Given that ABC has mA = 63°, b = 9, and c = 11, find the remaining side length a and angles B and C, rounded to the nearest tenth.
Answers
Given:
angle A = 63 degrees
side b = 9
side c = 11
Asked: Find angles B and C and the length of side a.
Solution:
First, we need to find the length of side a using the cosine law.
Cosine Law:
\(a^2=b^2+c^2-2bc\cos A\)Now, let's substitute the given to the formula.
\(\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ a=\sqrt[]{b^2+c^2-2bc\cos A} \\ a=\sqrt[]{9^2+11^2-2\cdot11\cdot9c\cos63} \\ a=10.58819536 \end{gathered}\)Now, to find the angles B and C, we will use the sine law.
Sine Law:
\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)Now, let's use the value of a in the sine law. Let's get angle B first.
\(\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ a\sin B=b\sin A \\ \frac{a\sin B}{a}=\frac{b\sin A}{a} \\ \sin B=\frac{b\sin A}{a} \\ B=\sin ^{-1}(\frac{b\sin A}{a}) \\ B=\sin ^{-1}(\frac{9\sin63}{10.58819536}) \\ B=49.2318706 \end{gathered}\)Let's repeat the process to get angle C.
\(\begin{gathered} \frac{a}{\sin A}=\frac{c}{\sin C} \\ a\sin C=c\sin A \\ \frac{a\sin C}{a}=\frac{b\sin A}{a} \\ \sin C=\frac{c\sin A}{a} \\ C=\sin ^{-1}(\frac{c\sin A}{a}) \\ C=\sin ^{-1}(\frac{11\sin 63}{10.58819536}) \\ C=67.7681294 \end{gathered}\)Note: The sum of the internal angles of a triangle is always 180 degrees.
We can check or work if it is equal to 180 degrees, then everything is correct.
\(\begin{gathered} A+B+C=180 \\ 63+49.2318706+67.7681294=180 \\ 180=180 \end{gathered}\)ANSWER:
length of side a = 10.6 (Rounded to the nearest tenth.)
Angle B = 49.2 degrees (Rounded to the nearest tenth.)
Angle C = 67.8 degrees (Rounded to the nearest tenth.)
Related Questions
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Question 3
Mr Dladla wants to open a training company, he will be training Learnerships and
ABET. He plans to operate at South Gate Mall with the total Market share of 4500
customers per month. He knows that he can only expect 50% of the market share for
the year.
His selling price will be R500 and the cost of running his course in R300. His training
company opens 20 days per month.
(10)
3.1 Calculate his gross profit per day and thereafter
Answers
Answer:
To calculate Mr. Dladla's gross profit per day, we first need to calculate his total revenue and total cost per month:
Total revenue per month = Selling price x Expected market share per month
Total revenue per month = R500 x (50% of 4500 customers) = R112,500
Total cost per month = Cost per course x Number of courses per month
Total cost per month = R300 x 20 days = R6,000
Gross profit per month = Total revenue per month - Total cost per month
Gross profit per month = R112,500 - R6,000 = R106,500
To calculate his gross profit per day, we can divide the gross profit per month by the number of days the training company opens per month:
Gross profit per day = Gross profit per month / Number of days per month
Gross profit per day = R106,500 / 20 days = R5,325 per day
Therefore, Mr. Dladla's gross profit per day is R5,325.
Step-by-step explanation:
Misty’s surgery lasted 214 hours. Convert the time to seconds.
Answers
Answer:
770,400
Step-by-step explanation:
770,400 seconds
Order the decimals from least to greatest.
-1.38
0.76
-0.5
-1.4
1.9
Answers
Answer:
answer in explanation
Step-by-step explanation:
-1.4
-1.38
-0.5
0.76
1.9
the √105 is between which two numbers
Answers
Answer:
Since 100<105<121, 10<square root of 105<11. So the square root of 105 is between 10 and 11.
Step-by-step explanation:
How to solve the problem of equivalent fractions
Answers
1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively
What is Equivalent Fraction?The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
1/2 = /6 = /8.
a. Multiply numerator and denominator by 3 for equivalenting the equation /6
Therefore,
3*3/6*3
=9/18
=1/2
therefore:1/2=1/2.
b. Multiply numerator by 4
Therefore,
4/8
=1/2.
Therefore:
1/2=1/2.
1/2=1/2=1/2.
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The lay in Burlington collected $3 930 in overdue fees last year. This year, the library
collectieted 3144 What is the percent of decrease in the amount collected?
Answers
Answer:
We conclude that the percent of decrease = 20%
Step-by-step explanation:
Given
Original amount = $3930Amount of decrease = $3930 - $3144 = $786Using the formula
Percent of decrease = ( amount of decrease / orignal amount × 100 ) %
= ( 786 / 3930 × 100 ) %
= ( 0.2 × 100 ) %
= 20%
Therefore, we conclude that the percent of decrease = 20%
HELP ME FAST WILL GIVE BRAINLY
A bag contains 16 white marbles, 10 blue marbles and 12 red marbles. Give each ratio as a reduced fraction.
A) The ratio of white marbles to blue marbles.
B) The ratio of red marbles to total marbles.
Answers
the total of marbles = 16 + 10 +12 =38
A) white : blue = 16/10 = 8/5
B) red : total = 12/38 = 6/19
Step-by-step explanation:
1. find the total of marbles
Helpme with this math
Answers
The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.
What is volume?Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:
LitersOunceCubic metersBased on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.
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Find all of square roots of 36i and write the answers in rectangular (standard) form
Answers
r = √(0^2 + 36^2) = 36
θ = tan^-1(0/36) + kπ = kπ (where k is an integer)
Since 36i lies on the positive imaginary axis, we can choose k = 1/2 so that θ = π/2.
Thus, 36i in polar form is 36(cos(π/2) + i sin(π/2)).
Now we can find the square roots of 36i by taking the square root of the magnitude and dividing the angle by 2:
√36(cos(π/4) + i sin(π/4)) = ± 3(cos(π/8) + i sin(π/8))
√36(cos(9π/4) + i sin(9π/4)) = ± 3(cos(9π/8) + i sin(9π/8))
Therefore, the square roots of 36i in rectangular form are:
±3(cos(π/8) + i sin(π/8)) and ±3(cos(9π/8) + i sin(9π/8))
C-3d = 11
-2c + 3d = -16
Answers
This looks like a system of equations:
We should solve for c on the first equation because we can substitute for c. There are a lot of ways we can do a system of equations, but I will do this.
c - 3d = 11
+3d +3d
c = 11 +3d
Now we can substitute.
-2(11+3d) + 3d = -16
solve
-22 + -6d + 3d = -16
-22 + -3d = -16
+22 +22
-3d = 6
/-3 /-3
d = -2
So we have found d. We can solve for c.
c - 3(-2) = 11
c + 6 = 11
-6 -6
c = 5
Now we know both D and C. d=-2 and c=5
4. Sketch the graph of F(x) = 1 +x/x²-1
Answers
The graph of the function is attached below.
What is the graph of a function?The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.
Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.
We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.
In the given problem;
The graph of the function f(x) = 1 + x / x² - 1 is attached below;
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Which parallelogram (if any) is a rectangle? By what property?
1
90°
H
A
B
B
D A
88°
11
440-40
Alcance
88
C
Answers
The conclusion on the properties of parallelogram is that only Parallelogram II is a parallelogram by Congruent diagonals property.
How to identify the properties of the parallelogram?If a quadrilateral possesses a pair of parallel opposite sides, then it’s referred to as a special polygon called Parallelogram. The properties of a parallelogram are as follows:
1) The opposite sides are parallel and equal
2) The opposite angles are equal
3) The consecutive or adjacent angles are supplementary
4) If any one of the angles is a right angle, then all the other angles will be at right angle
5) The two diagonals bisect each other
6) Each diagonal bisects the parallelogram into two congruent triangles
7) The Sum of the square of all the sides of a parallelogram is equal to the sum of the square of its diagonals. It is also called parallelogram law
Looking at the figure I, we see that it appears to be a parallelogram, but we don't know if the diagonals bisect each other.
However, for the second image II we see that the diagonals clearly bisect each other at point E and as such only Parallelogram II is a parallelogram by Congruent diagonals property.
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The perimeter of Marisa's garden is 32 feet. The width is 6 feet. What is the length of
Marisa's garden?
Answers
The length of Marisa's garden is 10
What is the length of Marisa's garden?The given parameters are:
Perimeter = 32 feet
Width = 6 feet
The perimeter is calculated as:'
Perimeter = 2 * (Length + width)
So, we have
2 * (Length + 6) = 32
Divide by 2
Length + 6 = 16
Subtract
Length = 10
Hence, the length of Marisa's garden is 10
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Translate 2 3 y − 9 < y + 1 into a sentence. Nine than two-thirds of number is less than the number .
Answers
The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:
"2/3y" represents two-thirds of a number.
"9" represents the number nine.
"y + 1" represents the number increased by one.
Now let's construct the sentence:
"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.
"is less than" - This is the comparison symbol in the inequality.
"the number" - This refers to the expression "y + 1," representing the number increased by one.
Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."
Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."
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Which statements are true based on the Pythagorean identities??
Answers
Answer:
2 .3 and 5
Step-by-step explanation:
The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. Construct a 92% Confidence Interval for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the Ice Chalet.
Answers
Answer:
The 92% Confidence Interval for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the Ice Chalet is (0.722, 0.878).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
For this problem, we have that:
64 + 16 = 80 children, of which 80 are girls. So
\(n = 80, p = \frac{64}{80} = 0.8\)
92% confidence level
So \(\alpha = 0.08\), z is the value of Z that has a pvalue of \(1 - \frac{0.08}{2} = 0.96\), so \(Z = 1.75\).
The lower limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 1.75\sqrt{\frac{0.8*0.2}{80}} = 0.722\)
The upper limit of this interval is:
\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 1.75\sqrt{\frac{0.8*0.2}{80}} = 0.878\)
The 92% Confidence Interval for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the Ice Chalet is (0.722, 0.878).
Please help me w this hehehehehh
Answers
Answer:
-25x-45y, because if we have got + and -, so we will write minus.
What is BD? BC=x DC=x+5
Answers
Answer:
BD is just equal to the sum of BC and CD.
So we have: BD = x + x + 5
Simplifying, we have BD = 2x+5
Let me know if this helps!
what are the answers? thank you.
Answers
Answer:
176.78cm squared,23.57cm,Step-by-step explanation:
inorder to solve the area of the shaded area;°/360ñRsquared
arc length you use ;°/360ñD
PLEASE ASAP, question in photo
Answers
Answer:
m<5 = 142
Step-by-step explanation:
does anyone have the keys for edmentum guided notes!!! please help
Answers
It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.
Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.
They are in the best position to provide you with the necessary guidance and support.
Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.
This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.
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Note: If p(a) = 0 then (x - a) is a factor of p(x)
given that f(-1), f(-2) are zeros of f(x) find the missing values of these coefficients p, q
f(x) = x³ + px² - qx - 4
After finding the values of the coefficients factor and find the solutions of x1, x2 and x3.
Answers
Answer:
Since f(-1) = 0 and f(-2) = 0, we can set up two equations:
(-1)³ + p(-1)² - q(-1) - 4 = 0
(-2)³ + p(-2)² - q(-2) - 4 = 0
Simplifying each equation, we get:
-1 + p - q - 4 = 0
-8 + 4p - 2q - 4 = 0
Simplifying further, we get:
p - q = 5
2p - q = 6
Solving for p and q, we can add the two equations together to eliminate q:
p - q + 2p - q = 5 + 6
3p - 2q = 11
Then, we can substitute the value of q from the first equation into this equation to solve for p:
3p - 2(q + 5) = 11
3p - 2q - 10 = 11
3p - 2q = 21
3p - 2(5 + p) = 21
p - 10 = 7
p = 17
Substituting this value of p into either equation for q, we get:
q = p - 5 = 12
Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:
-1 | 1 17 -12 -4
|__ -1 -16 28
1 1 12
This gives us the factorization:
f(x) = (x + 1)(x² + x + 12)
To find the solutions, we can use the quadratic formula on the quadratic factor:
x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)
x = (-1 ± sqrt(1 - 48)) / 2
x = (-1 ± sqrt(-47)) / 2
x1 = (-1 + i(sqrt(47))) / 2
x2 = (-1 - i(sqrt(47))) / 2
Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.
Step-by-step explanation:
give me thanks for more! your welcome bud!
I need help on this ?
Answers
Answer:
The Void
Step-by-step explanation:
no one can help you now
The sun of a number and 12 divided by 4 is -7
Answers
Answer:
-40
Step-by-step explanation:
-40+12=-28
-28/4
=-7
-4(3x - 2x + 4y)
Simplify the expression
Answers
Answer:
− 4 x − 16 y
Step-by-step explanation:
Answer:
− 4 x − 16 y
Step-by-step explanation:
The results of a linear regression are shown below.
y= ax + b
a = -1.15785
b= 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship between x and y?
1)Strong Postive Correlation
2)Strong Negative Correlation
3)Weak Positive Correlation
4)Weak Negative Correlation
Answers
Answer:
2) Strong Negative Correlation
Step-by-step explanation:
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
3. Which of the following equations represents a line that does not intersect the x-axis?
Explain your answer.
a. x = 4
b. y =-5
C. y = 2x - 4
d. 3x - 8y = 17
Answers
Having trouble with these questions, please help.
Answers
99.7 % random variable values are between
±
three standard deviation.
95 % random variable values are between
±
two standard deviation.
68 % random variable values are between
±
one standard deviation. There you go!
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean is y¯ = 3.15 kg and the standard deviation is 250 grams. (a) Calculate a 95% confidence interval for the population mean birth weight in these hospitals. (b) The typical weight of a baby at birth for the US population is 3.25 kg. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3.25 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct.
Answers
a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).
(b)The P-value is 0.0068.
What is hypothesis testing?To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.
Why is hypothesis testing used?A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.
C.I=x-t(alpha/2)xs/sqrt{n}
=3150+_2.01*250/sqrt{50}
=(3078.9358,3221.0642)
b) P value =P(t<-2.83)+P(t>2.83)
use calculator
=0.0034+0.0034
=0.0068
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