Please find the following for the
given Regular Hexagon and
Irregular Triangle:
Answers
\(w=3units\\a=120^\circ\\x=3\sqrt3units\\b=8.8units\\y=6units\\c=10^\circ\\z=60^\circ\\d=2.0units\\\text{perimeter of hexagon}=36units\\\text{area of hexagon}=54\sqrt3\text{ sq.units}\\\text{perimeter of traingle}=20.8units\\\text{area of traingle}=7.7\text{ sq.units}\)
The length of a side of the regular hexagon is \(6units\).
For \(w\):
Since the perpendicular line, \(x\), passes through the center of the hexagon, it bisects the side on which \(w\) lies. Therefore,
\(w=\dfrac{1}{2}\times \text{side}\\=\dfrac{1}{2}\times 6units=3units\)
For \(x\), \(y\), and \(z\):
The line \(x\) is perpendicular to the side of the hexagon and bisects a side of the hexagon.
The line \(y\) passes through the center of the hexagon, hence it bisects the interior angle of the hexagon. Also,
\(y=6units\)
since it is half the diagonal of the hexagon. The diagonal is twice the side-length.
To calculate the size of an interior angle of a hexagon, we use the formula
\(2z=\dfrac{180^\circ(n-2)}{n}\)
Each interior angle is twice \(z\). Since \(n=6\)
\(2z=\dfrac{180^\circ(6-2)}{6}\\\\2z=\dfrac{180^\circ\times4}{6}\\\\z=60^\circ\)
The lines \(x\), \(y\), and \(w\) form a right-angled triangle. Using Pythagoras theorem,
\(w^2+x^2=y^2\\3^2+x^2=6^2\\x^2=36-9=27\\x=3\sqrt3units\)
For \(a\):
\(a\) is an interior angle of the hexagon. Previously, we found that the interior angle
\(2z=a=120^\circ\)
For \(c\):
We have the relationship for the sum of the interior angles for the irregular triangle
\(50^\circ+120^\circ+c=180^\circ\)
the angle \(120^\circ\) is vertically opposite \(a\)
\(c=180^\circ-120^\circ-50^\circ=10^\circ\)
For \(b\):
Using the sine rule on the irregular triangle,
\(\dfrac{b}{sin50^\circ}=\dfrac{10}{sin120^\circ}\\\\b=\dfrac{10}{sin120^\circ}\times sin50^\circ\approx 8.8units\)
For \(d\):
\(\dfrac{b}{sin50^\circ}=\dfrac{d}{sin(c)}\\\\d=\dfrac{b}{sin50^\circ}\times sin(c)\\\\=\dfrac{8.8}{sin50^\circ}\times sin10^\circ\\\\\approx2.0units\)
The perimeter of the hexagon is
\(6\times \text{side}=6\times6=36units\)
The area of the hexagon is
\(6\times\dfrac{1}{2}\times \text{base}\times\text{height}\\\\3\times6\times x=3\times6\times 3\sqrt3\\=54\sqrt3\text{ sq.units}\)
perimeter of the triangle is
\(10+b+c=10+8.8+2.0\\=20.8units\)
area of the triangle is
\(\dfrac{1}{2}\times d\times 10sin50^\circ\\\\=\dfrac{1}{2}\times 2.0\times 10sin50^\circ\\\\\approx7.7\text{ sq.units}\)
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Related Questions
The area of a rectangle is 72.8cm? if one side of the length is 6.52cm. find the length of the other two to two decimal places
Answers
Answer:
11.17, my answer needs to be 20+ characters soooooooo
Lauren is making muffins. Her muffin recipe calls for 3 1 4 cups of flour. If Lauren plans to make 5 batches of the muffin recipe, use what you know about operating with rational numbers to predict the amount of flour she needs. Justify your prediction.
Answers
Answer:
15.14 cups is the answer, just do 5*3 then put the 14 into place it should be the answer
In a group of 30 students 18 have visited Australia 15 have visited botwanna
Answers
Answer:
ようrもmづっっっっっっっっhsつぽdねあr
Answer:
0
Step-by-step explanation:
Please help me !! would appreciate
Answers
The answers that describe the quadrilateral DEFG area rectangle and parallelogram.
The correct answer choice is option A and B.
What is a quadrilateral?A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.
Quadrilateral DEFG
if line DE || FG,
line EF // GD,
DF = EG and
diagonals DF and EG are perpendicular,
then, the quadrilateral is a parallelogram
Hence, the quadrilateral DEFG is a rectangle and parallelogram.
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Consider the following.
cos(x) = x3
A) Prove that the equation has at least one real root.
The equation cos(x) = x3 is equivalent to the equation f(x) = cos(x) − x3 = 0. f(x) is continuous on the interval (0, 1) there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x3, in the interval (0, 1).
B) Use your calculator to find an interval of length 0.01 that contains a root.
Answers
Answer:
Step-by-step explanation:
Given that:
cos(x) = x³
f(x) = cos (x) - x³
f(x) is continuous on the interval (0, 1)
when;
f(0) = cos (0) - (0)
f(0) = 1 - 0
f(0) = 1 > 0
f(1) = cos (1) - 1³
f(1) = 0.5403 - 1
f(1) = -0.4597
f(1) = - 0.46
f(1) = - 0.46 < 0
Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)
such that f(c) = 0
By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)
b) Given that:
The interval length = 0.01; this implies that it is 0.005 length from its root.
f(0.865) = 0.0014
f(0.87) = - 0.013
The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.
Which is the first step in simplifying the expression 2(x 3) 5? 2x 2(3) 5 2x 3 5 2 x 3 5 2(5) x 3
Answers
The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.
Given expression in 'x' is 2(x+3)+5.
In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.
So, 2(x+3) +5 = 2x + 2(3) +5
= 2x +6 +5
= 2x+11
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Please help and hurry 15 points
Answers
So substitute the x for 2
(2+4)^2-3
Pemdas
6^2
36-3
33
Answer:
23
Step-by-step explanation:
(x+4) ²-3 (Question)
x²+4x+16-3
x²+4x+13
(2)²+4(2)+13 (since x=2)
4+6+13
23
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2. 5x+3 represents the cost y of bowling x games. Interpret the parameters of the function.
Answers
The number that represents the shoe rental charge is $3 and the price per game is $2.5.
Given:
The function y=2.5x+3 represents the cost y of bowling x games.
y = 2.5x+3
In the equation the 2.5 represents additional fee.
For 1 game = 2.5*1 = 2.5
For 2 games = 2.5 * 2
= 5
3 is the flat fee for renting the shoes.
Therefore the number that represents the shoe rental charge is $3 and the price per game is $2.5.
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dasdasdasdasdasdasdasdasdas.
Answers
Answer:
dodododododododo
Step-by-step explanation:
Answer:
Haha lol
Have a wonderful day!
Step-by-step explanation:
9/53
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
Answers
The proof of DE is parallel to BC in the given triangle is shown.
What is defined as the parallel line?Parallel lines are defined as two lines that remain the same distance away and never intersect. To be parallel, two lines must be driven in the same plane, which is a perfectly flat surface such as a wall or sheet of paper.As per the given data in the question;
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)B has coordinates (2,-2)C has coordinates (-2,-4)Whereas,
D lies at the midpoint of AB.
E lies at the midpoint of AC.
The mid piont formula is;
Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
The coordinates of D is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and B (2,-2).
D = (4 + 2 / 2, 6 - 2 / 2)
D = (3, 2)
The coordinates of E is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and C (-2,-4)
E = (4 - 2 / 2, 6 - 4 / 2)
E = (1, 1)
Now, the slope is calculated by;
m of DE = (y₂ - y₁)/(x₂ - x₁)
The slope of E is
m of DE = (1 - 2)/(1 - 3) = 1/3
Slope of BC
M of BC = (-4 + 2)/(-4 - 2)
M of BC = 1/2
As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.
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If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B? 1.The range of set A is greater than the range of set B. 2. Sets A and B are both evenly spaced sets.
Answers
Step-by-step explanation:
(1) The range of set A is greater than the range of set B.
This statement gives only the range which means only outermost values but what about the other values. For example-11,0,0,0,11 and -10,-10,0,10,10
Clearly, Former one has higher range but lower standard deviation.
(2) Sets A and B are both evenly spaced sets.
Evenly spaced is fine. However, we don't know the spacing since that is required to know the deviation.
For, example, sets A{2,4,6,8,10} and B {1,2,3,4,5} so in this case SD of A> SD of B. Or, we can have B{2,4,6,8,10} and A{1,2,3,4,5} so in this case SD of B> SD of A.
Provide detailed answers including graphs for the following questions.
You invest $100,000 on January 1st in a lottery. The lottery provides you a 2% chance of winning $1 million on December 31st in each of the next 10 years. Are there any conditions under which would you make this investment?
A monopolist’s cost structure is such that its total costs are TC = 300 + 200Q + 3Q^2. The market demand is Q = 500 - P. What is the profit-maximizing price and quantity? Show this mathematically and graphically. What are the producer and consumer surpluses and firm profit?
Answers
The profit-maximizing price and quantity for the monopolist are $350 and 150 units, respectively ,The expected return is greater than the initial investment And the producer surplus is $33,750, consumer surplus is $31,875, and firm profit is $37,500.
Ignoring the time value of money and discounting, the expected value of the lottery winnings each year is 2% × $1 million = $20,000, and this goes on for 10 years.
Thus, the expected value of the investment is 10 × $20,000 = $200,000.
Hence, the expected return is greater than the initial investment, and there is a condition under which the investment can be made.
The monopolist’s total cost can be represented as:
TC = 300 + 200Q + 3Q².
The demand function for the monopolist is given as:
Q = 500 - P,
which can be rearranged to derive the price function as:
P = 500 - Q.
From the total cost function, we can obtain the marginal cost (MC) as the derivative of TC with respect to Q, and it can be represented as follows:
MC = dTC/dQ = 200 + 6Q.
From the marginal cost, we can set the marginal revenue (MR) equal to MC to get the profit-maximising quantity as follows:
MR = dTR/dQ = P + Q(500 - P) = 500 - Q + 500Q - Q² = 1000Q - Q² - 500 = MC = 200 + 6Q.
Substituting P = 500 - Q in the above expression and rearranging yields the following:
Q = 150, and hence, P = $350.
Therefore, the profit-maximising price is $350, and the quantity is 150. We can verify that the solution is a maximum by computing the second-order condition, which is negative.
To calculate the producer surplus, we first need to obtain the area above the marginal cost and below the price.
Thus, we have:
PS = ∫ MC to QdQ
= ∫ (200 + 6Q) dQ from 0 to 150
= [200Q + 3Q²] from 0 to 150
= $33,750.
Similarly, the consumer surplus can be computed as the difference between the market value of the product and what the consumers paid for it. The area below the price line and above the demand curve yields the consumer surplus.
Thus, we have:
CS = ∫ P to QdQ
= ∫ (500 - Q) dQ from 0 to 150
= [(500 × Q) - (Q²/2)] from 0 to 150
= $31,875.
Finally, the firm profit can be obtained by multiplying the profit-maximizing quantity by the profit-maximizing price and subtracting the total cost.
Thus, we have:
Profit = TR - TC = Q × P - TC = (150 × $350) - (300 + 200 × 150 + 3 × 150²) = $37,500.
Hence, the producer surplus, consumer surplus, and firm profit are $33,750, $31,875, and $37,500, respectively.
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3 Sarah viaja en su bicicleta a una velocidad de 22.7 millas por hora. ¿Cuál es la velocidad aproximada de Sarah, en kilómetros por minuto? justifica tu respuesta
(1) 0.2
(2) 0.6
(3) 36.5
(4) 36.6
Answers
Sarah's speed in kilometers per minute is 0.6 kilometers per minute.
What is Sarah's approximate speed, in kilometers per minute?To convert the speed from miles per hour to kilometers per minute, we need to perform the following conversions:
1 mile = 1.60934 kilometers
1 hour = 60 minutes
We will convert miles per hour to kilometers per hour:
= 22.7 miles/hour * 1.60934 kilometers/mile
= 36.525918 kilometers/hour
We will convert kilometers per hour to kilometers per minute:
= 36.525918 kilometers/hour / 60 minutes/hour
= 0.60876697
= 0.6 kilometers/minute.
Full question:
Sarah is riding her bicycle at a speed of 22.7 miles per hour. What is Sarah's approximate speed, in kilometers per minute? justify your answer
(1) 0.2
(2) 0.6
(3) 36.5
(4) 36.6.
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Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.
Answers
Using net worth statement, Andre's net worth is $159,573.
How to Construct a net worth statement to find Andre's net worth.Andre's net worth can be calculated by subtracting his total liabilities from his total assets.
Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800
Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227
Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573
Therefore, Andre's net worth is $159,573.
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A (blank) in matter results in a change in its identity and properties. Which best completes the statement?
chemical change
chemical property
physical property
physical change
Answers
Answer:
Hi there!
Your answer is:
A. Chemical change
Step-by-step explanation:
Chemical changes occur when a substance combines with another to form a new substance, called chemical synthesis or, alternatively, chemical decomposition into two or more different substances.
let s be the annual sales (in millions) for a particular electronic item. the value of s is 53.4 for 2008 . what does s
Answers
The meaning of s in the question is that it means the Annual Sales for a particular electronic item is 53.4millions for the year 2008
The Annual sales is the total amount of money that a company makes during the period of 12 months for the sale of a product.
In the question it is mentioned that the value of s is 53.4 for the year 2008.
and s denotes the annual sales for electronic item in that particular year .
S in the statement means Annual Sales for a particular electronic item in the year 2008 was of 53.4 millions.
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Need help i will give brainliest for whoever answers
Answers
Answer:
It is $25 per hour
Step-by-step explanation:
Answer is A
Answer: $25 per hour.
Step-by-step explanation: The waiter earned $250 in 10 hours. 250/10 = $25 per hour.
The table below represents a function. Which of the following equations could be its function rule?
Answers
Answer:
it's the 3rd choice, Y= -3x
lucinda surveyed 50 students in her school to find out how many students enjoy playing sports. the resultsare shown in the table. do you think lucinda chose a random sample? why or why not?
Answers
If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.
what are perpendicular lines?
Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.
Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.
However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:
Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.
Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.
Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.
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Help, please!!!!!!!!!!!!!!!!
Answers
23. based on 1988 census data for the 50 states in the united states, the correlation between the number of churches per state and the number of violent crimes per state was 0.85. what can we conclude? a. there is a causal relationship between the number of churches and the number of violent crimes committed in a city. b. the correlation is spurious because of the confounding variable of population size: both number of churches and number of violent crimes are related to the population size.
Answers
The conclusion is Option (b) strong positive correlation between the number of churches and the number of violent crimes, but we cannot infer causation due to the presence of a confounding variable.
Correlation refers to the relationship between two variables, where a change in one variable may be associated with a change in the other variable.
The correlation coefficient, denoted by r, measures the strength and direction of the relationship between two variables. The value of r ranges from -1 to +1, where a value of -1 indicates a perfect negative correlation, a value of +1 indicates a perfect positive correlation, and a value of 0 indicates no correlation.
In this case, the correlation coefficient between the number of churches and the number of violent crimes is 0.85.
However, we cannot conclude that there is a causal relationship between the number of churches and the number of violent crimes committed in a city.
There may be a confounding variable, which is a third variable that affects both the independent and dependent variables.
Therefore, the correlation between the number of churches and the number of violent crimes may be spurious, meaning that it is not a true causal relationship but rather a result of the influence of a third variable.
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What is the formula for coordinate plane?.
Answers
The coordinate plane's formula is (x, y), where x denotes the x-axis and y denotes the y-axis.
A linear equation is a two-variable equation with a line as the graph.
A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation.
If every variable has a real value, the equation can be graphed by placing enough points on the graph to identify a pattern, then connecting those points to include all of the points.
A linear equation must have at least two points in order to be graphed, however it's usually a good idea to utilize more.
Try to include zero as well as both positive and negative numbers when selecting your points.
The term "x-intercept" refers to the point where the graph crosses the x-axis, and the term "y-intercept" refers to the point where the graph crosses the y-axis.
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In the context of chi square, which pattern of cell frequencies in a 2x2 table would indicate that the variables are independent? a. Only the cells in the top row of the table have cases in them b. There are no cases in any celf c. There are a different number of cases in each of the tour cells d. All cell trequencics are exactly the same
Answers
Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.
In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.
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If you roll the die 60 times, how many twos can you expect to roll?
Answers
Answer:
10
Step-by-step explanation:
Rolling a single six-sided die, you would get two 1/6th of the time because there is one two out of the six sides.
So 60 rolls would be 60*(1/6)=60/6=10
What are the solutions to the following equation?
|3x - 9| = 12
Question 30 options:
x = 7
x = -7
x = -1
x = 1
x = 0
x = 12
Answers
Answer:
x=7
Step-by-step explanation:
12+9=21
21/3=7
3x7=21-9=12
f(x) = x2 + 2
g(x) = 2x
Which of the following expressions represents f(x) ⋅ g(x) ?
Answers
Which statements accurately compare the functions on
the graph? Select two options
The square root and quadratic function share a y
intercept
The square root and absolute value function share an
x intercept
The range of the square root and quadratic function
are the same
The range of the square root and absolute value
function are the same
The quadratic function and the absolute value
function have a minimum while the square root
function has a maximum
Answers
Answer:
this is the answer I came up with hope this helps
Answer:
E. The absolute value and square root function share an x-intercept.
Step-by-step explanation:
Pre-Calc on Edge 2022
round your answer to the nearest hundreth
Answers
Answer:
201.06 sq. ft.
Step-by-step explanation:
Area of a circle is found by using the equation:
\(A = \pi r^{2}\)
Radius = 1/2 (diameter) = 1/2 (16) = 8
So plug in:
\(A = \pi (8)^{2}\)
A = 64\(\pi\)
A = 201.06193
Rounded A= 201. 06
find the value of x Round your answer to the nearest tenth what does x equal hury please!!!!!!!!!!!!
Answers
Answer:
14
Step-by-step explanation:
tan41° = opposite / adjacent
tan41 = 12/x
x ( tan41 ) = 12
X = 12/tan41°
X = 13.80
when rounded off = 14
Central conservative forces: (a) Consider the force F= r2kr^ : Is this force conservative? Is it central? If it is conservative find the potential energy V(r). For full marks you need to justify your answer and explain any assumptions that you make.
Answers
The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force
To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.
A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:
∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.
Calculating the components of F = r^2k(r^):
Fx = 0, since there is no force component in the x-direction.
Fy = 0, since there is no force component in the y-direction.
Fz = r^2kr^.
Taking the partial derivatives, we have:
∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.
∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.
Substituting these values into the curl equation, we get:
∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).
Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.
Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).
For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.
Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.
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