Answers
Step-by-step explanation:
You have this rule, if there is < 30° then value of y is
y=12✓3:2
y=6√3
And Pitagora's theorem:
c²=a²+b²
In this case:
(12√3)²=y²+x²
Then x is:
x²= (12√3)²-y²
x²= (12√3)²-(6√3)²
x²=432- 108
x²= 324
x=✓324
x=18cm
Related Questions
Decide whether the curves of the functions given below have tangent lines at the indicated points. If yes, describe the tangent line and if no, explain why. a) f(x) = |x 2 − 1| x = 1 b) f(x) = ( √ x if x ≥ 0 − √ −x if x < 0 at x = 0
Answers
a) The function f(x) = |x² - 1| does not have a tangent line at x = 1.
The function has a corner or a sharp turn at that point, and the slope changes abruptly, making it impossible to define a unique tangent line.
b) The function f(x) = (√x if x ≥ 0, -√-x if x < 0) does not have a tangent line at x = 0.
a) The function f(x) = |x² - 1| has a tangent line at x = 1.
To determine if a function has a tangent line at a specific point, we need to check if the function is continuous and differentiable at that point.
For f(x) = |x² - 1|, the function is continuous for all values of x because it is composed of basic continuous functions (polynomials and absolute value).
However, at x = 1, the function has a corner or a sharp turn due to the absolute value function.
Therefore, f(x) = |x² - 1| does not have a well-defined tangent line at x = 1. At x = 1, the slope of the function changes abruptly, and there is no unique tangent line that can be defined.
b) The function f(x) = (√x if x ≥ 0, -√-x if x < 0) has a tangent line at x = 0.
To determine if the function has a tangent line at a specific point, we need to check if the function is continuous and differentiable at that point.
For f(x) = (√x if x ≥ 0, -√-x if x < 0), the function is continuous for all values of x.
To determine if the function is differentiable at x = 0.
we need to check if the left-hand and right-hand derivatives exist and are equal.
For x > 0, f'(x) = d/dx(√x) = 1 / (2√x), which is defined and continuous at x = 0.
For x < 0, f'(x) = d/dx(-√-x) = -1 / (2√-x) = -1 / (2i√x) = undefined.
Therefore, the left-hand derivative does not exist at x = 0.
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How do i total this please help
8.3m
5.2m
4.36m
42.1m
86.1m
Answers
You bought a shirt for $13.50 that was originally $45.00. In terms of percent, what discount did you get on the shirt?
Answers
Answer:
30%
Step-by-step explanation:
0.7 repeating a rational or irrational number
Answers
prime factorization of 52 using factor tree
Answers
Answer: 52 = 2, 4, 13, 52
Step-by-step explanation:
vertical angles 4x+7 and [5(x-4)] what is the value of x
Answers
Answer:
x = 27
Step-by-step explanation:
vertical angles are congruent , then
5(x - 4) = 4x + 7 ← distribute parenthesis on left side
5x - 20 = 4x + 7 ( subtract 4x from both sides )
x - 20 = 7 ( add 20 to both sides )
x = 27
Answer:
x = 27
Step-by-step explanation:
Vertical angles are congruent.
5(x - 4 ) = 4x +7
5x - 20 = 4x + 7 {Distributive property}
Add 20 to both sides
5x = 4x + 7 + 20
5x = 4x + 27
Subtract 4x from both sides
5x - 4x = 27
x = 27
Can someone help me please
Answers
Answer:
Perimeter=32
Step-by-step explanation:
Perimeter=Sum of all sides
=8+2+2(on opposite side) +3+3+6+6(on opposite side) +(8-(3+3)) [The bottom side] =32
John has decided to get in shape for the new year. He is planning to joining the local fitness club. The fitness club charges customers a $14.95 monthly fee plus a one time joining fee $110.00.
What is the total cost John will pay for a 12-month membership at the fitness club?
Answers
an urn contains four balls numbered 2, 2, 5, and 6. if a person selects a set of two balls at random, what is the expected value of the sum of the numbers on the balls?
Answers
7.500 (rounded to 4 decimals) sum of the numbers on the balls.
Suppose we select two distinct balls
Then we have the following possibilities of selecting two balls
(2,2), (2,2) ............, i.e. 2 ways to get a sum of 4...............(2+2 = 4 and 2+2 = 4)
(2,5), (2,5), (5,2), (5,2), i.e. 4 ways to get a sum of 7...............(5+2 = 7 and 2+5 = 7)
(2,6), (2,6), (2,6), (2,6), i.e. 4 ways to get a sum of 8...............(2+6 = 8 and 6+2 = 8)
(6,5), (5,6) , i.e. 2 ways to get a sum of 11...............(5+6 = 11 and 6+5 = 11)
total number of possible outcomes = 2(for a sum of 4) + 4(for a sum of 7) + 4(for a sum of 8) + 2 (for a sum of 11)
= 2 + 4 + 4+2
= 12
So, P(getting a sum of 4) = (number of ways to get a sum of 4)/total number = 2/12
similarly,
P(getting a sum of 7) = (number of ways to get a sum of 7)/total number = 4/12
P(getting a sum of 8) = (number of ways to get a sum of 8)/total number = 4/12
P(getting a sum of 11) = (number of ways to get a sum of 11)/total number = 2/12
We know that expected value E[x] = sum of all individual sum values by their respective probability
= 4*(2/12) +7*(4/12) +8*(4/12) +11*(2/12)
= 0.6667 + 2.3333 + 2.6667 + 1.8333
= 7.500 (rounded to 4 decimals)
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an ice cream truck that plays loud music is circling bulan's neighborhood. c(t)c(t)c, left parenthesis, t, right parenthesis models the volume of the music (in \text{db}dbstart text, d, b, end text) that bulan hears, ttt minutes after the truck arrives in her neighborhood. here, ttt is entered in radians.
Answers
The function c(t) = c(t) = c(t), left parenthesis, t, right parenthesis models the volume of the music (in dB) that Bulan hears t minutes after the ice cream truck arrives in her neighborhood. In this function, t is entered in radians.
The function c(t) represents how the volume of the music changes over time as t increases. The exact shape of the function depends on various factors like the distance between Bulan and the ice cream truck, the truck's speaker system, and any other interfering sounds in the neighborhood.
By analyzing the function c(t), one can determine the maximum and minimum volume levels Bulan experiences as the truck moves around her neighborhood. Additionally, the periodic nature of the function suggests that the music will repeat itself after a certain time interval.
In conclusion, the function c(t) = c(t) = c(t), left parenthesis, t, right parenthesis provides a mathematical representation of the volume of the music that Bulan hears as a function of time. This function helps us understand the changing volume levels and the periodicity of the ice cream truck's music in her neighborhood.
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Convert 1.5 days to seconds.
A. 36 seconds
B. 12,960 seconds
C. 129,600 seconds
D. 2,160 seconds
Please I need help
Answers
Answer:
C.129,600
Step-by-step explanation:
1 day = 24 hour
1.5 days = ?
(1.5days × 24 hour)/1day
=36hours
1hour = 3600 second
36hour = ?
(36hours × 3600second)/1hour
= 129,600
What are the 3 types of rigid transformations?
Answers
Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.
A rigid transformation, also called isometry, is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:
1. Reflection
→ is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.
The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.
2. Rotation
→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.
The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.
3. Translation
→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right), or vertical reflections (make a figure up or down).
Vertical translation is shifting the graph along \(y-\) axis
Horizontal translation is shifting the graph along \(x-\) axis.
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whats the mean of the numbers 3 7 2 4 7 5 7 1 8 8
Answers
Answer:
5.2
Step-by-step explanation:
adding all the numbers together and dividing it by 10.
Answer:
mean = 5.2
Step-by-step explanation:
The mean (or average) of a group of numbers is defined as the value calculated by adding all the given numbers together and then dividing the result by the number of numbers given.
Therefore,
\(\boxed{\mathrm{mean = \frac{sum \ of \ the \ numbers}{number \ of \ numbers}}}\).
In the question, the numbers given are: 3, 7, 2, 4, 7, 5, 7, 1, 8, and 8.
Therefore,
sum = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8
= 52
There are 10 numbers given in the question. Therefore, using the formula given above, we can calculate the mean:
\(\mathrm{mean = \frac{52}{10}}\)
\(= \bf 5.2\)
Hence, the mean of the given numbers is 5.2.
The equation of line m is y=3 x-1 . What is the equation of a line that goes through the point (3,-2) and is perpendicular to line m ? Show your work.
Answers
The equation of the line that is perpendicular to line m and passes through the point (3,-2) is y = -1/3 x - 1.
To find the equation of a line that is perpendicular to line m, we need to determine the negative reciprocal of the slope of line m. The slope of line m is 3. The negative reciprocal of 3 is -1/3. Therefore, the slope of the perpendicular line is -1/3.
Next, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the values from the given point (3, -2) and the slope -1/3, we have y - (-2) = -1/3(x - 3). Simplifying this equation gives y + 2 = -1/3x + 1. Rearranging the terms, we get y = -1/3x - 1. Therefore, the equation of the line that is perpendicular to line m and passes through the point (3, -2) is y = -1/3x - 1.
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10. Find y.
x is 127°
w is 53°
Answers
Finding Missing Angles and Sides and Round to the nearest tenth.
(FOR ALL PLEASE)
Answers
The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90 angle.
To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.
Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.
Without this information, no concrete calculations can be made.
Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.
Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.
Round your answer to the nearest tenth as specified.
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Which statement is true of rectangles Y and Z?
Rectangle Y has a length of 6 and width of 4. Rectangle Z has a length of 4 and width of 3.
Answers
Answer:
Rectangle Y has a length of 6 and width of 4
Step-by-step explanation:
Just did it
Answer:
Not too sure, but I think it's D.
Step-by-step explanation:
Gail paid 118.65foravarsityjacket.Thepriceincludesa5112.72 113.00117.00 $124.65
It is 112.72because5118.65. By doing that, you can get the original price by subtracting that value, which is 5.9325, from 118.65,youget ...
Answers
The original price of the varsity jacket before the discount was $5.93.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
To find the original price of the varsity jacket before the discount, we can subtract the discount amount from the total price.
In this case, the discount amount is $112.72, and the total price paid is $118.65.
Therefore, the original price of the varsity jacket can be calculated as follows:
Original Price = Total Price - Discount Amount
Original Price = $118.65 - $112.72
Original Price = $5.93
Hence, the original price of the varsity jacket was $5.93.
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Which of the following traingles is Cos B = 0.8?
Answers
ANSWER:
EXPLANATION:
Given:
To find:
Which triangle is cos B = 0.8
For the 1st Triangle:
We have to first determine the value of side BC using the Pythagorean theorem as seen below;
\(\begin{gathered} 5^2=4^2+BC^2 \\ 25=16+BC^2 \\ BC=\sqrt{25-16} \\ BC=\sqrt{9} \\ BC=3 \end{gathered}\)So cosine B will be;
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{3}{5} \\ \cos B=0.6 \end{gathered}\)For the 2nd Triangle:
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{5}{8} \\ \cos B=0.625 \end{gathered}\)For the 3rd Triangle:
We have to first determine the value of side AB using the Pythagorean theorem as seen below;
\(\begin{gathered} AB^2=4^2+5^2 \\ AB^2=16+25 \\ AB=\sqrt{41} \end{gathered}\)So cosine B will be;
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{4}{\sqrt{41}} \\ \cos B=0.62 \end{gathered}\)For the 4th Triangle:
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{4}{5} \\ \cos B=0.8 \end{gathered}\)So in the below triangle cos B = 0.8
A large right triangle is going to be a part
Answers
The given triangle in the question is a right-angled triangle. In order to get the length of each side, we will apply the Pythagoras theorem.
The Pythagoras theorem is,
\(\text{Hypotenuse}^2=Opposite^2+Adjacent^2\)Where,
\(\begin{gathered} \text{Hypotenuse}=5 \\ \text{Opposite}=2x-2 \\ \text{Adjacent}=x \end{gathered}\)Therefore,
\(5^2=(2x-2)^2+x^2\)Let us expand the above
\(\begin{gathered} 25=2x(2x-2)-2(2x-2)+x^2 \\ 25=4x^2-4x-4x+4+x^2 \\ 25=5x^2-8x+4 \end{gathered}\)Switch sides
\(5x^2-8x+4=25\)Subtract 25 from both sides
\(5x^2-8x+4-25=25-25\)Simplify
\(5x^2-8x-21=0\)Solve with the quadratic formula
\(x_{1,\: 2}=\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\cdot\:5\left(-21\right)}}{2\cdot\:5}\)Thus
\(\sqrt[]{(-8)^2-4\cdot\: 5(-21)}=22\)Therefore,
\(x_{1,\: 2}=\frac{-\left(-8\right)\pm\:22}{2\cdot\:5}\)Separate the solutions
\(x_1=\frac{-\left(-8\right)+22}{2\cdot\:5},\: x_2=\frac{-\left(-8\right)-22}{2\cdot\:5}\)Hence,
\(\begin{gathered} x=\frac{-(-8)+22}{2\cdot\: 5}=3 \\ x=\frac{-(-8)-22}{2\cdot\: 5}=-\frac{7}{5} \end{gathered}\)The solutions to the quadratic equations are
\(x=3,\: x=-\frac{7}{5}\)Therefore, from the above result, the length of a triangle can never be negative.
Hence, x = 3
Let us now solve the length of the remaining side
\(\begin{gathered} 2x-2=2(3)-2=6-2=4 \\ \therefore2x-2=4 \end{gathered}\)Therefore, the length of each leg is
\(3ft,4ft,5ft\)‼️WILL LIST BRAINLIEST ‼️
Answers
Answer:
77/9 is the correct awnser simplufied is -8 5/9 or -8.5
Step-by-step explanation:
Write a unite rate that compares the quantities described 48 cookies for 3 children
Answers
Answer:
48/3
Step-by-step explanation:
On june 1, 2021, portugal inc. reported a cash balance of $12,000. during june, portugal made deposits of $5,000 and made disbursements totalling $14,000. what is the cash balance at the end of june?
Answers
The cash balance at the end of June is $3000.
What are disbursements in accounting?The amounts transferring from one account to another are said to be disbursements in accounting.
So, there are subtracted from the initial balance to get the current balance.
Calculation:It is given that,
On June 1, 2021, Portugal inc. reported a cash balance of $12,000.
During June, Portugal made deposits of $5000 and made disbursements totaling $14,000.
The initial cash balance = $12,000
Made a deposit of $5000 = $12,000 + $50000
⇒ $17, 000
Also made disbursements of $14,0000
⇒ Cash balance at the end = $17,000 - $14,000 = $3000
Therefore, in the end, the cash balance is $3000.
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Rose has a vase with 13 flowers. She puts 7 more flowers in the vase. How many flowers are in the vase?
Answers
Answer:
20
Step-by-step explanation:
if she has 13 flowers and adds 7 more that is 20 because 13+7=20
Which of the following illustrates quadratic inequalities? I. 4x2 − 3x + 1 ≤ 0 II. (x + 9)(x − 7) > 0 III. 2 + 9 = 0
Answers
20 POINTS
what is the vertex of this quadratic function
Answers
Answer:
(-4,-9)
Step-by-step explanation:
vertex form: y=a(x-h)^2+k
hk=vertex of x and y
inside parentheses=horizontal (opposite signs)
that’s why it’s -4 instead of 4 for h (x) while -9 stays the same since it’s not inside the parentheses
which equation is correctly written in point-slope form using the point (−5,−2) as (x1,y1)?
Answers
Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).
The point-slope form of an equation of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line
m is the slope of the line.
We can use the given point (−5,−2) as (x1,y1)
Choose any value for the slope m to write the equation of the line in point-slope form.
For example:
Option 1:
Let's choose the slope m to be 2.
Then the equation of the line becomes:
y - (-2) = 2(x - (-5))
Simplifying the equation:
y + 2 = 2(x + 5)
Option 2:
Let's choose the slope m to be -3.
Then the equation of the line becomes:
y - (-2) = -3(x - (-5))
Simplifying the equation:
y + 2 = -3(x + 5)
Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).
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A small hotel in central London has 8 rooms. Based on data collected over the last five years, it was estimated that the probability a room is occupied on any particular "weekend" night (Saturday and Sunday) is 0.75. This is the probability of success. On any particular "weekend" night, a hotel is only occupied (Success) or not occupied (Failure). There are no other possibilities. Required: What is the probability that at least 4 of the 7 hotel rooms are occupied on any weekend night? Note: Show all your calculations in well laid-out Excel spreadsheet tables with clear headings and include formulas. Give your answers correct to 3 decimal places.
Answers
Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75. To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.
To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms.
For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339
For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923
Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.
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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75.
To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.
To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms. For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339
For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923. Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.
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Which angle is supplementary to ∠1?
Answers
research shows that ethnicity is often a bigger barrier to advancement into top leadership positions than being a woman.
Answers
It is important to approach statements like this with caution and consider the complexity of the factors at play in career advancement and leadership positions.
While research may indicate that ethnicity can be a significant barrier to advancement in some cases, it is crucial to recognize that experiences can vary based on individual circumstances, industries, and regions. Gender and ethnicity intersect in complex ways, and the challenges faced by women of different ethnic backgrounds can differ significantly.
It is essential to avoid generalizations and recognize that multiple factors contribute to the barriers individuals face in reaching top leadership positions. These factors can include implicit biases, cultural norms, lack of representation, access to opportunities, networking, and organizational structures. Intersectionality, which considers how different aspects of a person's identity can intersect and create unique experiences, is also a crucial perspective to consider when discussing barriers to advancement.
To fully understand and address the barriers individuals face in reaching top leadership positions, it is necessary to consider a comprehensive range of factors and engage in ongoing research, dialogue, and efforts to promote equity, diversity, and inclusion in the workplace.
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