find the three angles of the triangle with the given vertices: d(1,1,1), e(1,−1,2), and f(−5,2,4). give answers in radians, rounded to five decimal places.
Answers
A triangle is a polygon with three sides, three vertices, and three angles. It is one of the fundamental shapes in Euclidean geometry.
To find the angles of a triangle with the given vertices, we can use the dot product and cross product of vectors.
First, let's find the vectors formed by the three given points: d(1,1,1), e(1,-1,2), and f(-5,2,4). We can subtract the coordinates of one point from another to get the vector connecting them.
The vector DE can be found by subtracting the coordinates of point D from point E:
DE = (1, -1, 2) - (1, 1, 1) = (1-1, -1-1, 2-1) = (0, -2, 1)
Similarly, we can find the vector DF and EF:
DF = (-5, 2, 4) - (1, 1, 1) = (-5-1, 2-1, 4-1) = (-6, 1, 3)
EF = (-5, 2, 4) - (1, -1, 2) = (-5-1, 2+1, 4-2) = (-6, 3, 2)
Next, we can find the magnitudes of these vectors using the formula:
Magnitude of vector = √(x^2 + y^2 + z^2)
|DE| = √(0^2 + (-2)^2 + 1^2) = √(0 + 4 + 1) = √5
|DF| = √((-6)^2 + 1^2 + 3^2) = √(36 + 1 + 9) = √46
|EF| = √((-6)^2 + 3^2 + 2^2) = √(36 + 9 + 4) = √49 = 7
Now, we can find the cosine of each angle using the dot product formula:
cos(angle) = (vector1 · vector2) / (|vector1| * |vector2|)
cos(angle D) = (DE · DF) / (|DE| * |DF|)
cos(angle E) = (DE · EF) / (|DE| * |EF|)
cos(angle F) = (DF · EF) / (|DF| * |EF|)
DE · DF = 0 * -6 + (-2) * 1 + 1 * 3 = -2
DE · EF = 0 * -6 + (-2) * 3 + 1 * 2 = -4
DF · EF = -6 * -6 + 1 * 3 + 3 * 2 = 49
cos(angle D) = -2 / (√5 * √46)
cos(angle E) = -4 / (√5 * 7)
cos(angle F) = 49 / (√46 * 7)
To find the angles, we can use the inverse cosine function (arccos) to get the angles in radians:
angle D = arccos(cos(angle D))
angle E = arccos(cos(angle E))
angle F = arccos(cos(angle F))
Finally, we can substitute the values into the formulas to find the angles in radians, rounded to five decimal places.
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Related Questions
(1a) Are the fraction and decimal equivalent? Explain how you know. 3/4 & 0.75"
Your answer
Answers
Answer: Yes, the fraction and decimal are equivalent.
Step-by-step explanation: 0.75 is equal to 75/100. If you simplify 75/100, you get 3/4
A biased dice was rolled and the scores were recoreded in the table below. A is estimate the probabilty that on the next roll is 4. b if the dice was rolled 600 times how many 6 would u get.
Answers
Answer:
a. 1/4
b. 150
Step-by-step explanation:
Firstly, we want to calculate the probability that the next value will be 4
The total number of rolls is;
17 + 24 + 23 + 10 + 16 + 30 = 120
The probability of having 4 will be;
10/120 = 1/12
b) Let us get the probability of rolling a six
That would
be 30/120 = 1/4
So out of 600 rolls, the number of time we will have a six will
be 1/4 * 600 = 150
Find the missing side lengths. Leave your answer as radicals in simplest form.
Answers
The values of the sides are;
41. x = 18√3. Option D
42. x = 6√3. Option A
How to determine the valuesUsing the different trigonometric identities, we have;
41. Using the tangent identity, we have;
tan 60 = 9√2/y
cross multiply the values
y =9√2 ×√3
y = 9√6
Using the sine identity;
sin 45 = y/x
1/√2 = 9√6/x
cross multiply the values, we have;
x = 9√2 ×√3 ×√2
x = 18√3
42. Using the cosine identity
cos 60 = 3√3 /x
cross multiply, we have;
x = 6√3
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Identify the error and fix the mistake
Answers
Answer:
x = (9 ±√201) ÷ 12
Step-by-step explanation:
6x² -5x -9 = 0 ( rearranged)
a = 6 b = -5 c = -9
- - 9 = 9
-9² = 81 (the 81 must be positive, this is one error)
-4 x 6 x -5 = 120 ( the 5 must be a minus number, this is one error)
120 + 81 = 201
x = (9 ±√201) ÷ 12
Clay surveys members of his class to find out how many televisions they have in their homes. The thirteen responses he received are shown in the table. Which statement is true?
A) The mean is less than the mode.
B) The mean is less than the range.
C) The mean is greater than the range.
D) The median is greater than the mode.
Answers
Answer:
B, the mean is less than the range
Step-by-step explanation:
mean is 3.38 (rounded)
mode is 3
median is 3
range is 5
The mean is 3.38 and the range is 5, So the mean is less than the range. Option B is the correct one.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Mean = \(\frac{1+5+2+3+4+6+3+1+3+4+3+5+4}{13}\)
The mean is 3.38 (rounded)
Median represents the middle value of the given data when arranged in a particular order.
So, the Median would be 3.
Mode is that number that appears most frequently in the given set of data.
So, the Mode would be 3.
The range of a given set of data is the difference between the largest value and the smallest value.
So, the range would be 5
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Are 90 degrees (clockwise) and -270 degrees (counter clockwise) coterminal? WHY or why not?
Answers
Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.
What are coterminal angles ?Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.
To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:
-270 + 360 = 90
Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).
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Which of the following is not a condition to check when doing atwo-sample z-test of proportions?
A.
The samples are independent of each other and independent within samples
B.
The sample are random
C.
The samples are sufficiently large
D.
All of the above conditions are important conditions to check
Answers
Option D is not a condition to check when doing a two-sample z-test of proportions.
The correct option is D. All of the above conditions are important conditions to check when doing a two-sample z-test of proportions.
The two-sample z-test of proportions is a statistical test that is used to compare the proportion of two populations.
This statistical test helps in determining whether or not there is a significant difference between the two proportions.
The following are the conditions to check when doing a two-sample z-test of proportions:The samples are independent of each other and independent within samples.
The sample is random.
The samples are sufficiently large.
Therefore, the given statement "All of the above conditions are important conditions to check when doing a two-sample z-test of proportions" is correct.
In conclusion, option D is not a condition to check when doing a two-sample z-test of proportions.
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Molly was curious if quadrilaterals ABCDABCDA, B, C, D and EFGHEFGHE, F, G, H were congruent, so she tried to map one figure onto the other using transformations
Answers
Answer:
The answer is below
Step-by-step explanation:
A transformation of a point is the movement of an point from an initial position to a new position. If an object is transformed, all the point of an object is transformed. Two figures are said to be congruent if they have the same shape and the measure of each of their sides are the same.
An object is congruent to another object if the object can be mapped to the other object when transformed.
Answer:
The answer is c
Step-by-step explanation:
It is the correct solution because you are able to map circle m onto m
Q1a) What fraction, decimal and percentage of the diagram is shaded?
3 points
Your answer
Answers
Answer:
in this diagram their are boxes.
on which 21 are shaded so the fraction is
Step-by-step explanation:
21/100
because their are total 100 boxes and 21 are shaded
hope you like the answer.
Which number line model represents the expression 5 1/2 + (-3)
Answers
Answer: B
Step-by-step explanation:
Please stop and help me
Answers
Answer:
f(9)= 141
Step-by-step explanation:
f(x)=-\(x^{2}\)+5x+15
replace x's with 9f(9)=-9^2+5(9)+15solvef(9)=141Is 1.875 and rational number
Answers
Answer: 1.875 is a rational number because it can be represented as a ratio or a fraction.
Airfare from Atlanta,GA to Nashville,TN was decreased from $250 to $180.By what percentage did the cost of the airfare change?
Answers
Answer:
percentage cost of airfare change= (difference in cost / original cost )×100
% age = (250-180/ 250) ×100
=70/250 ×100
7000/250
= 28%
Find the present value of a sequence of annual payments of Rs 25000 each , the first being made at the end of 5th year and the last being paid at the end of 12th year, if money is worth 6%.
Answers
The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.
1: We can use the formula to calculate the present value of the annuity:
P = A x [1 - (1+i)^-n] / i
Where
P = Present Value
A = Annuity
i = Interest Raten = Number of payments
2: Calculate the present value of each payment using the formula:
P1 = 25000 / (1.06)⁵
P2 = 25000 / (1.06)⁶
P3 = 25000 / (1.06)⁷
P4 = 25000 / (1.06)⁸
P5 = 25000 / (1.06)⁹
P6 = 25000 / (1.06)¹⁰
P7 = 25000 / (1.06)¹¹
P8 = 25000 / (1.06)¹²
3: Substitute the values into the formula to find the present value:
P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8
P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)
P = 158620.39
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Find the slope of a line parallel to the given line: 7x - 3y = -6
Answers
Answer: 7/3
Step-by-step explanation:
Dylan has $20.00 on his gift card. After some purchases, he has $0.06 remaining on his gift card. Dylan has _____% of the original amount remaining on the gift card.
Answers
Answer:
Step-by-step explanation:
To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.
The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:
($0.06 ÷ $20.00) x 100% =
0.003 x 100% =
0.3%
Therefore, Dylan has 0.3% of the original amount remaining on his gift card.
can anyone solve this please asap
Answers
Answer:
= 1.268Step-by-step explanation:
= (3 + √3) (2 - √3)
= 6 - 3√3 + 2√3 - 3
= 3 - 3√3 + 2√3
= 3 - √3 (3 - 2)
= 3 - √3
= 3 - 1.732 ...... (√3 = 1.732)
= 1.268
2. A town is planning a circular walkway that will be 2 meters wide. The walkway will have an inter radius of 5 meters with a circumference of about 31. 4 meters. Find the area of the wallway
Answers
The area of the walkway is 24π square meters.
To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.
The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).
A_inner = π * \(5^{2}\) = 25π square meters.
The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.
The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).
A_outer = π * \(7^{2}\) = 49π square meters.
Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.
A_walkway = 49π - 25π = 24π square meters.
The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.
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The sum of the first nine terms in a sequence is 49,205. Each term is 3 times the previous term. What is the third term?
Answers
Answer:
a₃ = 32 805Step-by-step explanation:
Each term is 3 times the previous term:
r = 3
The sum of the first nine terms in a sequence is 49,205:
\(S_n=a_1\cdot\dfrac{1-q^n}{1-q}\\\\\\49205=a_1\cdot\dfrac{1-3^9}{1-3}\\\\49205=a_1\cdot\dfrac{1-19683}{-2}\\\\49205=a_1\cdot9841\\\\a_1=5\)
What is the third term?
\(a_n=a_1\cdot q^{n-1}\\\\a_3=5\cdot3^8=32805\)
Solve:
1/3(2x-6/5)=4/9(x+1/3)
Answers
\( \frac{1}{3} .( \frac{2x - 6}{5} ) = \frac{4}{9} .( \frac{x + 1}{3} )\)
\( \frac{2x - 6}{15} = \frac{4x + 4}{27} \)
\(54x - 162 = 60x + 60\)
\( - 222 = 6x\)
\(x = - 37\)
I guess it's right.We learnt this way in Turkey.
Find the Area of a rectangle whose width is 16 inches and diagonal is 20 inches?
What are the dimensions of the rectangle? Show your work and explain how you got your answer in complete sentences.
Answers
b=12
Area is 12x16=192
How to convert us dollar to thai baht?
Answers
Convert USD to THB, multiply amount of USD by the current exchange rate between USD and THB, which can be found on financial news or currency exchange websites, to get the equivalent amount in THB.
To convert US dollars (USD) to Thai baht (THB), you need to use the current exchange rate between the two currencies. Here are the steps to convert USD to THB:
Find the current exchange rate between USD and THB. This information can be found on financial news websites, currency exchange websites, or by contacting a bank or currency exchange service.
Multiply the amount of US dollars you want to convert by the current exchange rate to get the equivalent amount in Thai baht. For example, if the current exchange rate is 1 USD = 31.50 THB and you want to convert 100 USD to THB, the calculation would be:
100 USD x 31.50 THB/USD = 3,150 THB
Therefore, 100 USD is equal to 3,150 THB.
Note: The exchange rate between USD and THB can fluctuate over time, so make sure to use the current exchange rate for the most accurate conversion.
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what other patterns can you discover in the subway ridership dataset using calculations with multiple operators?
Answers
Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.
Why Subway ridership data reveal useful patterns through calculations?The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.
Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.
Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.
Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.
Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.
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Tina invests $3,700 into an account with a 4.4% interest that is compounded quarterly. How much money will she have in this account if she keeps it for 8 years? Round your answer to the nearest cent.
Answers
Answer:
I believe the balance would be 5,221.6 (Rounded to the Nearest Tenth)
Need help quiiickkkk
In 28.8 seconds, the piano plays 48 beats.
Piano Tempo
What is the tempo, in beats per minute, of the piano?
beats per minute
Answers
Answer:
100 beats per minute
Step-by-step explanation:
If it takes 28.8 secs for the piano to play 48 beats, then it would take 60 secs (1 minute) to play x number of beats.
To find the value of x, which is the number of beats the piano makes per minute, let's set the proportion as shown below:
28.8 secs = 48 beats
60 secs = x beats
Cross multiply
28.8*x = 60*48
28.8x = 2,880
Divide both sides by 28.8
x = 2,880/28.8
x = 100
✅Thus, if the Piano plays 48 beats in 28.8 secs, therefore, the tempo of the piano in beats per minute would be 100 BPM
A rectangular prism is 7 inches long 10 inches wide and 6 inches tall a what is the length of its longest diagonal to the nearest 10th of an inch
Answers
Answer:
c
Step-by-step explanation:
BRAINLIEST 3/5(x−710)=−314
Answers
Answer: x = 560/3
Step-by-step explanation:
First! We are going to be using the PEMDAS method! If you have any questions about this method please go ahead and ask below! The first step in our equation is the P - parenthesis, so we are going to multiply \(\frac{3}{5}\) to everything inside of the parenthesis (x and -710)!
\(\frac{3}{5} (x -710) = -314\)
\(\frac{3}{5}x+(\frac{3}{5}*-710)=-314\)
\(\frac{3}{5}x -426 = -314\)
Now, we are going to add 426 to both sides of the equation, to single out the "x" variable!
\(\frac{3}{5}x= 112\)
Finally, let's multiply both sides by \(\frac{5}{3}\) to cancel out the \(\frac{3}{5}\) fractions, to get the "x" variable alone.
\(x=\frac{560}{3}\)
↑This is our answer!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
6-8 weeks i hope this help:)
Answers
Answer:
I have no idea but okay
Which of the following inequalities are correct please help me ;-;
Answers
Answer:
A is correct
Step-by-step explanation:
b has a negative value cause it's before 0
but -b will become a positive value thus >0
example:
b is -1
-b = -(-1)
= 1
hope you understand
Answer:
⇨ Choice A.
Step-by-step explanation:
We'll consider three choices and compare the answers with the given number line and points.
⟺ Choice A
This is the correct answer and here is why.
\(-b>0\)
Solving Inequality is similar to solving equation. The difference is if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.
Thus, our new Inequality would be \(b<0\) which is true by the number line itself.
⟺ Choice B
The reason why choice B is not correct because the point a is lesser than the point b. It's obvious that point a cannot be greater than point b.
⟺ Choice C
The reason why choice C is not correct because if we solve the Inequality.
\(-b<-c\)
We can either solve for b-term or c-term, the outcome would be the same. I'll solve for both terms.
⇨ Solve for b-term
\(-b<-c\\b>\frac{-c}{-1}\\b>c\)
Also remember that moving a negative coefficient would swap the sign/operator of Inequality.
⇨ Solve for c-term
\(-b<-c\\\frac{-b}{-1}>c\\b>c\)
As b>c is not true in the number line. We notice that c point is greater than b point.
Thus, the clear answer is A choice.
HELP GIVING BRAINLIEST Carlene is selling T-shirts for a fundraiser. The T-shirts cost $20.50 each. To date, she has raised $900. Her goal is to raise more than $9,100. How many more T-shirts, x, does Carlene need to sell to reach her goal?
Select the number line that includes the fewest number of T-shirts Carlene can sell and still meet her goal.
Answers
FYI:
Sorry, I can't answer your second question because I can't see any number-lines in your question. But yes, I can answer the first one.
Answer:
400 T-Shirts
Step-by-step explanation:
If each T-Shirt is $20.50, that means that Carlene has to sell lots of them in order to earn the amount of money she wants. So, to find how many T-Shirts she needs to sell in order to get $9,100, we have first remove $900 dollars from the $9,100, because she ALREADY earned it!
9,100-900=8,200
Now we have to divide $8,200 by $20.50. like this...
8,200÷20.50=400
Now, that's our answer. 400.
Carlene has to sell 400 more T-Shirts in order to earn to her goal!
Thank You! Please mark me brainliest so that I can get encouraged to make more great answers like this one!