Question 3 of 12 Solve the given triangle. a = 5, c = 4, p = 117° Round your answers to one decimal place. A≈ i Y≈ i ! FIVE i < >
Answers
The approximate angle measures in degrees of A, B and C in the solved triangle are A ≈ 65.9°, B ≈ 53.4° and C ≈ 61.7°.
Given data;
a = 5c = 4p = 117°
Let's find b using the law of cosine, since it involves 3 sides of a triangle.
b² = a² + c² - 2ac cos (p)
b² = 5² + 4² - 2(5)(4) cos (117°)
b² = 25 + 16 - 40 cos (117°)
b² = 41 + 40 cos (117°)
b = √(41 + 40 cos (117°))
b ≈ 1.0∠106°
The angles can be found using the law of sine.
sin A/a = sin B/b = sin C/c
sin A/5 = sin 117°/1.0
sin A ≈ 0.9°A ≈ 65.9°
sin B/1.0 = sin 117°/b
Sin B ≈ (1.0)(sin 117°)/b
Sin B ≈ (1.0)(sin 117°)/(√(41 + 40 cos (117°)))
B ≈ 53.4°C ≈ 61.7°
The approximate angle measures in degrees of A, B and C in the solved triangle are A ≈ 65.9°, B ≈ 53.4° and C ≈ 61.7°.
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Related Questions
choose the x-intercept and y-intercept of the equation 6x-y=7a (0,-7)b (0,7)c (6/7,0)d (7/6,-7)e (7/6,0)
Answers
Given:
\(6x-y=7\)Find-: X-intercept and Y-intercept of the equation.
Sol:
For X-intercept value of "y" is zero.
\(\begin{gathered} 6x-y=7 \\ \\ y=0 \end{gathered}\)So, the x-intercept is:
\(\begin{gathered} 6x-y=7 \\ \\ y=0 \\ \\ 6x-0=7 \\ \\ 6x=7 \\ \\ x=\frac{7}{6} \end{gathered}\)The x-intercept is 7/6.
The Y-intercept of the equation then the value of "x" is zero.
\(\begin{gathered} 6x-y=7 \\ \\ x=0 \end{gathered}\)So, the y-intercept is:
\(\begin{gathered} 6x-y=7 \\ \\ x=0 \\ \\ 6(0)-y=7 \\ \\ 0-y=7 \\ \\ y=-7 \end{gathered}\)So, the y-intercept is -7.
\((x-\text{ intercept, }y-\text{ intercept\rparen = \lparen}\frac{7}{6},-7)\)A three-point estimate is an estimate that includes a(n) ____, most likely, and pessimistic estimate, such as three weeks, four weeks, and five weeks, respectively.
Answers
A three-point estimate is an estimate that includes an optimistic, most likely, and pessimistic estimate, such as three weeks, four weeks, and five weeks, respectively.
A three-point estimate is an estimate that includes a range of estimates based on different scenarios: the optimistic (best-case) estimate, the most likely estimate, and the pessimistic (worst-case) estimate.
This method helps to provide a more accurate project duration and cost estimation by considering potential variability and uncertainties.This type of estimation takes into consideration potential risks and uncertainties that may impact the project or task being estimated. By providing a range of estimates, a three-point estimate allows for a more accurate and comprehensive understanding of the possible outcomes and helps in making informed decisions. However, it is important to note that the three-point estimate is still just an estimate and is subject to change based on new information or changes in circumstances. In summary, a three-point estimate provides a more nuanced and detailed estimation approach that allows for better planning and decision-making.Thus, a three-point estimate is an estimate that includes an optimistic, most likely, and pessimistic estimate, such as three weeks, four weeks, and five weeks, respectively.Know more about the three-point estimate
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At a hotel, ( 3)/(4) of the 100 rooms are occupied today. Yesterday, ( 4)/(5) of the 100 rooms were occupied. On which day were more of the rooms occupied and by how much more?
Answers
Yesterday, 5 more rooms were occupied than today.
How to obtain the number of occupied rooms?The number of occupied rooms is obtained applying the proportions in the context of the problem.
Yesterday, the number of rooms occupied was given as follows:
4/5 x 100 = 0.8 x 100 = 80 rooms.
Today, the number of rooms occupied is given as follows:
3/4 x 100 = 0.75 x 100 = 75 rooms.
80 > 75, and the difference is given as follows:
80 - 75 = 5.
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what is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
0.688 will be the probability of getting a nickel from the jar.
Given,
Probability;-
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.
Therefore,
P(nickel) = 19/69
P(penny) = 17/68
That is,
P = 19/69 × 17/68
P = 323/4692
P = 0.0688
That is,
The probability of getting nickel from the jar is 0.06888
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19+4n
But "n=4"
IF YOU DON'T EXPLAIN OR PUT A FAKE ANSWER YOU WILL BE REPORTED
Answers
19 + 4(4)
= 19 + 16
= 35
multiplication is first because of bedmas
Answer:
35
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
19 + 4n
n = 4
Step 2: Evaluate
Substitute in n: 19 + 4(4)Multiply: 19 + 16Add: 35
Simplify each expression. Rationalize all denominators.
√(√16x⁴y⁴)
Answers
The expression √(√16x⁴y⁴) can be simplified to 2x²y.
To simplify the given expression, we need to apply the rules of square roots and simplify under the radical. Let's break down the steps:
Start with the expression √(√16x⁴y⁴).
Simplify the inner square root: √(16x⁴y⁴) = √(4²x⁴y⁴).
Apply the rule of square roots: √(a²) = a. In this case, a = 4xy.
Simplify the expression: √(4²x⁴y⁴) = 4xy.
Finally, simplify the outer square root: √(4xy) = 2xy.
Therefore, the simplified form of √(√16x⁴y⁴) is 2xy.
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What are the factors of 2x2 3x – 54? Select two options. 2x – 9 2x – 6 2x 6 x – 6 x 6.
Answers
The factors of expression \(2x^{2} +3x-54\) are (x+6) and (2x-9).
The given expression is: \(2x^{2} +3x-54\)
What is a factor?A factor is a number that divides another number leaving no remainder.
We can rewrite the given expression as:
\(2x^{2} +12x-9x-54\) (middle term has been splitted)
Take 2 as common from first two terms while take -9 as common from last two terms.
\(2x(x+6)-9(x+6)\)
Take (x+6) as common
\((x+6) (2x-9)\)
So, we got the factors (x+6) and (2x-9)
Therefore, The factors of expression \(2x^{2} +3x-54\) are (x+6) and (2x-9).
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solve this for me plz i need help
Answers
Answer:
it will be 9
Step-by-step explanation:
because I know it well
If you have $50 in yo ur bank account, deposit a $50 birthday check, and withdraw $20 to buy a shirt, how much is left in your account at the end?
Answers
Answer:
80
Step-by-step explanation:
50+50=100-20=80
50+50=100
100-20=80
please help i have no idea how to answer this
Answers
Multiple 1/4 x 1/8 to get your answer
Answer: 1/32
Step-by-step explanation: 1/4÷8+1/32 because, first, we have something called a reciprocal. 1/4÷8 is the original problem, but to make it easier we use a reciprocal. 1/4x1/8 is reciprocal. It used to be 8/1, but using the reciprocal we flip it over to make it 1/8, which gives us the answer 1/32. Good Luck and stay Brainly!
A bank manager wants to encourage new customers to open accounts with principals of at least $3000. He decides to make a poster advertising a simple interest rate of %3. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? Can the poster correctly say, "Open an account of $3000 and earn at least $10 interest in 1 month!"?
Answers
Therefore , the solution of the given problem of interest comes out to be Open an account of $3000 and earn at least $10 interest in 1 month! is false.
What exactly does interest mean?Divide the sum by the cost of funding, the remaining time, and other factors to obtain the simple interest rate. Principal college debt hrs. is the simplest return approach in marketing. The simplest technique for determining involvement is this one. As a percentage of the initial sum, income is typically calculated.
Here,
We can use the basic interest calculation to determine the principal:
=> I = Prt
12 months make one month.
We thus have:
=> 10 = P(0.03)(1/12)
When we simplify this solution, we obtain:
=> P = 10/(0.03)(1/12)
=> 10/(0.00333) = 3003
In order to make at least $10 in one month at a simple interest rate of 3%, the principal must be at least $3003.
Since a principal of $3000 would not make at least $10 in one month at a simple interest rate of 3%, the poster's claim that
"Open an account of $3000 and earn at least $10 interest in 1 month!" is false.
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Which of the following is a run on sentence
Answers
Answer:
D.
Step-by-step explanation:
It contains a comma, and a conjunction word.
Plz I need an Answer
Answers
Answer:
B
Step-by-step explanation:
Which one is non linear??
Answers
Answer:
The third one I think, I might be wrong.... hope this helps anyways :)
Step-by-step explanation:
Buying one movie ticket online costs $16.50. Two tickets cost $30.50. Assuming that the relationship is linear, what is the recursive formula? (remember recursive formula is An = An-1 + d)
1. An = A1 + (n - 1) +30.50
2. An = An-1 + 14 where A1 = 16.50
3. A20 = 231
4. An = 30.5 + 16.50
Answers
Answer:
c(n)= 14n+2.50
Step-by-step explanation:
Have a good day
Do not use EXCEL Assume that the average household expenditure during the first day of Christmas in Istanbul is expected to be $100.89. It is documented that the average spending in a sample survey of 40 families residing in Asian side of Istanbul is $135.67, and the average expenditure in a sample survey of 30 families living in European side of Istanbul is $68.64. Based on the past surveys, the standard deviation for families residing in Asian side is assumed to be $35, and the standard deviation for families living in European side is assumed to be $20. Using the information above, develop a 99% confidence interval for the difference between the expenditure of two average household residing in two different sides of Istanbul.
Answers
The 99% confidence interval for the difference in the mean expenditure between the two groups is $67.03 ± $14.84.
It is documented that the average spending in a sample survey of 40 families residing in Asian side of Istanbul is $135.67, and the average expenditure in a sample survey of 30 families living in European side of Istanbul is $68.64.
Based on the past surveys, the standard deviation for families residing in Asian side is assumed to be $35, and the standard deviation for families living in European side is assumed to be $20.
Using the above information, we can construct a 99% confidence interval for the difference between the two groups as follows:
Given that we need to construct a confidence interval for the difference in the mean spending of two groups, we can use the following formula:
\(CI = Xbar1 - Xbar2 \± Zα/2 * √(S1^2/n1 + S2^2/n2)\)
Here, Xbar1 = 135.67, Xbar2 = 68.64S1 = 35, S2 = 20n1 = 40, n2 = 30Zα/2 for 99% confidence level = 2.576Putting these values in the formula above, we get:
CI = 135.67 - 68.64 ± 2.576 * √(35^2/40 + 20^2/30)= 67.03 ± 14.84
Therefore,The difference in mean spending between the two groups has a 99% confidence interval of $67.03 $14.84.
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PLS HELP I WILL GIVE U BRAILIEST I need help
Copy and convert into numbers.
1.) 2.75 x 10-2 =
2.) 39,000,000,000 =
3.) .000002 =
4.) 7.368 x 104 =
Answers
Answer:
1)0.0275
2)3.9×10^10
3)2×10^-6
4)did u mean 10^4?
if so then it would be 73,680
explanation
1)2.75×10^-2
2.75×.01=0.0275
2)39,000,000,000.00
in scientific notations the first number has to be lower than 10 and higher than 1>
3.9 works so i would take the dot/period and bring it between 3 and 9, the dot would travel 10 places therefore you raise the 10 to the 10th power
3.9×10^10
4) and since 10 is raised to the 4th power you would just move the dot 4 places right and you get
7.368>73,680
A security camera in a neighborhood bank is mounted on a wall 12 feetabove the floor. What angle of depression should be used if the camera is tobe directed to a spot 4 feet above the floorand 40 feet from the wall?
Answers
Explanation
We are given the following:
• A security camera is mounted on a wall 12 feet above the floor.
We are required to determine the angle of depression when the camera is directed to a spot 4 feet above the floor and 40 feet from the wall.
This can be represented diagrammatically as:
We can extract a triangle from the diagram above as follows:
From the right-angled triangle above, we have:
\(\begin{gathered} Opposite=8ft \\ Adjacent=40ft \end{gathered}\)Finally, we can obtain the angle of depression as follows:
\(\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ \tan\theta=\frac{8}{40}=0.2 \\ \tan\theta=0.2 \\ \theta=\tan^{-1}(0.2) \\ \theta\approx11.3\degree \end{gathered}\)Hence, the angle of depression is 11.3°.
1. Find ALL x-value(s) for which the tangent line to the graph of y = x - 7x5 is horizontal. OA. x=0, x= -2.236, and x = 2.236 OB. x=0, x=-1, and x = 1 OC. x=-0.845 and x = 0.845 only OD. x = -2.236 a
Answers
The x-values for which the tangent line to the graph of y = x - 7x^5 is horizontal, we need to find the critical points where the derivative of the function is zero ,the correct answer is A. x = 0, x = -2.236, and x = 2.236.
First, let's find the derivative of y = x - 7x^5 with respect to x:
dy/dx = 1 - 35x^4
To find the critical points, we set dy/dx = 0 and solve for x:
1 - 35x^4 = 0
35x^4 = 1
x^4 = 1/35
Taking the fourth root of both sides:
x = ±(1/35)^(1/4)
x = ±(1/√(35))
Simplifying further:
x ≈ ±0.3606
x ≈ ±2.236
Therefore, the x-values for which the tangent line to the graph is horizontal are approximately x = -2.236 and x = 2.236.
Among the given answer choices:
A. x = 0, x = -2.236, and x = 2.236
B. x = 0, x = -1, and x = 1
C. x = -0.845 and x = 0.845 only
D. x = -2.236
The correct answer is A. x = 0, x = -2.236, and x = 2.236.
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el volumen de un cubo es de 125 cm3 ¿ cuantas veses aumentara el volumen de ese cubo si se duplica la medida de su arista
Answers
Answer: 8 times.
Step-by-step explanation:
I will answer in English:
This says:
The volume of a cube is 125cm^3
How many times the volume will increase if we duplicate the lenght of the side?
If L is the lenght of the side, we have that the volume of the cube is:
V = L^3
If we duplicate the lenght of the side, the new volume is:
V = (2*L)^3 = 8*L^3
So we can see that the volume of the new cube is 8 times the volume of the previous cube.
Now, we can do the math, for our original cube we have:
L^3 = 125cm^3
L = 5cm
the new cube has L' = 2*L = 10cm
The volume of this cube is:
V' = L'^3 = 10cm^3 = 1000cm^3
the ratio V'/V is:
1000cm^3/125cm^3 = 8
seventy-five percent of all u.s. adults use the internet. if a sample of 300 u.s. adults is taken, find the probability the sample proportion that use the internet is less than .80.
Answers
The probability that the sample proportion is less than 0.80 is approximately 0.989.
What is the given proportion of U.S. adults who use the internet in the problem?The probability that the sample proportion of U.S. adults using the internet is less than 0.80, we need to use the normal approximation to the binomial distribution. Given that 75% of all U.S. adults use the internet, the sample proportion will also be approximately 0.75.
We can calculate the standard deviation (σ) of the sample proportion using the formula sqrt((p*(1-p))/n), where p is the population proportion (0.75) and n is the sample size (300). In this case, σ is approximately 0.0217.
To convert the sample proportion to a standard normal distribution, we calculate the z-score using the formula (0.80 - 0.75) / 0.0217. The z-score is approximately 2.30.
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than 2.30 is approximately 0.989.
The probability that the sample proportion is less than 0.80 is approximately 0.989.
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which series of transformations shows that paralelogram abcd is congruent to parallelogram abcd by superimposing one onto the other
Answers
The series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other is a combination of translation and rotation that involves 150 degrees. A transformation refers to the process of changing an object's position, size, or shape.
Translation, reflection, rotation, dilation, and skew are the five basic transformation types that modify an object.In geometry, congruent shapes have the same shape and size. To superimpose one shape onto another means to make them coincide with each other.
The following series of transformations would show that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other: Step 1: Translation. Translate the parallelogram ABCD by 5 units to the right and 6 units down to obtain parallelogram A1B1C1D1.Step 2: Rotation. Rotate parallelogram A1B1C1D1 by 150 degrees counterclockwise around point A1 to obtain parallelogram A2B2C2D2.Step 3: Translation. Translate parallelogram A2B2C2D2 by 8 units to the right and 3 units up to obtain parallelogram A'B'C'D'.Thus, the series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other involves translation and rotation, with a rotation of 150 degrees.
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evaluate the variable expression 2n + 4 if n equals 3
Answers
Answer:
10
Step-by-step explanation:
00
8 ABCD is a parallelogram. E and F are respectively the orthogonal projections of A and
on line (BD).
1) Prove that the triangles AED and BCF are congruent.
allelogram
Answers
Answer:
LATIHAN ULASAN is a very good friend and a good person to work with and I am sure he will be a good candidate for the role
Step-by-step explanation:
Who is he going to travel there for a few days now and is there a way to
How do you prove f is one to one?
Answers
To prove that f is one-to-one function, it must be proven that f(x1)=f(x2) and x1=x2.
What is a one to one function?
The mapping of two sets is essentially what a one to one function refers to. When every element in a function's range and domain match exactly one another, the function is said to be one-to-one.
The one-to-one function, also known as an injective function, is one of the many different types of functions.
A function that transfers different components of its domain to different elements of its codomain is known as a one-to-one function.
For example, a function f:A→B is said to be one-to-one if -
f(x1)=f(x2)⇒x1=x2
for all elements x1,x2∈A.
To prove f:A→B is one-to-one -
Consider the fact that f(x1)=f(x2).
Then it must be true that x1=x2.
Therefore, it is now understood that f is one-to-one by definition if f(x1)=f(x2) and x1=x2.
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y 5 points The devilled eggs that Hayden made over Thanksgiving break required 10 cups of mustard. If he measured this in quarts, how many quarts would the 10 cups represent? 1 gallon (gal) = 4 quarts (qt) 1 quart (t) = 2 pints (pt) 1 pint (pt) = 2 cups (c) 1 cup (C) = 8 fluid ounces (fl oz) 2.5 quarts 5 quarts 20 quarts 40 quarts
Answers
Answer: 2.5 cups
Step-by-step explanation:
PLEASE HELP MEEEEEEEEEEEEEEEEE
Answers
Answer:
A- 5 banners
B- 2 banners
C- 2 banners
D- Shade banner 2
It takes 3 egg to make two dozen cookies about what fracion of an aegg are in two cookiies
Answers
Answer:1/4
Step-by-step explanation:3*2/(2*12)=1/4 so our answer is 1/4.
Which condition is characterized by cyanosis and pain in the fingers due to extreme vasoconstriction in the digits resulting from excessive sympathetic stimulation
Answers
The condition characterized by cyanosis and pain in the fingers due to extreme vasoconstriction in the digits resulting from excessive sympathetic stimulation is called Raynaud's phenomenon.
Raynaud's phenomenon occurs when blood vessels, specifically the small arteries that supply blood to the fingers, constrict excessively in response to cold or emotional stress. This constriction reduces blood flow to the affected areas, leading to cyanosis (bluish discoloration), pain, and numbness in the fingers.
The underlying cause of Raynaud's phenomenon is an imbalance in the autonomic nervous system, particularly an overactivity of the sympathetic nervous system. This system is responsible for the "fight or flight" response and, when stimulated, can cause blood vessels to constrict.
Raynaud's phenomenon is characterized by:
1. Cyanosis: Bluish discoloration of the fingers due to reduced blood flow.
2. Pain and numbness in the fingers.
3. Extreme vasoconstriction: Constriction of small arteries supplying blood to the digits.
4. Excessive sympathetic stimulation: Overactivity of the sympathetic nervous system leads to constriction of blood vessels.
If you experience symptoms of Raynaud's phenomenon, it is essential to consult with a medical professional for proper diagnosis and treatment.
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can the angles with measures 80o , 55o and 65o form angles on a line
Answers
Answer:
Nope, this is because the angles in a triangle add up to 180, whereas these values added are equal to 200 degrees
No, the angles with measures 80°, 55°, and 65° cannot form angles on a line.
In geometry, angles on a line are also known as "linear angles" or "straight angles." A straight angle measures 180°, and it is formed by two rays that point in opposite directions and share a common endpoint, creating a straight line. To determine if the given angles can form a straight angle, we need to add their measures.
Let's calculate the sum of the given angles:
Sum = 80° + 55° + 65°
= 200°
Since the sum of the given angles (200°) is not equal to 180°, it means that the angles cannot form a straight line. Instead, they form a shape that is not a straight angle, such as a triangle or a polygon.
In this case, the given angles form a triangle since they satisfy the triangle inequality theorem. The sum of any two sides of a triangle is always greater than the third side. Mathematically, for a triangle with sides of lengths a, b, and c, the inequality holds: a + b > c, b + c > a, and c + a > b.
Therefore, the angles with measures 80°, 55°, and 65° cannot form angles on a line but rather form a triangle with a sum of 180°, satisfying the triangle inequality.
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