The number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3265920.
To find the number of ID numbers that can be made, we can use the permutation formula:
P(n,r) = n! / (n-r)!
Where n is the total number of digits available and r is the number of digits in the ID number.
In this case, n = 10 (the digits 0-9) and r = 8 (the number of digits in the ID number).
Plugging these values into the formula gives us:
P(10,8) = 10! / (10-8)!
P(10,8) = 10! / 2!
P(10,8) = 3628800 / 2
P(10,8) = 1814400
However, we need to subtract the number of ID numbers that start with 0, since these would not be valid eight-digit numbers. To find this number, we can use the permutation formula again with n = 9 (the digits 1-9) and r = 7 (the remaining digits in the ID number):
P(9,7) = 9! / (9-7)!
P(9,7) = 9! / 2!
P(9,7) = 362880 / 2
P(9,7) = 181440
Subtracting this from the total number of ID numbers gives us:
3265920 - 181440 = 3084480
So the number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3084480.
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When QuickSort splits the list exactly in half we saw that T(n) = 2T(n/2) + O(n) and then T(n) = (n lgn) by the Master Theorem. Here we're going to examine the case where QuickSort splits the list into one sublist of size an and another sublist of size (1 –a)n for some 0
The running time of QuickSort in this case is O(n log(n)), which is the same as the running time when QuickSort splits the list exactly in half.
When QuickSort splits the list into one sublist of size an and another sublist of size (1-a)n, the recurrence relation for the running time of QuickSort becomes T(n) = T(an) + T((1-a)n) + O(n). This is because the two sublists have different sizes and therefore take different amounts of time to sort.
To solve this recurrence relation, we can use the recursion tree method. The recursion tree for this recurrence relation looks like this:
```
T(n)
/ \
T(an) T((1-a)n)
/ \ / \
T(a^2n) T(a(1-a)n) T(a(1-a)n) T((1-a)^2n)
...
```
At each level of the recursion tree, the size of the subproblems decreases by a factor of a or (1-a), and the number of subproblems doubles. The work done at each level is O(n), since the partitioning step takes O(n) time.
The recursion tree has log_{1/a}(n) levels, since the size of the subproblems decreases by a factor of a at each level. Therefore, the total work done by QuickSort is O(n log_{1/a}(n)) = O(n log(n)), since log_{1/a}(n) = log(n)/log(1/a) = log(n)/(-log(a)) = -log(n)/log(a) = O(log(n)).
So the running time of QuickSort in this case is O(n log(n)), which is the same as the running time when QuickSort splits the list exactly in half.
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If you apple these changes to the linear parent function, f(x) = x, what is the equation of the new function?
Answer:
C) g(x) = 1/5x + 7-----------------------------------
Vertical compression of a function by a factor of a is:
f(x) → a f(x), where a is between 0 and 1Vertical compression of a function by a factor of 5 is:
g(x) = 1/5 f(x)Shifting up by b units is:
f(x) → f(x) + bIf we apply both transformations we get:
g(x) = 1/5x + 7Option C is correct.
In the figure, line m is parallel to line n. The measure of <3 is 58 degrees. What is the measure of <7?
In the parallel line measure of angle [tex]m\angle 7[/tex] is 32°.
What is parallel lines?In a plane, two lines are said to be parallel if they never cross at any point. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".
Here we know that If two lines which are parallel are intersected by a transversal then the pair of corresponding angles are equal.
Then,
=> [tex]m\angle3= m\angle10[/tex]
Here the given [tex]m\angle3=58\textdegree[/tex] the [tex]m\angle10=58\textdegree[/tex].
Now we know that sum of all angles in straight line is 180°.Then,
=> [tex]m\angle6+m\angle7+m\angle10=180\textdegree[/tex]
=> [tex]90\textdegree+m\angle7+58\textdegree=180\textdegree[/tex]
=> [tex]m\angle7=180\textdegree-90\textdegree-58\textdegree=32\textdegree[/tex]
Hence the measure of [tex]m\angle 7[/tex] is 32°.
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Ok so we are supposed name each pair of angels this is due tomorrow so please help me :D
Answer:See below
Step-by-step explanation:
answers from top left to top right, then bottom left to bottom right.
First one is alternate interior, because they are on the inside, and are on opposite sides.
the second one is supplementary, because they supplement each other, or add up to 180 degrees.
the third one is alternate exterior, because they are opposite to each other on the outside.
the last one is corresponding, because they are in the same position on each side, and are almost like a copy and paste.
I found a few images on the internet to help you understand.
Hope this helped!
Determine whether the function is even, odd, or neither. Then describe the symmetry. g(s)=8s^2/3
o even o odd o neither
Symmetry: o no symmetry o y-axis symmetry o x-axis symmetry o origin symmetry o x=y symmetry
The function g(s) = 8s²/3 is an even function and its symmetry is y-axis symmetry.
The given function satisfies the condition g(-s) = g(s) which makes it an even function. This means that if we plug in the opposite value of s into the function, we will get the same result. For example, g(-2) = 8(-2)^2/3 = 8(4)/3 = 32/3 and g(2) = 8(2)^2/3 = 8(4)/3 = 32/3.
The symmetry of an even function is y-axis symmetry. This means that the graph of the function is symmetric with respect to the y-axis. In other words, if we fold the graph along the y-axis, the two halves will match up perfectly.
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a line segment is drawn between (4,7) and (9,7). find it’s gradient.
Considering the expression of a line, the gradient or slope is zero and the line is horizontal.
Definition of linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope. The gradient or slope of a line tells how steep it is.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Gradient in this caseIn this case, being (x₁, y₁)= (4, 7) and (x₂, y₂)= (9, 7), the slope m can be calculated as:
m= (7 -7)÷ (9 -4)
m= 0÷ 5
m= 0
Finally, the gradient or slope is zero.
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In Exercises 22–26, give a set-theoretic description of the given points as a subset W of R^2. 22. The points on the line x – 2y = 1 23. The points on the x-axis 24. The points in the upper half-plane 25. The points on the line y = 2 26. The points on the parabola y = x2
The set W of points described in Exercises 22-26 can be written as a subset of R2 as follows: 22. The points on the line x – 2y = 1: W = {(x, y) | x - 2y = 1}, 23. The points on the x-axis: W = {(x, y) | y = 0}, 24. The points in the upper half-plane: W = {(x, y) | y > 0}, 25. The points on the line y = 2: W = {(x, y) | y = 2} and 26. The points on the parabola y = x2: W = {(x, y) | y = x2}
In other words, the set W contains all points (x, y) that satisfy the equations given in Exercises 22-26. As such, it is a subset of the two-dimensional Euclidean space R2. In Exercises 22–26, give a set-theoretic description of the given points as a subset W of R² is a problem where we need to find a set-theoretic description of the given points in each exercise.
Therefore, we can write the set W asW = { (x, y) ∈ R² | y ≥ 0 } The points on the line y = 2The equation of the line is y = 2Therefore, we can write the set W asW = { (x, y) ∈ R² | y = 2 } The points on the parabola y = x²The equation of the parabola is y = x²Therefore, we can describe the set W asW = { (x, y) ∈ R² | y = x² }
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I need the answer to this
Answer:130
Step-by-step explanation:
2×5+3= 13
10×13=130
Answer:
130/5
Step-by-step explanation:
10x13=130
130/5
ghyhf f yyhgf
Find the missing variable and indicated
angle measure.
D
X =
7xº
G
I
62°
F
E
m²FDG =
Will mark brainiest if you answer fast please
Answer:
FDG is 28 degrees, and x = 4
Step-by-step explanation:
We can see for angle EDG that there is a little box at the angle. This means that it is a right angle, which means it is 90 degrees. This, in turn, means that the two angles formed there (angle EDF, and angle FDG) will add up to that number, 90 degrees because they are within the initial angle.
Let us create an equation using our angles. We know one is 62 degrees and the other is 7x degrees.
62 +7x = 90
7x = 28
x =4
This means that the unknown value is 4, and since the angle was 7x, it is really 7(4) = 28 degrees, and we know the other angle is 62 degrees.
If you like this answer, please mark brainliest on this answer, and the one you promised before...
can any of you help me please
The two equivalent expressions are the second one and the last:
(56x + 24)/8 and 3 + 7x
How to identify the equivalent expression?We want to find an equivalent expression to 56x + 24 divided by 8, so we want to simplify the expression:
(56x + 24)/8 (that is the second expression)
We can distribute that division so we get:
(56x + 24)/8 = (56x)/8 + 24/8
Now we can simplify these two quotients so we get:
(56x)/8 + 24/8 = 7x + 3 (that is the last expression).
Then the two equivalent expressions are:
(56x + 24)/8 and 3 + 7x
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plsssssssssssssssssss hurry i need it
The Equation to represent the amount she spend on the material
is y= 15 + 0.75 x.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
For First 10 pound the charges will be $1.50.
Each additional pound $0.75
let She bought x pounds then the price is 0.75x
Now, The Equation to represent the amount she spend on the material
y = 10 (1.5)+ 0.75x
y= 15 + 0.75 x
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Find the missing side
Answer: 30
Step-by-step explanation:
Use Pythagorean's Theorem, a² + b² = c²
18² + 24² = c²
324 + 576 = c²
900 = c²
√900 = c
c = 30
The missing side is 30.
Hope this helps!
[(0)/(1) Points ] DETAILS PREVIOL Perform the indicated division. (4x^(3)-5x^(2)+8x-8)/(x^(2)-3x)
The division of polynomials "(4x^(3)-5x^(2)+8x-8)/(x^(2)-3x)" gives the expression "4x+7+(29x-8)/(x^(2)-3x)".
To perform the indicated division, we will use polynomial long division.
First, we will divide the first term of the dividend, 4x^3, by the first term of the divisor, x^2, to get 4x. This will be the first term of our quotient.
Next, we will multiply 4x by the divisor, x^2-3x, to get 4x^3-12x^2. We will then subtract this from the dividend to get 7x^2+8x-8.
We will then repeat this process by dividing the first term of the new dividend, 7x^2, by the first term of the divisor, x^2, to get 7. This will be the second term of our quotient.
We will then multiply 7 by the divisor, x^2-3x, to get 7x^2-21x. We will subtract this from the new dividend to get 29x-8.
Since the degree of the new dividend, 29x-8, is lower than the degree of the divisor, x^2-3x, we are done with the division and 29x-8 will be our remainder.
Therefore, the final answer is:
(4x^(3)-5x^(2)+8x-8)/(x^(2)-3x) = 4x+7+(29x-8)/(x^(2)-3x)
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Cooper decides to estimate the volume of a grapefruit by modeling it as a sphere. He measures its radius as 6.7 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic............
(c) In a test of a new package design, you drop a carton of a dozen eggs from a height of 1 foot and count the number of broken eggs
The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective. However, if there are several broken eggs, the package design may need to be improved to provide better protection.
When testing a new package design, it is important to simulate real-world conditions as much as possible. In this case, dropping a carton of a dozen eggs from a height of 1 foot is a good way to simulate the types of impacts that the package may experience during shipping and handling.
To conduct the test, you will need to follow these steps:
Obtain a carton of a dozen eggs and the new package design.Place the eggs inside the package according to the manufacturer's instructions.Find a suitable location to drop the package from a height of 1 foot. Make sure the area is clear and there is nothing that could interfere with the drop or damage the package.Drop the package from a height of 1 foot.Open the package and examine the eggs. Count the number of broken eggs.
The number of broken eggs will give you an idea of how well the new package design protects the eggs from impacts. If there are no broken eggs, the package design may be effective.
However, if there are several broken eggs, the package design may need to be improved to provide better protection.
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LINEAR EQUATIONS AND INEQUALITES Solving a linear equation with several o Solve for v. 3(v-4)-6=-7(-4v+4)-7v Simplify. your answer as much as possible. v
To solve for v in the equation 3(v-4)-6=-7(-4v+4)-7v, we need to simplify the equation and isolate the variable v on one side of the equation. Here are the steps:
Step 1: Distribute the 3 and -7 on the left and right sides of the equation respectively:
3v - 12 - 6 = 28v - 28 - 7v
Step 2: Combine like terms on both sides of the equation: 3v - 18 = 21v - 28
Step 3: Move the variable terms to one side of the equation and the constant terms to the other side: 3v - 21v = -28 + 18
Step 4: Simplify both sides of the equation:
-18v = -10
Step 5: Divide both sides of the equation by -18 to solve for v: v = -10/-18
Step 6: Simplify the fraction: v = 5/9
Therefore, the solution for v is 5/9.
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Who many times larger is f(x)=-2.5x^2+2.5x+5 than g(x)=-x^2+6x+2
f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.
What is a function?A relation is a function if it has only One y-value for each x-value.
To find out how many times larger f(x) is than g(x), we need to divide the value of f(x) by the value of g(x).
Then we simplified the expression and found that it is always larger than g(x) except at two values of x where it is undefined.
To determine how much larger f(x) is than g(x), we looked at their leading coefficients and found that f(x) is always larger than g(x) for large positive or negative values of x.
Finally, we took the limit of f(x) / g(x) as x approaches infinity or negative infinity and found that it approaches -5/2.
Hence, f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.
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If your client completed a barbell back squat of 109lb for 5 repetitions (the 6th repetition could not be performed). What would be their predicted/estimated 1RM (in lbs) for the barbell back squat exercise when using the %1RM to number of repetitions table in the lecture?
Round your final answer to the nearest whole number and DO NOT include units
Using the %1RM to number of repetitions table, your client's estimated 1RM for the barbell back squat exercise would be 125 lbs, rounded to the nearest whole number.
To estimate the predicted 1RM (one repetition maximum) for the barbell back squat exercise, we can use the %1RM to number of repetitions table from the lecture. According to the table, performing 5 repetitions corresponds to 87% of the 1RM.
To find the estimated 1RM, we can use the following formula:
1RM = weight lifted / %1RM
Plugging in the values from the question:
1RM = 109lb / 0.87
1RM = 125.287lb
Rounding to the nearest whole number, the estimated 1RM for the barbell back squat exercise is 125lb.
Therefore, the answer is 125.
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2log_(3)(x)=4 log_(3)(x^(2))=4 x^(2)=3^(4) x^(2)=81 x=9,-9 x=9 and x=-9 are true solutions x=9 and x=-9 are extraneous solutions x=9 is an extraneous solution and x=-9 is a true solution x=9 is a true solution and x=-9 is an extraneous solution
Answer:
9
Step-by-step explanation:
if I get an annual income of 420 600,000 and get an increase of 8.2% calculate my new income
Answer:
Step-by-step explanation:
To calculate your new income after an increase of 8.2%, you can use the following formula:
New income = Old income + (Percentage increase * Old income)
Plugging in the values given in the problem, we get:
New income = 420,600,000 + (8.2% * 420,600,000)
New income = 420,600,000 + (0.082 * 420,600,000)
New income = 420,600,000 + 34,524,120
New income = 455,124,120
Therefore, your new income after an increase of 8.2% would be 455,124,120.
helppp pls is urgent
The value of x, considering the angle addition postulate, is given as follows:
x = -5.
What does the angle addition postulate state?The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.
The larger angle in this problem is QRS, hence the equation to obtain the value of x is given as follows:
3x + 93 + 66 + x = -x + 134
4x + 159 = -x + 134
5x = -25
x = -25/5
x = -5.
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An engineer is working on the measurements for a satellite dish. The dish is 15 cm deep and has a diameter of 120 cm. The collector (which protrudes from the dish) will be supported by struts of length x (see the diagram). How long are these struts of length x?
Answer:
75 cm
Step-by-step explanation:
You want to know the length of the struts between the edge of a parabolic dish 120 cm in diameter and 15 cm deep, and the collector at the focus of the dish.
EquationThe equation of a parabola with its vertex at the origin and passing through points (±60, 15) can be written as ...
y/15 = (x/60)² . . . . parabola scaled vertically by 15, horizontally by 60
240y = x² . . . . . . multiply by 3600
4(60)y = x² . . . . . factor out 4 from the coefficient of y
FocusThis equation is of the form ...
4py = x²
where p = 60 is the distance from the vertex to the focus. Since the dish is 15 cm deep, the focus lies 60-15 = 45 cm above the edge of the dish.
StrutsThe length of each strut from the edge of the dish to the focus will be the hypotenuse of a right triangle with legs 45 and 60. The Pythagorean theorem tells us that length is ...
c² = a² +b²
c = √(a² +b²) = √(45² +60²) = 15√(9+16) = 75
The length x of each strut is 75 cm.
Which rational expression is equivalent to this expression? (4)/(x-3) A. (x-3)/(x+2)-:(4)/(x+2) B. (x+2)/(x-3)-:(4)/(x+2) C. (x+2)/(x-3)*(4)/(x+2) D. (x-3)/(x+2)*(x+2)/(x^(4))
Option C. (x+2)/(x-3)*(4)/(x+2) is the equivalent rational expression to (4)/(x-3).
The rational expression that is equivalent to this expression (4)/(x-3) is option C. (x+2)/(x-3)*(4)/(x+2).
We can simplify the rational expression (x+2)/(x-3)*(4)/(x+2) by canceling out the common factor (x+2) from the numerator and denominator. This will give us the equivalent rational expression:
(x+2)/(x-3)*(4)/(x+2) = (4)/(x-3)
Therefore, option C. (x+2)/(x-3)*(4)/(x+2) is the equivalent rational expression to (4)/(x-3).
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What’s the measure of the bolder arc is 4cm is in the boldes arc and 118 is outside
As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.
what is angle ?The vertex of the angle is the common endpoint shared by two rays or line segments that make up an angle in geometry. The sides or limbs of the angle are the rays or line segments that make up the angle. Angles are used to describe the amount of spin or turn between two lines or objects. They are usually measured in degrees or radians. Numerous areas of mathematics, such as geometry, trigonometry, and calculus, depend on angles.
given
We must apply the following algorithm to determine the size of the bolded arc:
arc length is equal to (angle / 360) times 2r.
where r is the radius, angle is the central angle in degrees, and is a mathematical constant roughly equivalent to 3.14.
Inputting the numbers provided yields:
(118/360) * 2 = arc length (4)
8.24 cm arc length is equal to (0.3278) × (25.12) arc length.
As a consequence, the bolded arc is approximately 8.24 centimetres long when the bolder arc is 4cm long.
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Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
The gradient of line A is 4 and the gradient of line B is -2.
What is graph?Graph is a data structure that consists of nodes (or vertices) connected by edges. It is a way of representing data in a structured form and can be used to represent any type of real-world relationship. It can be used to represent geographical relationships between cities, social networks, and even computer networks. Graphs are often used in computer science, mathematics, and engineering to represent relationships between data points.
To calculate the gradient of a line, the formula is rise/run. Thus, the gradient of line A can be calculated as rise/run = 72/4 = 18. On the other hand, the gradient of line B can be calculated as rise/run = 6/-2 = -3
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Of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls. What is the probability that a student surveyed was either a boy or had a bicycle?
A. 620/1000 ≈ 0.62
B. 450/1000 ≈ 0.45
C. 680/1000 ≈ 0.68
D. 810/1000 ≈ 0.81
The probability that a student surveyed was either a boy or had a bicycle is 0.62.
What is probability?
The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.
We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.
So, Total number of boys = 490
Total number of girls with bicycle = 130
Total number of students that was either a boy or had a bicycle is
490 + 130 = 620
The probability is
620 / 1000 = 0.62
Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.
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Express each fraction as a percentage round of your answer to one decimal to2 20 by 325
20/325 is equivalent to 6.15% rounded off to one decimal place.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To express a fraction as a percentage, you need to multiply the fraction by 100. Therefore, we have:
20/325 = 0.0615
Multiplying by 100, we get:
0.0615 x 100 = 6.15%
So, 20/325 is equivalent to 6.15% rounded off to one decimal place.
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IfA=[aij]us a2×3matrix, such thataij=5(−i+2j)2. Thena12is: Select one:535953656
The value of a12 is 45.
The given matrix A = [aij] is a 2x3 matrix, which means it has 2 rows and 3 columns. The given condition is aij = 5(-i + 2j)^2. We need to find the value of a12, which means the element in the first row and second column.
To find the value of a12, we need to substitute i = 1 and j = 2 in the given condition.
a12 = 5(-1 + 2*2)^2
= 5(3)^2
= 5*9
= 45
Therefore, the value of a12 is 45.
So, the correct option is:
Select one:
a. 53
b. 59
c. 45
d. 56
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How to prove |z+w| |z| + |w|, z and w
are two complex numbers. (Use algebraic proof,
please don't use geometric proof! I want detailed explanation.
)
To prove that |z+w| ≤ |z| + |w| for two complex numbers z and w, we can use an algebraic proof.
First, let's rewrite z and w in terms of their real and imaginary parts:
z = a + bi
w = c + di
Now, we can use the definition of the absolute value of a complex number to write:
|z+w| = |(a+c) + (b+d)i|
= √((a+c)² + (b+d)²)
Similarly, we can write:
|z| = |a + bi| = √(a² + b²)
|w| = |c + di| = √(c² + d²)
Now, we can use the triangle inequality to prove that |z+w| ≤ |z| + |w|:
√((a+c)² + (b+d)²) ≤ √(a² + b²) + √(c² + d²)
Squaring both sides of the inequality gives us:
(a+c)² + (b+d)² ≤ (a² + b²) + (c² + d²) + 2√((a² + b²)(c² + d²))
Expanding the left-hand side of the inequality gives us:
a² + 2ac + c² + b² + 2bd + d² ≤ a² + b² + c² + d² + 2√((a² + b²)(c² + d²))
Simplifying and rearranging terms gives us:
2ac + 2bd ≤ 2√((a² + b²)(c² + d²))
Dividing both sides of the inequality by 2 gives us:
ac + bd ≤ √((a² + b²)(c² + d²))
Squaring both sides of the inequality again gives us:
(a² + b²)(c² + d²) - (ac + bd)² ≥ 0
Expanding and simplifying gives us:
a²c² + a²d² + b²c² + b²d² - a²c² - 2abcd - b²d² ≥ 0
a²d² + b²c² - 2abcd ≥ 0
(a²d² - 2abcd + b²c²) ≥ 0
(a² - 2ab + b²)(d² - 2cd + c²) ≥ 0
(a - b)²(d - c)² ≥ 0
Since the square of any real number is always greater than or equal to zero, this inequality is always true. Therefore, |z+w| ≤ |z| + |w| for any two complex numbers z and w. This completes the algebraic proof.
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12. Solve the following triangles using Law of Sines or Law of Cosines (round to nearest tenth when necessary and find all solutions) *Must show path/process/work for full credit": a. A-58 a. B- b=12
Answer:
sin(B)/b = sin(A)/a
sin(B)/12 = sin(58)/a
a = 12(sin(58)/sin(B))
Now we can use the Law of Cosines to find the remaining sides of the triangle:
a^2 = b^2 + c^2 - 2bc*cos(A)
a^2 = 12^2 + c^2 - 2(12)(c)*cos(58)
c^2 - 24c*cos(58) + 144 - a^2 = 0
Using the quadratic formula, we get:
c = (24*cos(58) ± sqrt((24*cos(58))^2 - 4(1)(144 - a^2)))/2(1)
c = 12*cos(58) ± sqrt(144*cos(58)^2 - 4(144 - a^2))
c = 12*cos(58) ± sqrt(576*cos(58)^2 - 4a^2)
c = 12*cos(58) ± sqrt(576*(1 - sin(58)^2) - 4a^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 4a^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 4(12(sin(58)/sin(B)))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/sin(B))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(180 - A - B)))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(180 - 58 - B)))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - B)))^2)
Now we can substitute the value we found for a into the equation for c to get:
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - B)))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(a/b))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(12/a))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(12/(12(sin(58)/sin(B)))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(sin(58)/sin(B))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(sin(58)/(12*sin(58)/a))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(a/12))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - arcsin(1/12)*a))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(122 - 4.98)*a))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(sin(117.02)*a))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(sin(58)/(0.97*a))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*a/sin(58))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*(12*sin(58)/sin(B))/sin(58))))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*(12/sin(B)))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*(12/sin(180 - A - B)))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*(12/sin(180 - 58 - B)))))^2)
c = 12*cos(58) ± sqrt(576 - 576*sin(58)^2 - 576(1.03*(12/sin(122 - B)))))^2)
Now we can solve for c using the two possible values of B:
B = arcsin(b*sin(A)/a)
B = arcsin(12*sin(58)/a)
B = arcsin(12*sin(58)/(12*sin(58)/sin(B)))
B = arcsin(sin(B))
B = 58
or
B = 180 - arcsin(b*sin(A)/a)
B = 180 - arcsin(12*sin