The required measures of m ZAED, mZDAE, and mZBCE are 37°, 143°, and 37°, respectively.Rhombus: A rhombus is a quadrilateral with four sides of equal length and opposite angles with equal measures.
Quadrilateral ABCD is a rhombus, with the following angles:
mZEDA = 37
Given a rhombus, it is expected that all sides have equal length, so;
ZEDA is a straight angle, the sum of all angles in a straight line is 180°.
∴m ZDEA = 180 - mZEDA = 180 - 37 = 143°
From the definition of a rhombus, all sides are equal in length and all angles are equal in measure.
Thus,mZEDA = mZDEA = mZDAB = mZCBA = 37°
Since mZDEA = 143°, then; m ZAED = 180 - mZDEA = 180 - 143 = 37°
∵ZADE is a straight angle
∴ mZDAE = 180 - mZAED = 180 - 37 = 143°
∵ ZBCE is a straight angle
∴ mZBCE = 180 - mZDEA = 180 - 143 = 37°.
Hence the required measures of m ZAED, mZDAE, and mZBCE are 37°, 143°, and 37°, respectively.
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Five chess players take part in a tournament. Every player plays once with each of his/her opponents. How many games are play?
There is a total of 10 games played.
How many games are played?
There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.
So we have 4 games at the moment.
Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.
Now we do the same with the remaining 3, this time we add 2 more games.
Now we do that with the remaining 2, now we add 1 more game.
Adding all the games we have:
4 + 3 + 2 + 1 = 10
There is a total of 10 games played.
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A hotel packed a breakfast for each of three guests. Each breakfast should have consisted of three types of rolls, one each of nut, cheese, and fruit rolls. The preparer wrapped each of the nine rolls, and, once they were wrapped, the rolls were indistinguishable from one another. She then randomly put three rolls in a bag for each of the guests. Given that the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers, find m+n.
The probability that each guest of each type m+n will receive a roll is 79.
Given that the breakfast should have consisted of three types of rolls, one each of the nut, cheese and fruit rolls, and the cook should have wrapped each of the nine rolls.
The denominator of m/n equals the total number of possible role configurations assigned to the three people. It [tex]${9 \choose 3}{6 \choose3}$[/tex] is the same as the number of ways to choose three roles out of 9 to give to the first person [tex]${9 \choose 3}$[/tex], and three rolls of 6 [tex]${6 \choose3}$[/tex]. After that, the remaining three roles have no more configurations.
The numerator is the number of ways to assign a roll of each type to each of the three people, which can be done by defining the three types of roles such as flavored x, flavored y and flavored z.
xxx, yyy, zzz
So we have to choose one x, one y and one z to give to the first person. There are 3x, 3y and 3z to choose from, resulting in 3³ combinations. Multiply that by the combinations of xs, ys and zs for the second person, which is clearly 2³ since there are two of each letter left. simplify to our fraction m / n, which is 9/70. If you add them together, you get 9 + 70 = 79.
Thus, the probability that each guest has obtained a roll of each type is m / n, where m and n are relatively prime, so m + n is 79.
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There were 150 females surveyed, evenly divided for all levels of expertise. there were 450 males surveyed. there were 80 expert players and 180 novice players.
The values which would help complete the table according to the complete part of the task content are as evaluated.
What value would help complete the table?First, the total number of average players can be evaluated by summing up the total number of players vertically as follows;
180 + average + 80 = 600
The number of average players is therefore; 600-180-80 = 340 average players.
Also, the number of female expert players can be evaluated vertically as;
50 + 50 + female expert = 150
Female expert = 150-50-50 = 50 female experts.
The number of male novice players can be evaluated horizontally as;
Male novice + 50 = 180
Male novice = 180 - 50 = 130.
The number of average male players is therefore easily evaluated vertically as;
130 + male average + 30 = 600
male average = 600-130-30 = 440.
Remarks: The table which is required to be completed is that which is in the attached image.
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Answer:
130, 290, 340, 50
Step-by-step explanation:
just do the math, I got it right on edmentum.
The biotic factors of an ecosystem are arranged in feeding levels based on what they utilize for food or energy. Each of these feeding levels is called a
The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.
What is a trophic level?The trophic level of an organism is the position it occupies in a food web. The trophic level of an organism is the number of steps it is from the start of the chain.
Below are the list of the trophic levels:
1st Trophic Level (Producer) : Makes its own food2nd Trophic Level (Primary Consumer): Consumes producers3rd Trophic Level (Secondary Consumer): Consumes primary consumers4th Trophic Level (Tertiary Consumer): Consumes secondary consumersThe biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.
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(d) Percentage of viewers given they are 18 to 34 who prefer videos on a mobile or laptop device. (Round your answer to 2 decimal places.)\
52.94% of the viewers prefer videos on a mobile or laptop device
How to determine the percentage?The given parameters are
Viewers that prefer videos on a mobile or laptop device = 18
Total number of viewers = 34
The percentage of voters in this category is then calculated as
Percentage = 18/34 * 100%
Evaluate the expression
Percentage = 52.94%
Hence, 52.94% of the viewers prefer videos on a mobile or laptop device
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How will the volume of the pyramid change if each side is multiplied by a factor of one-half? a rectangular pyramid. the volume will be 2 times the original volume. the volume will be 8 times the original volume. the volume will be one-fourth times the volume. the volume will be one-eighth times the volume.
The volume will be one-eighth times the volume.
How to determine the volume?The scale factor k is given as
k = 1/2
Let the initial volume be v
When each side is multiplied by the scale factor, we have the new volume to be
V = k^3 * v
Substitute 1/2 for k in the above equation
V = (1/2)^3 *v
Evaluate the exponent
V = 1/8 *v
This gives
V = 1/8v
Hence, the volume will be one-eighth times the volume.
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What is the surface area of the figure below?
Round your answer to the nearest tenth square foot?
(The answer choices are in the picture. Thank you!)
Answer:
856.5ft^2
Step-by-step explanation:
I took the test.
Darlene says that 1/4 is greater than 1/3 because 4 is great than 3. is she correct?
No she is not correct 1/3 is great that 1/4
Answer:
No, she isn't correct because if the numerator are same but if denominators is different,then the fraction with smaller denominator is greater.
Your family is going on vacation for two nights. You don't want to spend more than $135 on a hotel room for your vacation. Write an inequality to represent how much you can spend each night on your hotel room.
Answer:
x ≤ 135/2
Step-by-step explanation:
x is the cost per night. You have to pay for 2 nights, and you do not want to spend more than $135 total. Another way to say that, is you want to spend less than or equal to $135.
x = cost per night
2 = number of nights
2x = total cost
Total cost must be less than or equal to $135.
2x ≤ 135
Divide each side by 2.
x ≤ 135/2
Factor the polynomial expression 3x2+2.
A. (3‾√x+2‾√i)(3‾√x−2‾√i)
B. (3‾√x+i)(3‾√x−i)
C. (3‾√x+2‾√)(3‾√x−2‾√)
D. (3x+2‾√i)(3x−2‾√i)
Using the Factor Theorem, the expression 3x² + 2 is factored as follows:
[tex]3x^2 + 2 = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, the expression is:
3x² + 2.
The roots are found as follows:
[tex]3x^2 + 2 = 0[/tex]
[tex]x^2 = -\frac{2}{3}[/tex]
[tex]x = \pm \sqrt{-\frac{2}{3}}[/tex]
[tex]x_1 = -i\sqrt{\frac{2}{3}}[/tex]
[tex]x_2 = i\sqrt{\frac{2}{3}}[/tex]
Hence the factored expression is:
[tex]3x^2 + 2 = \left(x + i\sqrt{\frac{2}{3}}\right)(x - 1\sqrt{\frac{2}{3}}\right) = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]
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what is meant by green mathematics?
give meaningful answer .
[tex]4222125.[/tex]
who can give the first answer
The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
According to the statement
we have to explain the green mathematics.
In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.
In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.
The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.
Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.
In this there is a green theorem, which relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.
So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
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The angle formed by the line of sight and the horizontal line can best be described as a(n)
The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.
Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.
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Graph the rational function
by identifying its key features.
The graph of the rational function is shown below
Graph of rational functionsFrom the question, we are to graph the given rational function
To determine the graph that corresponds to the given rational function,
First, we will graph the given rational function.
The given rational function is
x²+3x-1/x+1
The graph of the rational function is shown below
Now, we will compare each of the rational graphs in the provided options with the attached graph
The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.
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Determine the slope of the line.
The slope of the line is - 3 / 2 .
How to find slope?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, using (0, 6)(4, 0)
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
slope = 0 - 6 / 4 - 0
slope = -6 / 4
slope = - 3 / 2
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A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a:
A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a negative correlation.
What is negative correlation?When two variables move in opposite sizes and directions from one another, so that when one increases, the other drops, and vice versa, this is referred to as having a negative correlation or inverse correlation.
In order for investors to profit from price increases in some assets when others decline, negative correlation is used when building diverse portfolios.
Over time, the correlation between two variables might change significantly. Bonds and stocks typically have negative correlation.
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Geometry: write a formal proof, ASAP!!!
We have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem
Proof of anglesFrom the question, we are to write a proof to prove that ∠BEC ≅ ∠BCE
From the given information, we have that
BC || EF
Note that line DE is a transversal
Thus, by the alternate interior angles theorem, we have that
∠BCE ≅ ∠FEC
Also, we were given that line EC bisects ∠BEF
That is,
Line EC divides ∠BEF into two equal angles.
Therefore,
∠BEC ≅ ∠FEC
By the substitution property of equality, we get
∠BEC ≅ ∠BCE
Hence, we have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem
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Please help me with this question
Used formula
d/dx(x^n)=nx^{n-1}Answer:
6x+5
Step-by-step explanation:
the derivative of a sum is equal to the sum of derivatives:
(3x^2 + 5x + 2)' = (3x^2)' + (5x)' + (2)' = 6x + 5
Q.E.D.
if you shift the absolute value parent function, F(x)= IxI, right 9 units, what is the equation of the new function?
A. G(x)=IxI-9
B. G(x)=Ix+9I
C. G(x)=Ix-9I
D. G(x)=IxI+9
What are the domain and range of g of x equals negative 3 times the square root of the quantity x minus 1? D: (1, ∞) and R: (0, ∞) D: [–3, ∞) and R: [0, ∞) D: (–3, ∞) and R: (–∞, 0) D: [1, ∞) and R: (–∞, 0]
The domain of the function is [1, ∞) and the range is [0, ∞)
How to determine the domain and the range?The equation of the function is given as:
g(x) = 3√x - 1
The domain is the possible values of x.
Set the radicand to greater than or equal to 0
x - 1 >= 0
Add 1 to both sides
x >= 1
This can be rewritten as:
[1, ∞)
Breakdown
g(x) = 3√x - 1
x - 1 >= 0
x >= 1
[1, ∞)
The range is the possible values of y.
Set the radicand to 0
g(x) = 3 * 0
Evaluate the product
g(x) = 0
This can be rewritten as:
[0, ∞)
Breakdown
g(x) = 3√x - 1
g(x) = 3 * 0
g(x) = 0
[0, ∞)
Hence, the domain of the function is [1, ∞) and the range is [0, ∞)
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Answer:
Correct answer is D: [1, ∞) and R: (-∞, 0]
Step-by-step explanation:
Insert the given function on desmos to observe the following explanation.
The domain (x values) begin at 1, and go on to positive infinity (the squared bracket indicates a stop/start at that certain point). The range goes into negative infinity (y values) and begins at the y value of 0, so it does not go above that point on the y axis (hence the squared bracket).
Determine whether the point (1,5) is a solution to the system of equations g(x)=3x+2 f(x)=|x-1|+1
Point [tex](1,5)[/tex] is a solution of the equation [tex]g(x)=3x+2[/tex] and point [tex](1,5)[/tex] is not a solution of equation [tex]f(x)=|x-1|+1[/tex]
Why point [tex](1,5)[/tex] is solution of the equation [tex]g(x)=3x+2[/tex] ?
If point [tex](1,5)[/tex] is solution of the equation then they must satisfy the equation.
So we need to check one by one
[tex](x,y)=(1,5)[/tex]
equation [tex]g(x)=3x+2[/tex]
We can write as
[tex]y=3x+2\\5=3*1+2\\5=5[/tex]
So point [tex](1,5)[/tex] is solution of this equation.
Equation [tex]f(x)=|x-1|+1[/tex]
We can write as
[tex]y=|x-1|+1\\5=|1-1|+1\\5=0+1\\5\neq 1[/tex]
So point [tex](1,5)[/tex] is not solution of equation [tex]f(x)=|x-1|+1[/tex]
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2. There are 10 pieces of paper, numbered
consecutively from 20 to 29, stuffed in a box.
What is the probability of choosing a prime
numbered paper if one piece is chosen at
random?
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Prime numbers between 20 - 29 = 23 and 29.
There are 2 prime numbers out of these 10.
Therefore,
P(choose prime number) = [tex]\frac{2}{10} \\=\frac{1}{5}[/tex]
Bailey tossed a coin 10 times. The results were 7 heads and 3 tails.
What is the experimental probability of tossing tails?
answer as a fraction
Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical form.
17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.
How do you find the length of the diagonal of a regular hexagon?Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.
For a polygon, the SUM of the internal angles is:
(n-2) * 180 (n=6 for hexagon)
(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees
Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.
There are 180 degrees in any triangle:
(180-120) / 2 = 30 degrees for each of the smaller angles.
Now use the law of sines:
10/sin30 = x/(sin120)
10/(.5) × (sqrt3 )/ 2 = x
10 sqrt 3
10/sin30 × sin 120 = 17.32
17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.
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Suppose you want to purchase a home for $425,000 with a 30-year mortgage at 5.44% interest. Suppose also that you can put down 30%. What are the monthly
payments? (Round your answer to the nearest cent.)
$
What is the total amount paid for principal and interest? (Round your answer to the nearest cent.)
$
What is the amount saved if this home is financed for 15 years instead of for 30 years? (Round your answer to the nearest cent.)
$
Need Help?
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Answer:
a) payment: $1677.99
b) total repaid: $604,076.40
c) saved: $168,231.60
Step-by-step explanation:
The amortization formula can be used to find the monthly payment on the loan. The total repaid will be the sum of payments made. The amount saved will be the difference between the total repaid amounts for the different loans.
Amortization formulaThe payment A on a loan of principal P at annual rate r for t years is given by ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
ApplicationThe loan of interest is for $425,000 × (1 -30%) = $297,500. Then the payments on a 30 year loan are ...
A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-360) ≈ $1677.99
For a 15-year loan, the payments are ...
A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-180) ≈ $2421.36
a)The above calculation shows the monthly payment is $1677.99.
b)The total repaid is the sum of 360 monthly payments:
360×$1677.99 = $604,076.40
c)The total repaid is the sum of 180 monthly payments:
180×$2421.36 = $435,844.80
and the savings is ...
$604,076.40 -435,844.80 = $168,231.60
__
Additional comment
We are asked to round to the nearest cent. The payment amounts here are accurately calculated to that precision. The total repaid on an actual loan will be slightly different, because the final payment will be slightly different.
The 30-year mortgage will have a slightly lower final payment because the monthly amount is rounded up. The 15-year mortgage will have a slightly higher final payment because the monthly amount is rounded down.
Overall, this means the totals of payments shown here, and their difference, vary slightly from the reality of loans of this kind. (They're probably not accurate to the nearest cent.)
Even using the "exact" payment value may not give the actual loan values. This is because the actual amortization schedule is rounded to the nearest cent each month. The cumulative effect of this rounding seems to be calculable only by figuring the 360 (or 180) actual monthly balance amounts.
We have calculated the answers in the manner we suppose is expected. Producing an actual amortization spreadsheet is a bit more work.
Say you have (-4x)^2, why and how would it translate to 16x^2? it's the same thing as (-4x)(-4x) so wouldn't you double distribute it?
Which of the following best explains the value of Sine StartFraction pi Over 3 EndFraction on the unit circle below
The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
According to the statement
we have to give the terms which explain the sin (pi/3) perfectly.
And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.
And Now we explain all terms below
So,
"Right Triangle is a triangle whose one of the angle measures 90° "
And "The hypotenuse is a longest side of the right triangle.
And"Unit Circle is a circle with radius 1."
For given question,
We have been given a unit circle.
So, We need to find the sin (pi/3)
We know, in a right triangle for any angle , θ
Sinθ = Opposite side of angle / Hypotenuse
So, for , Sin(pi/3) = Opposite side of angle / 1
Sin(pi/3) = Opposite side of angle
Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.
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A scalene triangle whose angles are all congruent possible or impossible
Answer:
impossible
Step-by-step explanation:
a scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.
because all 3 angles must be different, they cannot be congruent.
because if angles are congruent, it means that they are of equal size.
the desired definition is a paradox or oxymoron. it contradicts itself and can never be true.
Answer:
it cannot have all angles congruent: impossible.
Step-by-step explanation:
by the definition scalene, it means no angle is the same length. meaning, to have all the sides congruent (the same length) that would be impossible and it can never happen. if you would like a congruent triangle, an isosceles or equilateral is the triangle you're looking for.
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
(2, 12)
(2, 18)
(2, 7)
(3, 7)
Answer: (2, 18)
Step-by-step explanation:
When x=2, [tex]f(2)=2(3)^{2}=18[/tex].
So, it should pass through (2, 18).
Determine if the expression −7m³ + m + 9m³ is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial
1: "represents" a polynomial
2: "does NOT represent" a polynomial
⊰___________________ ___________________________________ __⊱
Answer:
Yes, it is a polynomial
Step-by-step explanation:
This polynomial is a trinomial, since it has 3 terms (the prefix tri means three) and its degree is 3 (the degree of a polynomial is the largest exponent in that particular polynomial).
Done !! Hope this made sense to you !!
⊰________________________________________________________⊱
[tex]\small{\pmb{\tt{CALLIGRAPHY}}[/tex]
Someone help me please
Answer:
x=15
Step-by-step explanation:
Use the Pythagorean Theorem: a^2+b^2=c^2
1. a = 20, b = x, c = 25
2. 20^2+b^2= 25^2
3. Expand: 400+b^2= 625
4. Subtract + Simplify: b^2= 625-400
5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225
6. Last Step: Simplify: b = 15.
Here is a similar problem for you to solve, put your answer in the comments.
a= 12, b=5, c=?
Solve for c using the Pythagorean theorem.