Use the Law of Cosines to find the values of x°and y°. Round to the nearest tenth.
Answers
The value of x and y° are 29.1 and 76.6°.
What is rounding to tenth?
Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.
The length of sides of the triangle are x, 35, and 40.
Assume that AB = c = x, BC = a = 35, and AC = b = 40
m∠C = 45° and m∠B = y°.
Cosine law:
c² = a² + b² - 2ab cos C ....(i)
b² = a² + c² - 2ac cos B ....(ii)
a² = b² + c² - 2bc cos A ....(iii)
Putting a = 35, b = 40, c = x, and C = 45° in law (i)
x² = 35² + 40² - 2×35×40 cos 45°
x² = 2825 - 2800 × (1/√2)
x = 29.07
x = 29.1 (nearest tenth)
Putting a = 35, b = 40, c = 29.1, and B = y° in law (ii)
40² = 35² + 29.1² - 2×35×29.1 cos y
1600 = 1225 + 846.81 - 2037 cos y
2037 cos y = 471.81
cos y = 471.81/2037
y = 76.60°
y = 76.6°
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Related Questions
Ariana solved the equation as shown. Explain her error and correct the solution.
9x² - 144= 0
9x² = 144
x² = 16
√ x² = √ 16
x=+8
Answers
The square root of 16 = +4 and -4
Ariana divided 16 by 2
Graph the solution set for 4y+3x-y> -6x+12
Answers
Answer:
XSdfgfcxdcd
Step-by-step explanation:
What is the area of a half circle if the diameter is 36 inches?
Answers
Answer:
508.94 in²
Step-by-step explanation:
5. What is "Data Triangulation" in general? Give 2 real-world examples.
Answers
Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.
Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.
Two real-world examples of data triangulation are:
Qualitative-Quantitative Triangulation in Market Research: In market research, qualitative methods like focus groups or interviews can be combined with quantitative methods like surveys or sales data analysis. By triangulating these data sources, researchers can gain a deeper understanding of consumer preferences, behaviors, and market trends, combining the richness of qualitative insights with the statistical power of quantitative data.Methodological Triangulation in Educational Research: In educational research, methodological triangulation can be employed by using multiple research methods to investigate a learning phenomenon. For example, a researcher may use classroom observations, interviews with teachers, and student performance data to gain a comprehensive understanding of a teaching strategy's effectiveness. By triangulating these data sources, the researcher can capture a more complete picture of the learning environment and draw robust conclusions.Learn more about Data Triangulation at
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what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
Answers
Ratio of the area of a square inscribed in a semicircle with radius 'r' to the area of a square inscribed in a circle with radius 'r' is equal to 2: 5.
As given in the question,
Let ABCD be the square with side 'a' inscribed in a semicircle with radius 'r'.
'O' be the center of the semicircle.
'M' be the midpoint of AB such that MB = a/2
Join OM, OB and OM ⊥ AB
OB = r
OM = BC = a
In ΔOMB.
OB² = OM² + MB²
⇒ r² = a² + (a/2)²
⇒r² = 5a²/4
⇒a² = 4r²/5
Area of the square inscribed in a semicircle = a²
= 4r²/5
Let PQRS be the inscribed in a circle with side 'x'
Diagonal of the square inscribed in a circle = 2r
In ΔPQR,
PR = diagonal
= 2r
PQ = QR = x
PR² = PQ² + QR²
⇒(2r)² = x² + x²
⇒x² = 4r² /2
⇒x² = 2r²
Area of the square inscribed in a circle = x²
= 2r²
Ratio of the area of the square inscribed in ( semicircle to the : circle )
= 4r²/5 / 2r²
= 2 / 5
= 2 : 5
Therefore, ratio of the area of the squares inscribed in a semicircle to the circle is 2 : 5.
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Enter the coordinates of the point
on the unit circle at the given angle.
270°
Answers
Answer: 0,-1
Step-by-step explanation:
Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?
They are commutative, because f(x) and g(x) are constant functions.
They are commutative, because f(g(x)) and g(f(x) are constant functions.
They are not commutative, because f(x) and g(x) are not equal.
They are not commutative, because f(g(x)) and g(f(x) are not equal.
Answers
Answer:
first option
Step-by-step explanation:
They are cumulative because they are constant functions.
Huey can wash 6 cars or mow 3 lawns in one hour. Dewey can wash 3 cars or mow 3 lawns in one hour. Louie can wash 3 cars or mow 6 lawns in one hour. They each work 8 hours per day. If two of them wash cars and one mows lawns then at most they can wash cars and mow lawns. Enter whole numbers.
Answers
At most, they can wash 96 cars and mow 96 lawns.
To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.
Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.
Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.
Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.
Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.
The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.
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remember, when something is below sea level we use a negative integer. write an integer to represent the elevation of the helicopter
Answers
Answer: If anything below sea level is a negative integer then anything above sea level is a positive integer. An integer that could represent a helicopter could be anything from +1 to +1000 and on.
How long is a banana
Answers
Answer:
6 - 9 inches long
Step-by-step explanation:
It depends on the size (small, medium, large) but this is the range.
Hope this helps!
Help please giving out brainless
How many moles of NaCI are needed to make 16.6 l of a 59.7 M NaCI solution
Answers
Answer:
3 moles NaCl to grams = 175.32831 grams 4 moles NaCl to grams = 233.77108 grams 5 moles NaCl to grams = 292.21385 grams 6 moles NaCl to grams = 350.65662 grams
\
Step-by-step explanation:
Which triangle is congruent to PQR?
A. aSTU
B. aJKL
C. aDEF
D. none
PLEASE HELP!!
Answers
chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
Answers
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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Daniella listened to a popular radio station for 1 hour. Then she made a circle graph ro summarize what she had heard.
Answers
Step-by-step explanation:
divide 2 add 5 divide 2 again
What is the solution to the equation 1/4x-1/8=7/8+1/2x?
X=-5
X=-4
X=4
Answers
the answer is x=-4 hope it helps
Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit
Answers
Answer:
its not 1, its the second one (B)
Step-by-step explanation:
Answer:
I know I'm 1 year late but B is the correct answer choice. I just did it on edge 2021.
I'm just big brain.Suppose that the function h is defined, for all real numbers, as follows.
Answers
Answer:
gsgdjdjchdvvdbdjzjsjsushsvvsvsvs I don't know
Answer:
see explanation
Step-by-step explanation:
h(- 3) with x = - 3, that is x ≠ 1 , then
h(- 3) = - \(\frac{1}{2}\) (- 3) + 2 = \(\frac{3}{2}\) + 2 = \(\frac{7}{2}\)
h(1) with x = 1 , then
h(1) = 1
h(3) with x = 3, that is x ≠ 1 , then
h(3) = - \(\frac{1}{2}\) (3) + 2 = - \(\frac{3}{2}\) + 2 = \(\frac{1}{2}\)
As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in 2012. (Source: Pew Research Center for the People and the Press). Each house-hold, of course, is independent of the others. Using the cooperation rate from 2012,
a) what is the probability that the next household on the list will be contacted but will refuse to cooperate?
b) what is the probability of failing to contact a house-hold or of contacting the household but not getting them to agree to the interview?
c) show another way to calculate the probability in b).
Answers
a) Thus, the probability of refusal is 86%. b) The probability of either failing to contact a household or contacting them but not getting them to agree to the interview is also 86%. c) Thus, the probability of either failing to contact a household or contacting them but not getting them to agree to the interview is 53.32%.
a) The probability that the next household on the list will be contacted but refuse to cooperate can be calculated by subtracting the cooperation rate from 100%. Since the cooperation rate is 14%, the probability of refusal is 100% - 14% = 86%.
b) The probability of either failing to contact a household or contacting them but not getting them to agree to the interview is also 86% based on the given information. This is because the cooperation rate represents the percentage of households that agree to participate, which implies that the remaining percentage (100% - 14% = 86%) includes both households that were not reached and households that were contacted but refused to cooperate.
c) Another way to calculate the probability in b) is by considering the two scenarios separately and then adding their probabilities. The probability of failing to contact a household can be calculated as the complement of the percentage of households reached, which is 100% - 62% = 38%. The probability of contacting a household but not getting them to agree to the interview is the cooperation rate multiplied by the percentage of households reached, which is 14% * 62% = 8.68%. Adding these probabilities together, we get 38% + 8.68% = 46.68%. However, since the question asks for the probability of either scenario occurring, we subtract this result from 100% to get 100% - 46.68% = 53.32%. Therefore, the probability of either failing to contact a household or contacting them but not getting them to agree to the interview is approximately 53.32%.
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32 times 49302019284848484
Answers
As you were organizing your closet you counted 20 shirts and 12 pairs of pants what was the pants to shirt ratio?
Answers
Answer is the ratio 3:5
Explanation:
To write the pants to shirt ratio, we write the numbers 12 and 20 in that order (since they correspond to the counts of each clothing item). Separate them with a colon to get 12:20
The last step is to divide both parts by the GCF 4
12/4 = 3
20/4 = 5
The ratio 12:20 fully reduces to 3:5
For every 3 pairs of pants, you have 5 shirts.
Urgent Please Help
Find the length of side x in simplest radical form with a rational denominator.
Answers
9514 1404 393
Answer:
x = 6
Step-by-step explanation:
The sides of an isosceles triangle are equal to each other in length.
x = 6
Can you guys help me answer question 1 and 2
Answers
what is the product of 5/12 and 8/15
Answers
Answer: 2/9
Step-by-step explanation:
Simplify the expression.
Solve, 7x-5y=20
-8x-3y=12
Answers
Answer:
x=0 y=-4
Step-by-step explanation:
SOMEBODY PLEASE HELP ME!!!!
Answers
Answer:
So the perimeter of the larger rectangle = 160
Step-by-step explanation:
We are given the scale factor of the two rectangles. We are given the perimeter of the smaller rectangle = 120.
Since the two rectangles are scaled, this means they have a common ratio. In other words:
\( \frac{perimeter \: of \: larger \: rectangle}{perimeter \: of \: smaller \: rectangle} = \frac{4}{3} \)
As given in the question.
Now we know the smaller rectangle has a perimeter of 120.
Let's take the perimeter of the larger rectangles as x.
\( \frac{x}{120} = \frac{4}{3} \\ \\ multiplying \: both \: sides \: by \: 120 \\ x = \frac{4}{3} (120) \\ x = 160\)
So the perimeter of the larger rectangle = 160
Amy wanted to review what others thought of a movie she was interested in before she rented it. She noticed that on the website from a large online retailer, the movie received an overall rating of 3.5 stars.
Which of the following, if true, represents selection bias?
Answers
Amy only reads the one star reviews to make a decision on whether or not to rent the movie.
What is selection bias?
An assertion that it is possible to produce mathematically important objects by choosing particular elements from predetermined sequences of sets is known as a selection principle in mathematics.
So one star reviews may contain:
1. their problem with the performance.
2. their main issue.
So, Amy needs to read one star reviews to decide whether to give a try or not.
BTW, the complete question is:
Amy wanted to review what others thought of a movie she was interested in before she rented it. She noticed that on the website from a large online retailer, the movie received an overall rating of 3.5 stars.
Which of the following, if true, represents selection bias?
1.Ratings and reviews for the movie where all submitted volunteerly to the online retailer's website
2.Amy reviews and equal number of different stars rating to get a sense of what all views thought about the movie.
3.Every person who rented the movie from the online retailer gave it a rating and review.
4.Amy only read some one star reviews to make a decision on whether or not to rent the movie
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if you dog a 6ft hole...how deep is that hole??
-Beetlejuice
Answers
Answer:
im confused lol
Step-by-step explanation:
Answer:
6ft
Step-by-step explanation:
8 x -1/4 x -7 cara ngerjain nya bagaimana?
Answers
8*(-1/4)*-7
=2*(-1)*(-7)
=14
please help me answer this question asap
Answers
Answer:
It's quite easy
Step-by-step explanation:
people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23
Therefore there are 23 people less than 30 years old.
pls mark me as brainliest pls.
5.
Bread
Cost ($)
Weight (oz)
16
Whole wheat
2.24
Pita
20
3.60
7-grain
16
2.56
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are th
38
Help me
Answers
Answer:
search on chrome 4 mor answer mwa mwa
Step-by-step explanation: