square meters. Find the dimensions of the rectangle.
Answer:
L = 18 and w = 16
Step-by-step explanation:
The area of a rectangle is found by A = l*w. Since the length here is 2 more than the width or 2 + w and the width is w, substitute these values and A = 288 to solve for w.
[tex]A = l*w\\288 = w(2+w)\\288 = w^2 + 2w[/tex]
To solve for w, move 288 to the other side by subtraction. Then factor and solve.
[tex]w^2 + 2w - 288 = 0 \\(w +18)(w-16) = 0\\[/tex]
Set each factor equal to 0 and solve.
w - 16 = 0 so w = 16
w + 18 = 0 so w = -18
Since w is a side length and length/distance cannot be negative, then w = 16 is the width of the rectangle.
This means the length is 16 + 2 = 18.