Answers
The sum of the series when evaluated are ∑aₙ² + 1 = 45, ∑bₙ² - 1 = 35, ∑(2aₙ + bₙ) = 0, ∑(aₙ + 3bₙ) = 0, ∑(aₙ/bₙ)² = 2, ∑(aₙ/bₙ)³ = -2, ∑aₙ² + ∑bₙ² = 80 and ∑aₙ² - ∑bₙ² = 0
Evaluating the sum of the seriesSeries 61
This series represents the summation of aₙ² + 1 from n = 1 to 5
From the graph, we have
a₁ = -4; a₂ = -2; a₃ = 0; a₄ = 2 and a₅ = 4
So, we have
∑aₙ² + 1 = (-4)² + 1 + (-2)² + 1 + (0)² + 1 + (2)² + 1 + (4)² + 1
∑aₙ² + 1 = 45
Series 62
This series represents the summation of bₙ² - 1 from n = 1 to 5
From the graph, we have
b₁ = 4; b₂ = 2; b₃ = 0; b₄ = -2 and b₅ = -4
So, we have
∑bₙ² - 1 = (4)² - 1 + (2)² - 1 + (0)² - 1 + (-2)² - 1 + (-4)² - 1
∑bₙ² - 1 = 35
Using the above formats, the sum of the remaining series is
Series 63
∑(2aₙ + bₙ) = (2 * 4 - 4) + (2 * 2 - 2) + (2 * 0 - 0) + (2 * -2 + 2) + (2 * -4 + 4)
∑(2aₙ + bₙ) = 0
Series 64
∑(aₙ + 3bₙ) = (4 - 3 * 4) + (2 - 3 * 2) + (0 - 3 * 0) + (-2 + 3 * 2) + (-4 + 3 * 4)
∑(aₙ + 3bₙ) = 0
Series 65
∑(aₙ/bₙ)² = (2/-2)² + (4/-4)²
∑(aₙ/bₙ)² = 2
Series 66
∑(aₙ/bₙ)³ = (2/-2)³ + (4/-4)³
∑(aₙ/bₙ)³ = -2
Series 67
∑aₙ² + ∑bₙ² = (-4)² + (4)² + (-2)² + (2)² + (0)² + (0)² + (2)² + (-2)² + (4)² + (-4)²
∑aₙ² + ∑bₙ² = 80
Series 68
∑aₙ² - ∑bₙ² = (-4)² - (4)² + (-2)² - (2)² + (0)² - (0)² + (2)² - (-2)² + (4)² - (-4)²
∑aₙ² - ∑bₙ² = 0
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Related Questions
please help meeeeee! pleaseeeee
Answers
Answer:
905in²
Step-by-step explanation:
Question 3 Find whether the vectorrs are parallel. (-2,1,-1) and (0,3,1)
a. Parallel
b. Collinearly parallel
c. Not parallel
d. Data insufficient
Answers
To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.
To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.
The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:
Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)
The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:
Direction vector of (0,3,1) = (0, 3/√10, 1/√10)
Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.
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what is the perimeter
Answers
Answer:
16
.................
The population of a city has decreased by 400 residents over the past 5 years. The same number of residents left each year. What was the change in the city's population each year?
A.80
B.400
C.-80
D.-400
Answers
Answer:
B. 400
Is my house plis reportes?
Heat loss, h, in calories per hour through a glass window varies jointly as the difference, d,
between the inside and outside temperatures and as the area, A, of the window and
inversely as the thickness, t, of the pane of glass. If the temperature difference is 30
degrees, there is a heat loss of 9000 calories per hour through a window with an area of
1500 square centimeters and thickness of 0.25 centimeter. Find the heat loss through a
window with the same area and a thickness of 0.2 centimeter when the temperature
difference is 15 degrees.
Answers
The heat lost when the temperature difference is 15 degrees Celsius and thickness 0.2 cm is 5625 Calories.
What is the heat lost through the window?
The heat lost through the window is calculated by determining the value of constant in the joint variation.
h = ( kdA / t )
where;
k is the constantd is the difference between inside and outside temperatureA is the area of the windowt is the thickness of the windowk = ( ht ) / ( dA )
k = ( 9000 x 0.25 ) / ( 30 x 1500 )
k = 0.05
The heat lost when the temperature difference is 15 degrees Celsius and thickness 0.2 cm is calculated as;
h = ( kdA / t )
h = ( 0.05 x 15 x 1500 ) / ( 0.2 )
h = 5,625 calories
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You have ten books to arrange on your bookshelf. How many different orderings of all ten books are possible?
Answers
Answer: They can be arranged 720 different ways
∴ hence the total number of arrangements = 8! x 9P2 ways E
5x – 18 > 2(4x – 15).
Answers
Answer:
x<4
Step-by-step explanation:
5x-18>2(4x-15)
5x-18> 8x-30
-18>3x-30
12>3x
4>x
x<4
find the smallest perimeter and the dimentions for a rectangle with an area of 25in^2
Answers
The dimensions of the rectangle are:
Length = 5 inches
Width = 5 inches
To find the smallest perimeter for a rectangle with an area of 25 square inches, we need to find the dimensions of the rectangle that minimize the perimeter.
Let's start by using the formula for the area of a rectangle:
A = l × w
In this case, we know that the area is 25 square inches, so we can write:
25 = l × w
Now, we want to minimize the perimeter, which is given by the formula:
P = 2l + 2w
We can solve for one of the variables in the area equation, substitute it into the perimeter equation, and then differentiate the perimeter with respect to the remaining variable to find the minimum value. However, since we know that the area is fixed at 25 square inches, we can simplify the perimeter formula to:
P = 2(l + w)
and minimize it directly.
Using the area equation, we can write:
l = 25/w
Substituting this into the perimeter formula, we get:
P = 2[(25/w) + w]
Simplifying, we get:
P = 50/w + 2w
To find the minimum value of P, we differentiate with respect to w and set the result equal to zero:
dP/dw = -50/w^2 + 2 = 0
Solving for w, we get:
w = sqrt(25) = 5
Substituting this value back into the area equation, we get:
l = 25/5 = 5
Therefore, the smallest perimeter for a rectangle with an area of 25 square inches is:
P = 2(5 + 5) = 20 inches
And the dimensions of the rectangle are:
Length = 5 inches
Width = 5 inches
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What is 1 2/3 - 2 1/3
Answers
Answer:
Sorry Im wrong
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
$30
Step-by-step explanation:
Over 5 years she will have been paid $30 in interest. To find the amount of interest first find the total amount the account has after 5 years. The formula for simple interest is A=P(1+rt). Where A is the total amount, P is the principal (initial amount), r is the rate in decimal form, and t is the time in years.
Plug in the values to solve, A=200(1+0.03*5). Then, simplify to get A=230. Finally, to get only the interest, I, use the formula A-P=I. So, 230-200=30. Therefore, the interest Leila earned was 30 dollars.
Suppose Set B contains 16 elements and the total number elements in either Set A or Set B is 39. If the Sets A and B have 9 elements in common, how many elements are contained in set A? Answer = elements Question 22 Submit Question Let S be the universal set, where: S = {1, 2, 3,..., 18, 19, 20) Let sets A and B be subsets of S, where: Question 30 Set A = {1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 18, 19) The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set. Set B = {1, 2, 4, 5, 7, 8, 12, 14, 15, 17, 20) A B Find the following: 8 15 4 5 6 LIST the elements in the set (AUB): (AUB) - { Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (An B): (ANB) = { Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question. 7 Question 1 n( ABC)- Let S be the universal set, where: S = {1, 2, 3, ..., 28, 29, 30} Let sets A and B be subsets of S, where: Set A - (1, 3, 12, 17, 29) Set B = {3, 10, 15, 23) Set C = {2, 8, 11, 13, 14, 18, 21, 24, 26, 27} LIST the elements in the set (AUBUC) (AU BUC) - { Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set ( ABC) (ABC) - Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
Answers
For the given questions, we are asked to find the cardinality and list the elements of various sets using the information provided.
Question 22:
Given that Set B contains 16 elements and the total number of elements in either Set A or Set B is 39, and both sets have 9 elements in common, we can determine the number of elements in Set A by subtracting the number of elements in Set B from the total number of elements:
Number of elements in Set A = Total number of elements - Number of elements in Set B - Number of common elements
Number of elements in Set A = \(39 - 16 - 9\)
Number of elements in Set A = 14
Therefore, Set A contains 14 elements.
Question 30:
Based on the provided Venn diagram and the intersection of sets A and B, we can determine the elements in the union and intersection of the two sets.
Elements in the set (A U B) are the elements present in either Set A or Set B, or both. From the Venn diagram, we can list the elements as: 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20.
Elements in the set (A ∩ B) are the elements that are common to both Set A and Set B. From the Venn diagram, we can list the elements as: 1, 2, 4, 5, 7.
Therefore:
(A U B) = {1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20}.
(A ∩ B) = {1, 2, 4, 5, 7}.
Question 1:
Using the given sets A, B, and C, we can determine the elements in the union and intersection of the sets.
Elements in the set (A U B U C) are the elements present in either Set A, Set B, or Set C. We can list the elements as: 1, 2, 3, 8, 10, 11, 12, 13, 14, 15, 17, 18, 21, 23, 24, 26, 27, 29.
Elements in the set (A ∩ B ∩ C) are the elements that are common to all three sets. In this case, the intersection of sets A, B, and C is empty.
Therefore:
(A U B U C) = {1, 2, 3, 8, 10, 11, 12, 13, 14, 15, 17, 18, 21, 23, 24, 26, 27, 29}.
(A ∩ B ∩ C) = DNE (The intersection is empty).
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a college student takes the same number of credits each semester. they had 22 credits when they started, and after 4 semesters, they had 82 credits.
Answers
The college student began with 22 credits and finished with 82 credits after four semesters. By subtracting the initial credits from the final credits, we find out that the student earned 60 credits in total. To determine the number of credits taken per semester, we divide 60 by 4, which gives us 15 credits.
A college student who takes the same number of credits each semester had 22 credits when they started. After 4 semesters, they had 82 credits. To find out how many credits they took each semester, we can subtract the initial number of credits from the final number of credits and then divide by the number of semesters. So, the difference in credits between the initial and final semester is 82 - 22 = 60. And since this student took the same number of credits each semester, we can divide 60 by three (the number of semesters in between the initial and final semester) to find out how many credits they took per semester.
The student took 20 credits per semester (60/3). In conclusion, the college student took 20 credits each semester over the course of 4 semesters to accumulate a total of 82 credits. To find out how many credits the college student takes each semester, we need to determine the total number of credits earned over four semesters and divide that by the number of semesters.
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I need help in the simplest way!
Answers
Find the 65th term in the following arithmetic sequence
7,15,23,31
Answers
Answer:
519
Step-by-step explanation:
an = 8n - 1
a65 = 519
final answer is 519
use the synthetic division and the Remainder Theorem to find P(a). P(x)=x^4+x^3-5x^2+9x-6; a=3a.) 78b.)84c.)3d.)16
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
P(x) = x^4 + x^3 - 5x^2 + 9x - 6
a = 3
Step 02:
Synthetic division:
3 | 1 1 -5 9 -6
|
_____3 __12__21__90_______
1 4 7 30 84
remainder = 84
Remainder Theorem:
p(a):
a = 3
\(p(3)\text{ = \lparen3\rparen}^4+(3)\placeholder{⬚}^3-5(3)\placeholder{⬚}^2+9(3)-6=81+27-45+27-6=84\)The answer is:
p(a) = p(3) = 84
true or false: for a scalar valued function f(x,y), it makes sense to talk about its maximum or minimum value
Answers
it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.
True, for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value.
A scalar-valued function f(x, y) is a function that takes two inputs (x and y) and outputs a single value. These types of functions are often used to represent the relationship between two variables, such as the height of a surface above a plane, temperature distribution, or profit of a business depending on two factors.
To find the maximum or minimum value of a scalar-valued function f(x, y), we need to examine its critical points. Critical points are the points where the gradient of the function is either zero or undefined. The gradient is a vector consisting of the partial derivatives of the function with respect to x and y. We can calculate the partial derivatives (∂f/∂x and ∂f/∂y) and then set them equal to zero to find the critical points.
Once we have found the critical points, we can determine whether they correspond to a maximum, minimum, or saddle point (neither a maximum nor a minimum) by examining the second partial derivatives. The second partial derivatives help us determine the curvature of the function around the critical point. We can use the second partial derivative test, which involves calculating the determinant of the Hessian matrix (composed of the second partial derivatives) to classify the critical points.
In conclusion, it is true that for a scalar-valued function f(x, y), it makes sense to talk about its maximum or minimum value. We can find these values by analyzing the critical points and their corresponding second partial derivatives.
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Three circles with radii of 4, 5, and 6 cm, respectively, are tangent to each other externally. Find the angles of the triangle whose vertexes are the centers of the circles.
Answers
Note that the angles of the triangle whose vertexes are the centers of the circles are 50.48°, 58.99°, 70.53°.
How is this so?Three circles with radii 4, 5, and 6 from a triangle whose sides are the sum of their radii in pairs.
Thus, the sides of the triangle are
4 + 5, 4 + 6, and 5+6.
⇒ 9,, 10, 11.
To find the interior angles
CosC = a² + b² + c²/ 2ab
Cost C = (9² + 10² -11²) / (2 x9x10)
= 81 + 100 -121/180
= 60/180
= 1/3
C = 70.53°
Similar
Cos A = (10² + 11² - 9²) / (2 x10x11)
= 100 + 12181 + /180
= 140/220
= 7/11
A = 50.48°
Cos B = 9² + 11² - 10²/ 2x 9 x 11
= 102/198
B = 58.99°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
PLEASE HELP ME! PRETTY PLEASE?
Answers
Answer: I believe the correct answer is C.
Step-by-step explanation:
Answer:
its C
Step-by-step explanation:
Angel made 20% of his free throws over the season. If he shot 160 free
throws, how many did he make?
Answers
The number of free throws made by Angel is 32.
How to find the numbers of free throw Angel made?Angel made 20% of his free throws over the season. If he shot 160 free throws, the number of throws he made can be calculated as follows:
Hence,
number of free throws made by Angel = 20% of 160
number of free throws made by Angel = 20 / 100 × 160
number of free throws made by Angel = 3200 / 100
Therefore,
number of free throws made by Angel = 32 throws
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Answer:
32
Step-by-step explanation:
‘this right
Watches and bacteria: A group of researchers investigated the contamination of medical personnel watches at a New York hospital, since there is a potential for patient exposure to potentially dangerous bacteria.They sampled watches worn by physicians, physician assistants, and medical students at a teaching hospital in New York. Nearly half (46.6%) of the watches tested harbored microorganisms that can cause illness. By comparison, only one of the 10 watches worn by security guards tested positive for a disease-carrying microorganism. The researchers want to determine if the difference is statistically significant.Which of the following is an appropriate statement of the null hypothesis, H0?A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.B. The proportion of contaminated wrist-watches from medical personnel is not the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p not equal 46.6%.C. The proportion of contaminated wrist-watches from medical personnel is greater than the proportion of contaminated wrist-watches from security guards, i.e., H0: p > 46.6%.
Answers
An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.
What is a null hypothesis?In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.
For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:
H₀: p = 10.
Ha: p < 10.
In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.
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A rectangle has a length of (x + 6) units and a width of (x - 5) units. What is the area of the rectangle in terms of x?
Answers
Answer:
Area = x2 +x - 30
Step-by-step explanation:
area = length x width
(x+6) (x-5) = x2 +6x -5x -30 = x2 + x -30
13. The table represents some points of a linear function.
X
-4
-2
-1
1
2
у
-2
-10
-14
-22
-26
Which equation represents the same relationship?
a.
y=-4x - 18
c.
y = 4x - 2
b. y=-4x-2
d. y - 4x - 18
Answers
Answer:
y=-4x-18
Step-by-step explanation:
To find the slope of the function, you need two points in order, the first point having its x and y coordinates labeled as x1 and y1, and the second point having its coordinates labeled as x2 and y2. then, use the equation for slope, which is m=(y2-y1)/(x2-x1), and plug in the numbers. You should get m=(-10+2)/(-2+4)= -8/2= -4.
Then, use the slope and a point on the graph, and plug it into point slope form, which is y-y1=m(x-x1). No matter what point you use, you should get the same thing. I used the point (-2, -4). Using this point, the steps to arrange the equation in slope intercept form is: y+2=-4(x+4)=> y+2=-4x-16 => y=-4x-18.
x-y=3 what is this in slope intercept form
Answers
Answer:
y=x-3
Step-by-step explanation:
i really need help please
Answers
Answer:
56⁰
Step-by-step explanation:
I hope it helps you
If any doubts do let me know in the comments
A square pyramid has a base with a side length of 4 feet and lateral faces with heights of 3 feet. What is the lateral area of the pyramid?
Answers
The Lateral area of the pyramid is 40 square feet.
A square pyramid has a base with a side length of 4 feet and lateral faces with heights of 3 feet.
The lateral area of a pyramid is the area of its lateral faces, which are all triangular. The lateral area of a square pyramid can be calculated using the formula: LA = (1/2) where
LA is the lateral area, P is the perimeter of the base, and l is the slant height of each triangular face
.To find the perimeter of the base, we need to know the length of each side. Since the base of this pyramid is a square with a side length of 4 feet, its perimeter is 4+4+4+4=16 feet.
To find the slant height of each triangular face, we can use the Pythagorean Theorem. Since we know the height of each face is 3 feet and the base of each face is a side of the square base, we can find the slant height using the equation: a² + b² = c², where a and b are the legs of the right triangle formed by one of the lateral faces, and c is the hypotenuse. In this case, a=b=4 feet and c=l,
so we have:4² + 3² = l²16 + 9 = l²25 = l²5 =
Now that we know the perimeter of the base (P = 16 feet) and the slant height of each face (l = 5 feet), we can use the formula for the lateral area: LA = (1/2)PlLA = (1/2)(16 feet)(5 feet)LA = 40 square feet
therefore, the lateral area of the pyramid is 40 square feet.
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if p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, what is the cumulative probability of surviving for 3 years?
Answers
If p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, then the cumulative probability of surviving for 3 years is p1 + p2 + p3
The probability of surviving for 1 year = p1
The probability of surviving for 2 year = p2
The probability of surviving for 3 year = p3
The probability is the ratio of the number of favorable outcomes to the total number of outcomes.
The cumulative probability is defined as the probability distribution of random variables
The cumulative probability = p1 + p2 + p3
Therefore, the cumulative probability of surviving for 3 years is p1 + p2 + p3
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Write an explicit formula for a_na
n
, the n^{\text{th}}n
th
term of the sequence 175, 35, 7, ...
Answers
The explicit formula for the sequence is \(a_n\) = 175, where n represents the position of the term in the sequence.
How to find the explicit formula for a given sequence?To find an explicit formula for the given sequence, we need to observe the pattern and determine how each term relates to its position in the sequence.
Notice that each term is obtained by dividing the previous term by 5. We can represent this pattern mathematically as:
\(a_n\) = \(\frac{a_{n-1} }{ 5}\)
where\(a_n\)represents the \(n^{\text{th}}\) term and \(a_{n-1}\) represents the \((n-1)^{\text{th}}\) term.
We can start with the first term, \(a_1\) = 175, and use the recursive formula to generate subsequent terms:
\(a_2 = \frac{a_1 }{ 5} = \frac{175}{ 5}\) = 35
\(a_3 = \frac{a_2 }{ 5 }= \frac{35 }{ 5}\) = 7
...
To find the explicit formula, we can rewrite the recursive formula in a general form:
\(a_n = \frac{a_{n-1} }{ 5}\)
To eliminate the recurrence, we can solve for a_{n-1} in terms of a_n:
\(a_{n-1} = a_n * 5\)
Substituting this expression back into the formula, we get:
\(a_n = \frac{(a_n-1 * 5) }{ 5}\)
To simplify, we have:
\(a_n = a_n-1\)
Since \(a_1 = 175\)we can see that each term is equal to the previous term. Therefore, the explicit formula for the sequence is:
\(a_n = 175\)
This means that every term in the sequence is equal to 175, regardless of the value of n.
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\(\frac{4}{\sqrt{5}-1 } -\frac{4}{\sqrt{5}+1\\ }\)
Answers
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btw,, the formula you insert is incorrect:)
![[tex]\frac{4}{\sqrt{5}-1 } -\frac{4}{\sqrt{5}+1\\ }[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/G1Q7i2Yn5DGkxqAxS53ovP7nIOZdhc6G.jpeg)
Answer:
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Two questions 20 points
Please pick the TWO properties of a circumcenter
*
Equidistant from the vertices
Equidistant from the sides
Where the angle bisectors cross
Where the perpendicular bisectors cross
Please pick the TWO properties of a incenter
*
Equidistant from the vertices
Equidistant from the sides
Where the angle bisectors cross
Where the perpendicular bisectors cross
Answers
1]
Equidistant from the vertices.Where the perpendicular bisectors cross.2]
Equidistant from the sidesWhere the angle bisectors cross.Circum centre of a triangle is the point of origin of a circum circle i.e., a triangle inscribed in a circle.
Properties of circum center are -
The circumcenter of a triangle is equidistant from all the vertices, i.e., OA = OB = OC.All the new triangles that are formed by joining the circumcenter of a triangle to its vertices are isosceles.For an acute-angled triangle, the circumcenter lies inside the triangle.In the case of an obtuse-angled triangle, the circumcenter lies outside the triangle.In the case of right angled triangle, circum center lies on the hypotenuse.In center of a triangle is the center of the triangle where bisectors of all the angles intersect.
Properties of In center are -
It is the center of the incircle.It always lies inside the triangle.It is equidistant from the sides of the triangle.Hence, circum centre is equidistant from the vertices and is a point where the perpendicular bisectors cross while In center is a point which is equidistant from the sides and is point where the perpendicular bisectors cross.
To understand more about Triangles refer -
https://brainly.com/question/27996834
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7m+5(m-1)= -5+12m solve the problem
Answers
Then you can add like terms.
12m-5 = -5+12m
Add 5 to both sides
12m = 0+12m
Subtract 12 to both sides
0=0
This equation has infinite solutions