Consider a triangle ABC like the one below. Suppose that A = 31°, C = 52°, and b = 29. (The figure is not drawn to scale.) Solve the triangle.Round your answers to the nearest tenth.If there is more than one solution, use the button labeled "or".
Answers
a = 15, b = 29 and c = 23
A= 31º B= 97º C= 52º
1) To solve a triangle is to find out its angles and measures. Since we have angle A= 31º, C =52º, and b= 29 we can solve this by using the Sum of Interior angles and the Law of sines:
\(\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}\)2) The sum of the interior angles of a Triangle is 180º So, we can find angle B this way
∠A +∠B+∠C= 180º
31º +∠B +52º = 180º
∠B + 83º = 180º Subtract 83 from both sides
∠B =97º
\(\begin{gathered} \frac{29}{\sin(97)}=\frac{c}{\sin(52)} \\ \\ c=\frac{29\cdot\sin(52)}{\sin(97)}\Rightarrow c\approx23 \end{gathered}\)2.2) Now we can find the leg "a "
\(\begin{gathered} \frac{a}{\sin (31)}=\frac{29}{\sin (97)} \\ a\cdot\sin (97)\text{ = 29 }\cdot\sin (31) \\ a=\frac{29\cdot\sin (31)}{\sin (97)}\Rightarrow a\approx15 \end{gathered}\)3) Hence, the answer is
a = 15, b = 29 and c = 23
A= 31º B= 97º C= 52º
Related Questions
A pair of equations is shown below.
x + y = 5
y = one halfx + 2
If the two equations are graphed, at what point do the lines representing the two equations intersect?
(2, 5)
(5, 2)
(2, 3)
(3, 2)
Answers
Answer:
(2,3)
Step-by-step explanation:
graph the equations of the lines and then look which point they intersect which in this case is over 2 and up 3 so (2,3)
Answer:
C (2' 3) is the correct one i got it right on my test
Step-by-step explanation:
work out the total surface area of this triangular prism 12cm by 5cm by 10cm by 13cm
Answers
To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.
The triangular faces have base 5cm and height 12cm, so each one has an area of:
(1/2) x 5cm x 12cm = 30cm²
There are two of these faces, so their combined area is:
2 x 30cm² = 60cm²
The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:
5cm x 10cm = 50cm²
5cm x 13cm = 65cm²
Again, there are two of these faces, so their combined area is:
2 x (50cm² + 65cm²) = 230cm²
Finally, we add up the areas of all the faces to get the total surface area:
60cm² + 230cm² = 290cm²
Therefore, the total surface area of this triangular prism is 290cm².
math math math math math math math
Answers
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
learn more on angles here: brainly.com/question/18854964
#SPJ1
The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
Learn more about bisecting of angles on https://brainly.com/question/23984603
#SPJ1
Freshman, sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question - agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have
Answers
Answer:
The degrees of freedom is 6 for the chi square independence test.
Step-by-step explanation:
This is test hypothesis of independence. The test statistic under H0 is
χ²= ∑ (O - E)²/ E
where O is the observed and E is the expected frequency
which has an approximate chi square distribution with ( r-1) (c-1) degrees of freedom, where r= rows and c= columns.
Here there are 4 rows and 3 columns
Hence the degrees of freedom will be
( 4-1) ( 3-1)= 3*2= 6
!!
8 cm
20 cm
O 503 cm
O 4,021 cm
O 1,005 cm?
O 1,407 cm?
Answers
Answer:
1,005cm²
Step-by-step explanation:
First, you need to know the area of a cylinder and also the value of pi.
Area = 2πrh
pi = π = 3.14
r = radius = 80cm
h = height of cylinder = 20
now let's substitute
\(2 \times 3.14 \times 80 \times 20 = 1004.9{cm}^{2} \)
but to the nearest square centimetre is.
1005cm²
because the number after the point is more than 4 so we add one to the last number before the point.
Which fraction is NOT equivalent to 20%?* 0 20/100 04/20 6/40 O 2/10
Answers
Answer:
6/40
Step-by-step explanation:
its 6/40 because 6 is not 20 percent of 40.
Pleaseeeeeee help me
Answers
Answer:
-56
Step-by-step explanation:
(6 ✕–8) – 8
–48–8
= –56
If I read 4 pages of a book in 5 minutes, how many pages did I read per minute?
Answers
Answer:
about a half a page
Step-by-step explanation:
Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares.
Answers
The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units
The radius of the base = 4 units
The length of the side of the square = 2x
The area of the square = a^2
Where a is side of the square
The area of the square = (2x)^2
= 4x^2
The equation of the circle is
x^2 + y^2 = 16
x^2 = 16 - y^2
The area = 4(16 - y^2 )
= 64 - 4y^2
The volume of the square
V = \(\int\limits^a_b {A(y)} \, dy\)
= \(\int\limits^4_0 {64-4y^{2} } \, dy\)
= 64×4 - 4×(4^3/3)
= 256 - 256/3
= 512/3 cubic units
Therefore, the volume of the solid is 512/3 cubic units
Learn more about volume here
brainly.com/question/29676992
#SPJ4
What is the solution to the equation -3(h+5) + 2 = 4(h+6)-9?
n = 4
n=-2
n=2
n=4
Answers
-3(h+5) + 2 = 4(h+6) -9
-3h-5 + 2 = 4h+24 -9
-3h-4h = 24-9+5-2
-7h = 18
h = -18 = -2.57
7
Which of the following would you see on a circle graph?
OA. Percentages
OB. Bars
C. Points
OD. A y-axis
Answers
A, percentages
You would see percentages on a circle graph, because it's how many parts of the whole that they take up.
Happy to help, have a great day! :)
In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
Answers
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
For similar question on length.
https://brainly.com/question/30582409
#SPJ8
Conrad paid $52.26 for a pair of shoes. Michelle paid $3.89 more for a pair of shoes than Conrad paid for his.
Answers
Answer:Michelle paid $56.15 for her shoes
Step-by-step explanation:
Answer:Michelle paid $56.15 for her shoes
Step-by-step explanation:
Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.
$3.89+$52.25= $56.15
Read more on Brainly.com - https://brainly.com/question/12415872#readmore
What Is a constant or the product of a constant and one or more variables
Answers
Answer:
A constant or the product of a constant and one or more variables is called a coefficient.
Hope it helps you.The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 17 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) For a single randomly selected movie, find the probability that this movie's production cost is between 55 and 58 million dollars. For the group of 17 movies, find the probability that the average production cost is between 55 and 58 million dollars. For part d), is the assumption of normal necessary? NoYes
Answers
Using the normal distribution, we have that:
The distribution of X is \(X \approx (57,22)\).The distribution of \(\mathbf{\bar{X}}\) is \(\bar{X} \approx (57, 5.3358)\).0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).In this problem, the parameters are given as follows:
\(\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358\)
Hence:
The distribution of X is \(X \approx (57,22)\).The distribution of \(\mathbf{\bar{X}}\) is \(\bar{X} \approx (57, 5.3358)\).The probabilities are the p-value of Z when X = 58 subtracted by the p-value of Z when X = 55, hence, for a single movie:
X = 58:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{58 - 57}{22}\)
Z = 0.05.
Z = 0.05 has a p-value of 0.5199.
X = 55:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{55 - 57}{22}\)
Z = -0.1.
Z = -0.1 has a p-value of 0.4602.
0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.
For the sample of 17 movies, we have that:
X = 58:
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{58 - 57}{5.3358}\)
Z = 0.19.
Z = 0.19 has a p-value of 0.5753.
X = 55:
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{55 - 57}{5.3358}\)
Z = -0.38.
Z = -0.38 has a p-value of 0.3520.
0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
Answer this (the question is in the picture)
Answers
The slope of the line perpendicular to line B is given as follows:
-2/5.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The slope of a linear function is calculated as the change in y divided by the change in x, hence the slope of line B is given as follows:
m = (5 - (-5))/(3 - (-1))
m = 10/4
m = 5/2.
When two lines are perpendicular, the multiplication of their slopes is of -1, hence:
5m/2 = -1
5m = -2
m = -2/5.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
Determine the equation of the parabola that opens to the right, has focus (13,-6),
and a focal diameter of 28.
Answers
The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.
To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:
\((x - h)^2 = 4p(y - k)\)
Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).
We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.
We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.
Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.
for such more question on parabola
https://brainly.com/question/18274774
#SPJ11
Find the polar equation of the conic with focus at the pole, directrix y=3 and eccentricity of 2.
Answers
To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.
The general form of the polar equation for a conic with focus at the pole is given by:
r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)
Where:
- r is the distance from the origin (pole) to a point on the conic.
- e is the eccentricity.
- d is the distance from the pole to the directrix.
- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.
- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.
In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.
Substituting these values into the general equation, we get:
r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)
Simplifying further:
r =\(\frac{6}{1+2\cos(\theta)}\)
Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:
r =\(\frac{6}{1+2\cos(\theta)}.\)
This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.
For more such question on polar equation
https://brainly.com/question/9363127
#SPJ8
NEED HELP NEED ANSWERED TODAY
Answers
By composite compostion f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions
How to show that f(x) and f⁻¹(x) are inverse functions using composite composition?
A function is a relationship between inputs where each input is related to exactly one output.
Given: f(x) = 5x-6 and f⁻¹(x) = (x+6)/5
To show the inverse relationship exists using composite composition, f(f⁻¹(x)) must be equal to f⁻¹(f(x))
Let's check:
f(f⁻¹(x)) = f((x+6)/5)
Substitute x = (x+6)/5 into f(x) = 5x-6:
f(f⁻¹(x)) = 5((x+6)/5) - 6
f(f⁻¹(x)) = (x+6)- 6
f(f⁻¹(x)) = x
Also,
f⁻¹(f(x)) = f⁻¹(5x-6)
Substitute x = 5x-6 into f⁻¹(x) = (x+6)/5:
f⁻¹(f(x)) = ((5x-6)+6)/5
f⁻¹(f(x)) = 5x/5
f⁻¹(f(x)) = x
Since f(f⁻¹(x)) = f⁻¹(f(x)). Therefore, f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions
Learn more about composite composition of inverse function on:
brainly.com/question/29363352
#SPJ1
Find the product
4x4 1/2 =
Answers
Answer:
8
\(4 \times 4(1 \div 2) \\ \)
4 gets cancelled by 2 for times i.e
4
\( 4 \times 2\)
=8
Write 80% as a decimal.
I
help me??
Answers
Answer:
0.8
Step-by-step explanation:
Use the graph of the parabola to fill in the table.
(a) Does the parabola open upward or downward?
upward
downward
(b) Find the coordinates of the vertex.
vertex: (2,-6)
(c) Find the equation of the axis of symmetry.
equation of axis of symmetry:
(d) Find the intercept(s).
For both the x- and y-intercept(s), make sure
to do the following.
If there is more than one, separate them
with commas.
If there are none, select "None".
x-intercept(s):
Answers
(b) The vertex is (2,-6).
(c) The equation of the axis of symmetry is x = 2.
(d) The x-intercepts are (0,12) and (4,12) and the y-intercept is (0,0).
9-12 Use the properties of logarithms to expand the quantity.
11. \(\ln \frac{x^{2}}{y^{3} z^{4}}\)
Answers
Step-by-step explanation:
lnx² - lny³ - lnz⁴
2lnx - 3lny -4lnz
question is in the picture, thank you so much in advance.
Answers
Answer:
y¹⁰
Step-by-step explanation:
Let’s say y=2.
This means 2 to the power of 4 is 16.
Then, we do 16 times 2, because it says y4 times 6.
16 times 2 is 32.
Now we find what 2 to the power of 5 is.
That is also 32.
Finally, we do 32 times 32 which is 1,024.
As you can see, we used 2, aka y 10 times. This is because y4 has 4 y’s, and y5 has 5 y’s. Then, there is one extra y in the middle.
Therefore, 4 + 5 + 1 is equal to 10.
This can be written as y10.
hope this helped!
Correct answer only plz!!!
Answers
=====================================================
Explanation:
Since we have two pairs of congruent opposite sides, we can prove this quadrilateral is a parallelogram (using the SSS congruence rule).
Any parallelogram has opposite angles that are congruent. Therefore, angle A = angle D = 116
what this solving system of equations?
x+y=-3
y=x^2+4x+1
Answers
Answer:
Step-by-step explanation:
y = -x-3
y = x^2 + 4x + 1
x^2 + 4x + 1 = -x-3
x^2 + 5x + 4 = 0
Quadratic Formula
x = [-5±√(5²-4⋅1⋅4)]/[2⋅1] = [-5±√9]/2 = [-5±3]/2 = 1,-4
(x,y) = (1,-4) of(-4,1)
Answer:
x = -4, y = 1
x = -1, y = -2
Step-by-step explanation:
(1) x + y = -3 (2) y = \(x^{2} +4x + 1\)
y = -x - 3 -x - 3 = \(x^{2} +4x + 1\)
\(x^{2} + 5x + 4 = 0\\\)
(x + 4)(x + 1) = 0
x = -4 or x = -1
y = -(-4) - 3 = 4 - 3 = 1
y = -(-1) - 3 = 1 - 3 = -2
name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
Answers
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
The numbers 24, 22, 34, 28, 29, 24, 25 29, a and b have a median of 27 and a mode of 29. Given that a
Answers
Answer: Median is 26,5 and modes are 24 and 29
Step-by-step explanation: In increasing order numbers are
22, 24 24, 25 , 28, 29 , 29 , 34. Because amount of number is even
median is (25 + 28) / 2 = 26,5 and modes are 24 and 29 because both
numbers exist twice
I will give brainliest and ratings if you get this correct
Answers
Using Cramer's rule for first-order condition:
x₁ = -149/444x₂ = -69/222x₃ = 139/444Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.
How to determine 1st and 2nd order condition?(a) Using Cramer's rule for the first-order condition:
To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:
∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]
Setting the gradient equal to zero:
6x₁ - x₂ - 3x₃ - 5 = 0 (1)
-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)
2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)
Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:
|A| =
| 6 -1 -3 |
|-1 12 2 |
|-3 2 -3|
|A| = 444
The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:
|A₁| =
| 5 -1 -3 |
| 0 12 2 |
| 0 2 -3|
|A₁| = -149
The determinant of the matrix obtained by replacing the second column of A with the constants is:
|A₂| =
| 6 5 -3 |
|-1 0 2 |
|-3 0 -3|
|A₂| = -138
The determinant of the matrix obtained by replacing the third column of A with the constants is:
|A₃| =
| 6 -1 5 |
|-1 12 0 |
|-3 2 2|
|A₃| = -278
Therefore, using Cramer's rule:
x₁ = |A₁|/|A| = -149/444
x₂ = |A₂|/|A| = -69/222
x₃ = |A₃|/|A| = 139/444
(b) Using the Hessian for the second-order condition:
To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:
(y) =
| 6 0 -3 |
| 0 12 2 |
|-3 2 8 |
Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):
H(y) =
| 6 0 -3 |
| 0 12 2 |
|-3 2 8 |
The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.
Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.
Find out more on first-order condition here: https://brainly.com/question/31451579
#SPJ1
What is -20/2(7 2/3)
Answers
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
for such more question on simplified form
https://brainly.com/question/11680269
#SPJ8