Answers
∠ABC = ∠CDA (given)
∠BCA = ∠DAC (given)
CA = AC (common side)
ASA congruence criterion = when two angles of two triangles are equal and their included side is also equal, we can consider those triangles to be congruent to each other.
Since two angles in triangle △ABC and△CDA are equal and since their included side is also equal we can conclude that they are congruent.
Therefore, △ABC ≅ △CDA under the ASA congruence criterion.
Related Questions
I have no idea how to do this
Answers
The United Nations Security Council consists of 15 members, 10 of which are elected, and 5 of which are permanent members. For a resolution to pass, 9 members must support it, which must include all 5 of the permanent members. Set up a weighted voting system to represent the UN Security Council and calculate the Banzhaf power distribution.
Answers
Banzhaf power distribution for the USA is 0.208.
How to calculate Banzhaf power distribution?To calculate the voting power of each elected member, we can use the following formula:
Voting power = (9 - number of permanent members) / 2
This formula takes into account the fact that all 5 permanent members must support a resolution for it to pass, leaving 10 remaining votes.
The remaining votes must be divided equally among the non-permanent members, with the total number of votes needed for a resolution to pass 9.
Using this formula, we can calculate the voting power of each elected member:
\(Voting \ power = \dfrac{(9 - 5)} { 2}\)
Voting power = 2
Therefore, each of the 10 elected members will have a weight of √(2) ≈ 1.414.
To calculate the Banzhaf power distribution, we need to consider all possible coalitions of members that could pass a resolution.
There are 2¹⁵ = 32,768 possible coalitions, but we can narrow our focus to only those coalitions that have at least 9 members.
For each of these coalitions, we can calculate the minimum number of members whose support is necessary for the coalition to pass a resolution. If this number is less than 5 (i.e., the number of permanent members), then the coalition has no power.
If the number is exactly 5, then the coalition has power if and only if all 5 permanent members are included. Otherwise, the coalition has power if and only if it includes at least one non-permanent member whose weight is greater than 1.
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Please help
find All disuntiniteas
Log x + 4x³
——————
X
Answers
I believe the expression you provided is:
(log(x) + 4x^3) / x
To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.
There are two types of discontinuities to look for:
Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.
Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.
To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.
So we solve the equation:
x = 0
This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.
Therefore, the only discontinuity of the expression is at x = 0.
Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.
Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is 7 inches wide in the drawing. The actual bakery is 42 feet wide. What is the scale of the drawing?
Answers
Answer:
1:72
Step-by-step explanation:
The scale of a drawing is the ratio of the length in the drawing to the real length.
Drawing length: 7 inches
Real length: 42 ft × 12 in. / ft = 504 in.
Scale:
7 in. to 504 in.
Divide both numbers by 7:
1 in. to 72 in.
Scale: 1:72
if h(x) =x+2/x-2, then dy/dx= ?
Answers
dy/dx = [(x - 2)(1) - (x + 2)(1)]/(x - 2)^2
Simplifying the numerator:
dy/dx = (-4)/(x - 2)^2
So the derivative of h(x) with respect to x is -4/(x - 2)^2.
Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.
Using this rule, we can find the derivative of h(x) as follows:
h(x) = (x + 2) / (x - 2)
h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator
h'(x) = (-2 - 2x) / (x - 2)^2
Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.
Step-by-step explanation:
whats the answer to 4.23872345.25135x4446.56559=
Answers
Answer: the correct answer is 18,847.76184947253
Answer:
1.884776184E1284776184947.2528110465
Step-by-step explanation:
I dont have one
A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
Answers
The sum of the given series can be found by simplification of the number
of terms in the series.
A is approximately 2020.022Reasons:
The given sequence is presented as follows;
A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021
Therefore;
\(\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}\)The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;
\(\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}\)Therefore, for the last term we have;
\(\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}\)2 × 2043231 = n² + 3·n + 2
Which gives;
n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0
Which gives, the number of terms, n = 2020
\(\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}\)
\(\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)\)
Which gives;
\(\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)\)
\(\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}\)
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A is equal to 1,685.00049.
Given that A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021, the following calculation must be performed to determine the result of this operation:
337/2 = 168.5 1011/10 = 101.1 337/5 = 67.4 1/2021 = 0.00049 1011 + 337 + 168.5 + 101.1 + 67.4 + 0.00049 = A 1685.00049 = A
Therefore, A is equal to 1,685.00049.
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Convert from radians to degrees.
1/4π
Answers
1/4π radians is approximately equal to 45 degrees.
To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.
Degrees = Radians × 180/π.
Therefore, to convert 1/4π radians to degrees, we have:
Degrees = (1/4π) × (180/π) ≈ 45°
Hence, 1/4π radians is approximately equal to 45 degrees.
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Choose the following choice is correct way to write the following number in word form? 176.003
Answers
Answer:
one hundred seventy-six and three thousandths
Step-by-step explanation:
A teacher asked her students how many pets they own. Here
are the results:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
On a piece of paper, draw a dot plot to represent the data.
Then determine which answer choice matches the dot plot
you drew.
Answers
Step-by-step explanation:
the answer is (c)
because 0 is 3 in number,
1 is 4 in number,
2 is 3in number
3 is 2 in number,
4 is 2 in number,
no 5,6,7
8 is 1 in number
and no 9
The dot plot ( C )is solved and each dot represents one student's response
What is a dot plot?A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.
Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.
Given data ,
Let the data of the number of pets owned by student be represented as A
Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }
The frequency of 0 = 3
The frequency of 1 = 4
The frequency of 2 = 3
The frequency of 3 = 2
The frequency of 4 = 2
The frequency of 8 = 1
In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.
For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.
Hence , the dot plot is solved
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16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Answers
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
I am lost on this question i found both but it keeps on telling me i am incorrect
Answers
Answer:
I have completed the answers and attached them to the explanation.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The question asks for a subtraction expression:
length is always a positive number so bigger number first here.
OB = 4-(-1) >only moves in x direction so subtract x's
AB = 4-(-2) >only moves in y direction so subtract y's
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
What should you substitute for x in the second equation (bottom equation) in order to solve the system by the substitution method?
Answers
We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
The given system of equations are 2x-1/3y = -2...(1)
3x+y=1...(2)
We solve this system of equations by using substitution method.
Let us solve for x in equation to substitute it in equation (2).
2x=-2+1/3y
Divide both sides of equation by 2.
x=-1+1/6y
Now plug in the value of x in equation 2.
Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.
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Given the figure below, find the values of x and y(5x + 56)101Y
Answers
In this problem we can use the properti of the oposite angle to know that:
\(5x+56=101\)and we can solve for x so:
\(\begin{gathered} 5x=101-56 \\ x=\frac{45}{5} \\ x=9 \end{gathered}\)now we can use the sum of complementary angle so:
\(5x+56+z=180\)and we replace the value of x and solve for z so:
\(\begin{gathered} 5(9)+56+z=180 \\ z=180-56-45 \\ z=79 \end{gathered}\)A neighborhood is trying to set up school carpools, but they need to determine the number of students who need to travel to the elementary school (ages 5-10), the middle school (ages 11-13), and the high school (ages 14-18). A histogram summarizes their findings:
Histogram titled Carpool, with Number of Children on the y axis and Age Groups on the x axis. Bar 1 is 5 to 10 years old and has a value of 3. Bar 2 is 11 to 13 years old and has a value of 7. Bar 3 is 14 to 18 years old and has a value of 4.
Which of the following data sets is represented in the histogram?
{3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4}
{5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18}
{5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13}
{3, 5, 10, 11, 13, 7, 18, 14, 4}
Answers
The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)
The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.
The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.
Therefore, the data set that is represented in the histogram is:
{3, 7, 4}
None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)
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Any help would be appreciated
Answers
I think the answer is 5.
Sorry if it's wrong.
Answer:
5
Step-by-step explanation:
This question is based on vector
By applying its formula
AC = AB + BC
we were given AC as 14 and BC as 9 so let find AB
AC = AB + BC
14 = AB + 9
AB = 14 – 9
AB = 5
i hope this helped
Complete the equations of the line through (-9,-9) and (-6,0)
Answers
The equation of a line can be written in slope-intercept form like this:
y = mx + b
Where m is the slope of the line and b is the Y-intercept. The slope of a line is given by the following formula:
\(m=\frac{y2-y1}{x2-x1}\)Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case, by taking the points (-9, -9) and (-6, 0) we get:
\(m=\frac{0-(-9)}{-6-(-9)}=\frac{0+9}{-6+9}=\frac{9}{3}=3\)Then we can rewrite the equation of the line like this:
y = 3x + b
By replacing the coordinates of the points (-6, 0) we get:
0 = 3(-6) + b
0 = -18 + b
18 = -18 + 18 + b
18 = b
b = 18
By replacing 18 for b and 3 for m we get:
y = 3x + 18
What is the sum of the series?
5
Σ3i
i=1
Answers
Σ
6
1
(
3
i
−
1
)
-1 is repeated 6 times
Σ
6
1
(
3
i
)
−
6
=
3
(
1
+
2
+
3
+
4
+
5
+
6
)
−
6
=
3
(
21
)
−
6
=
63
−
6
=
57
Step-by-step explanation:
Write 2.71 repeating as a simplified fraction.
271/100 is wrong
Answers
Answer:
269/99
Step-by-step explanation:
Simplify 0.4(−4.5). (5 points)
Answers
Answer:
-1.8, multiply them, then add the negative sign
Step-by-step explanation:
Answer:
its -1.8
Step-by-step explanation:
i got it right on my exam :)
-Hope this helps!
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AB=34 and EB=38, solve for EA. Round to the nearest tenth if necessary
Answers
The value of side EA is,
EA = 16.9
We have to given that;
Circle E with diameter CD and radius EA.
And, AB is tangent to E at A.
Here, AB = 34 and EB = 38
Hence, By using Pythagoras theorem we get;
AB² + AE² = EB²
34² + AE² = 38²
1156 + AE² = 1444
AE² = 1444 - 1156
AE² = 288
AE = √288
AE = 16.9
Thus, The value of side EA is,
EA = 16.9
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James has 2 kids, 1 son and 1 daughter. what is the number of James kids.
Answers
Michael launched a new website to share news and photos of his town. The equation below estimates the number of followers, y, in x weeks after his launch. y = 82(1.045)^x Complete each of the 2 activities for this Task. Activity 1 of 2 What is the rate of growth for the number of followers each week? A 45% B. 1,045% C. 4.5% D. 82% Activity 2 of 2 How many followers should Michael expect in the 4th week? Round to the nearest whole number. Show your work please!
Answers
Consider the given expression,
\(y=82(1.045)^x\)The first derivative gives the rate of growth for the number of followers.
Solve for the first derivative as,
\(\begin{gathered} \frac{dy}{dx}=82\times\frac{d \square}{dx}(1.045)^x \\ \frac{dy}{dx}=82\times(1.045)^x\ln (1.045) \\ \frac{dy}{dx}=y\times0.045 \\ \frac{dy}{dx}=4.5\text{ percent of y} \end{gathered}\)Thus, the rate of growth of followers is approximately 4.5% each week.
Therefore, option C is the correct choice.
The number of followers corresponding to the 4th week is calculated as,
\(y=82\times(1.045)^4=82\times1.1925=97.7865\approx98\)Thus, Michael should expect approximately 98 followers in 4th week.
Order the numbers from least to greatest
Answers
Answer:
-1/2, -7/10, 3/4, 4/5
Step-by-step explanation:
-1/2 (-5/10) is smaller than -7/10
3/4 (15/20) is smaller than 4/5 (16/20)
Please help!! Thank you
Answers
Find the equation to the line
Answers
The equation of the line is y = 2/3x + 1
How to determine the equation of the line?The graph represents the given parameter
From the graph, we have the following points that can be used in our computation:
(x, y) = (0, 1) and (3, 3)
The equation of the line is then calculated using the following equation
y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁
Where
(x, y) = (0, 1) and (3, 3)
Substitute the known values in the above equation, so, we have the following representation
y = (3 - 1)/(3 - 0) * (x - 0) + 1
Evaluate
y = 2/3 (x - 0) + 1
So, we have
y = 2/3x + 1
Hence, the line equation is y = 2/3x + 1
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4 children each have some beads, the mean number of beads is 8 Rajiv brings some more beads. The mean number of 5 children is now 9 what is the numberx of beads Rajiv brings
Answers
Answer:
The number of beads Rajiv brings is: 13Step-by-step explanation:
Make a plan:In this question, we need to use the formula of means to solve the. We can set the number of beads Rajiv brings as X, and use the formula of mean to get the total number of beads that the Four(4) children have and the total number of beads that the Five(5) children have.
Solve the problem:Four(4) children each have some beads, the mean number of beads is: 8
We can get the total number of beads the Four(4) children have:4 * 8 = 32
Rajiv brings some more beads:We set the number of beads Rajiv brings as:
x, so the total number of beads that the Five(5) children have is:
32 + x
The mean number of the Five(5) children is now: 9
We can get the total number of beads that the Five(5) children have:5 * 9 = 45
Now, we have the equation:32 + x = 45
x + 32 = 45
- 32 = -32
x = 13
By solving the above equation, you can get:
x = 13
Hence, The number of beads Rajiv brings is:13
Hope this helps!
The surface area of a rectangular prism is 178 in.2
What is the height of the figure if its length is 3 in. and its width is
4 in.? Explain how you got your answer.
Answers
Answer:
The height of the figure is 12 in
Step-by-step explanation:
Recall the Akaike information Criterion (AIC) as well as the related Bayesian Information Criterion (BIC) from our study of Variable Selection and Model Building. Without heavy mathematical notation, explain how both the AIC and BIC emphasize goodness-of-fit of a regression model while also controlling model complexity. Why would we wish to do this (that is, to promote goodness-of-it while at the same time controlling model complexity)
Answers
Step-by-step explanation:
To check out how efficient or accurate a model is, we use the akaike information criterion or the Bayesian. If the AIC or BIC are lower, then this model would be better. They are also used to control for model complexity
Akaike information criterion = 2k-2ln where k is the number of parameter. A higher k gives a higher AIC.
In the real world complex models are discouraged and avoided since
1. They cause data to be over fitted and can capture noise and information from this data.
2. They are complex and therefore difficult to interpret
3. They consume a lot of time and computing them has several inefficiencies.
Using these two as measure of performance, we can select optimal choice of independent variable.
With forward/backward regression, we are able to put new variables in the model or remove from it. The best is the one with lowest AIC.