2. Determine the number of real solutions of the system
You HAVE to show your work to get full credit.
(y=x²-3
y = -2x +4

The exact length of the curve of the equation y = 1/4 x² − 1/2 ln(x), 1 ≤ x ≤ 4 is 1.125

Here we have given an equation y = 1/4 x² − 1/2 ln(x) with the limit as 1 ≤ x ≤ 4.

Now, the arc length is calculated by differentiating the terms, then we get,

=> dy/dx = x/2 - 1/2x

Now, we have to apply these derivative on the arc length formula, then we get,

=> length =  [tex]\int\limits^4_1 {\sqrt{1 + (\frac{x}{2} -\frac{1}{2x})^2 } } \, dx[/tex]

When we simplify this one then we get,

=> length = [tex]\frac{1}{2} \int\limits^4_1 {\sqrt{x^2 + 2 + \frac{1}{x^2} } } \, dx[/tex]

When we further simplify this one then we get,

=> length = [tex]\frac{1}{2} \int\limits^4_1 {x + \frac{1}{x} } \, dx[/tex]

Now, the result of the differentiation is

=> length = 1/2 [17/4 - 2]

=> length = 1/2 [9/4]

=> length = 1.125

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Answer:

The answer is 35.

Step-by-step explanation:

The given polynomial is p(x) = 5x² -4x + 2 we substitute x = 3 in the polynomial:

p(3) = 5(3)² -4(3) + 2 = 5×9 - 12 + 2 = 45 - 12 + 2 = 47 - 12 = 35

Hence, p(3) =35

The range and median birth weight are the same for both genders.

Step-by-step explanation:

The average birth weight for babies is around 7.5 lb (3.5 kg). However, a birth weight between 5.5 lb (2.5 kg) and 10 lb (4.5 kg) is considered normal. The general observations with regard to birth weight are as follows:

   Boys are usually a little heavier than girls.

   First babies are usually lighter than later siblings.

   Large parents generally have large babies, while small parents generally have small babies.

   Conditions like diabetes in the mother may lead to increased birth weight.

   Zika virus causes the birth weight to be lower and the size of the head is small.

   The range and median birth weight are the same for both genders.

a) The probability the home team wins is of: 0.7291 = 72.91%.

b) The conditional probability that the home team wins, given that is is behind 5 points by the end of halftime is of: 0.3409 = 34.09%.

c) The conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter is of: 0.9015 = 90.15%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for each quarter are given as follows:

Hence for each case, the mean and the standard deviation are given as follows:

The probability of the home team winning is the probability of X being greater than zero for four quarters, hence it is one subtracted by the p-value of Z when X = 0, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (0 - 6)/9.8

Z = -0.61

Z = -0.61 has a p-value of 0.2709.

1 - 0.2709 = 0.7291 = 72.91%.

When the home team is down five points at the end of the halftime, the probability of winning is P(X > 5) for two quarters, hence one subtracted by the p-value of Z when X = 5 as follows:

Z = (5 - 3)/4.9

Z = 0.41

Z = 0.41 has a p-value of 0.6591.

Z =  has a p-value of 0.6591.

1 - 0.6591 = 0.3409 = 34.09%.

When the home team is up five points at the end of the first quarter, the probability of winning is P(X > -5) for three quarters, hence one subtracted by the p-value of Z when X = -5.

Z = (-5 - 4.5)/7.35

Z = -1.29

Z = -1.29 has a p-value of 0.0985.

1 - 0.0985 = 0.9015 = 90.15%.

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The decimal that should be represented as a negative rate in this problem is the 2.2 millimeters per year because it represents a decrease in water level.

The two factors that Ericka should multiply to find the total variation in water level are the rate of change (2.2 millimeters per year) and the time period over which the change occurred (6.2 years). In other words, she should multiply 2.2 by 6.2 to find the total variation in water level.

A novel and somewhat paradoxical tool for monetary policy, negative interest rates are not common. The goal of negative interest rates is to encourage lending and spending rather than saving and hoarding. When cash is placed with a bank, it results in a storage fee rather than the chance to receive interest income. When cash is placed with a bank, it results in a storage fee rather than the chance to receive interest income.

The quantity you are measuring is said to be increasing over time if the rate of change is positive, whereas the opposite is true if the rate of change is negative.

The complete question is:-

Ericka is also in Mr. Whittaker’s science class and she recorded the variation in water level at a different part of the river. She observed that the water level there fell 2.2 millimeters per year over a period of 6.2 years This data is compared to the average annual trend, which shows the water level rising 1.8 mm/year. Which of the decimals in the problem should be represented as a negative rate? Which two factors should Ericka multiply to find the total variation in water level?

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The kangaroo must take at least 23 leaps to catch up to the rabbit.

To catch up to the rabbit, the kangaroo must travel a total distance of 150 feet. For every 12-foot leap of the kangaroo, the rabbit leaps 7 feet, so the kangaroo must take one more leap than the rabbit in order to cover the same distance.

The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):

150 feet / 7 feet/leap = 21.43 leaps

Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.

However, since the number of leaps must be a whole number, the kangaroo must take at least 23 leaps to catch up to the rabbit.

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The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):

150 feet / 7 feet/leap = 21.43 leaps

Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.

The ratio for the Illustration a+b/a-b=5/3 is 5:4.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

From the information given, the equation is written thus:

a + b / a - b = 5 / 3

Cross multiply

5(a - b) = 3 (a + b)

5a - 5b = 3a + 3b

Collect the like terms

5a - 3a = 3b + 5b

2a = 8b

Divide

a = 8b / 2

a = 4b

Therefore (a + b) / a will be:

= (4b + b) / 4b

= 5b / 4b

= 5/4

= 5 : 4

The ratio is 5:4.

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No, a square root is not always an irrational number because the perfect square roots are rational number.

Any real number that cannot be written as p/q, where p and q are both integers, the quotient of two integers.

If a number is not a perfect square, the square root of that number is not rational.

For example, the square root is 4 is 2.

The square root of 9 is 3.

But whereas the square root of 5 is 2.23606797755555...... which is irrational

The square root of 8 is 2.8284271247555..... which is irrational.

So, therefore square root of a number is not irrational always it can be rational also.

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The area of the region bounded by the given curves is   [tex]32lnx-\frac{58}{3}[/tex]

Given curves,

y = [tex]6x^{2} lnx[/tex]

y = 24lnx

We will find the intersection points of these two curves by equating and then solving.

The intersection of these two curves will be at x = 1,2.

The area under the curves,

A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]

To solve, concentrate on the unbounded (indefinite) integral:

a = [tex]\int\limits {(24lnx-6x^{2} lnx)} \, dx[/tex]

  = [tex]-6\int\limits {(lnx)(x^{2} -4)} \, dx[/tex]

We will use integration by parts to solve this integration.

[tex]\int\limits {u} \, dv=vu-\int\limits{v} \, du[/tex]

Let us assume,

u = lnx and v = [tex]\frac{1}{3}x^{3} -4x[/tex]

Therefore,

[tex]du = \frac{1}{x}dx[/tex]

[tex]dv=x^{2}-4[/tex]

Putting the values,

a = [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - \int\limits{(\frac{1}{x} )(\frac{1}{3}x^{3}-4x)} \, dx ][/tex]

  = [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - (\frac{1}{9}x^{3}-4x)][/tex]

  = [tex]-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x[/tex]

Returning to the definite integral, now

A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]

   = [tex][-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x]^{2} _{1}[/tex]

   = [tex]-6ln2(\frac{8}{3}-8)+\frac{16}{3}-48-\frac{2}{3}+24[/tex]

   =  [tex]32lnx-\frac{58}{3}[/tex]

Hence, The area of the region bounded by the given curves is [tex]32lnx-\frac{58}{3}[/tex].

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The multiplication of the given two matrices AC will be [tex]\left[\begin{array}{ccc}-15&12&17\\5&-9&1\end{array}\right][/tex].

matrix, a collection of numbers lined up in rows and columns to produce a rectangular array. The elements of the matrix, also known as the entry, are the numerals.

In another word, a matrix is a set of variables that are arranged in such a good way that we can create an algebraic equation from that.

As per the given matrices,

A = [tex]\left[\begin{array}{ccc}2&-1&3\\0&2&-1\end{array}\right][/tex]

C = [tex]\left[\begin{array}{ccc}-5&0&5\\2&-3&2\\-1&3&3\end{array}\right][/tex]

The number of columns in matrix A is the same as the number of rows in matrix C.

The multiplication will be as,

AC = [tex]\left[\begin{array}{ccc}2&-1&3\\0&2&-1\end{array}\right]\times\left[\begin{array}{ccc}-5&0&5\\2&-3&2\\-1&3&3\end{array}\right][/tex]

AC = [tex]\left[\begin{array}{ccc}(2(-5)-1(2)+3(-1)&(0+-1(-3)+3(3))&2(5)+-1(2)+3(3)\\(0+2(2)+(-1(-1))&(0+2(-3)+-1(3)&2(5)+0+2(2)+-1(3)\end{array}\right][/tex]

AC = [tex]\left[\begin{array}{ccc}-15&12&17\\5&-9&1\end{array}\right][/tex]

Hence "The multiplication of the given two matrices AC will be [tex]\left[\begin{array}{ccc}-15&12&17\\5&-9&1\end{array}\right][/tex]".

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AAA is a triangle similarity theory. Which means all the respective angles of two triangles are equal.

AAA Postulate: (Angle Angle Angle)

It states that if all three angles of a triangle are equal to all three respective angles of another triangle, then the two triangles will be similar.

Let's say the angles ABC , BCA ,CAB of a triangle ABC are equal to the sides XYZ, YZX, ZXY of triangle XYZ then we can say that according to AAA postulates both the sides are similar and as a result we can say that their respective sides will be also same.

AAA postulates sate that if the all three angles of two triangle is equal then they will be called as similar triangle.

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For solving algebra Determine the issue, Describe your knowledge, Plan beforehand, Execute the plan ,and Check to see whether the response makes sense.

One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is, roughly speaking, the study of mathematical symbols and the rules for using these symbols in formulae. With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ integers that have a fixed or definite value in algebra, such as 2, 7, 0.068, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.

to do algebra for beginners - Determine the issue, specify your knowledge, Plan, execute, and confirm that the solution makes sense.

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The gradient of the vector field of function f(x, y, z) is (12x,2y,2z)

The term gradient of the vector in math is calculated as the vector whose components are given by the partial derivatives of the function and it can be evaluated at any given point, and the gradient represents the direction and magnitude of greatest increase of the function at that point.

Here we have given the function f(x, y, z) = 6x² + y² + z²

Now we have to calculate the gradient of the function by using the following step.

In the given question, we have identified the values of the following as,

=> x = 6x²

=> y = y²

=> z = z²

Now, in order to find the gradient of a function (which is a vector), differentiate the function with respect to each variable.

=> ∇f=(∂f/∂x, ∂f/∂y, ∂f/∂z)

Now, the value of

=> ∂f/∂x = 12x

=> ∂f/∂y = 2y

=> ∂f/∂z = 2z

Now, we have to plug in the point:

=> ∇f(x, y, z) = (12x,2y,2z)

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We determine the value of log₂16 = 4 by using logarithm laws.

What is logarithm?

Logarithm is the alternative way of representing an exponent. The power at which a number is needed to raise to get the other values is termed as logarithm.

It is called log base 2 or binary logarithm. It is the inverse of the power of function 2.

We stated before that log base 2 is an inverse expression of the power 2. let N is a real positive number and x is the number of exponents. Now, logarithm form of the exponent is written as log₂ N = x

                                                                        2ˣ = N

We are given, log₂ 16

 N= 16

  log₂16 = x

    2ˣ =16

we know that 2⁴ =16

hence, x= 4

hence, log₂ 16 = 4

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The steps to solve expressions easily are:

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

To solve expressions we must organize:

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The probability that the student competed in Rhythm given they had competed in Smooth or Standard: P(Rhythm |Smooth or Standard) or P ( A/( B or C)) is 0.6613 = 66.13%.

We have, A survey was conducted at a local ballroom dance studio asking students with three dance categories. The above Venn diagram shows the number of students in these three categories of dance.

Total number of students in all dance categories n(A or B or C) = 5 + 6 + 8 + 12 + 14 + 15 + 10 + 4

= 74

let us consider the events

A : students in Rhythm dance category

B : students in Standard dance category

C : students in Smooth dance category

Using the conditional probability,

Probability that student has competed in Rhythm and they have competed in Smooth, P(Rhythm/ smooth) = P(A/C) = P(A and C)/P(C)

= (12+14)/74 = 26/74 = 0.703

but we have to calculate probability that the student competed in Rhythm given they had competed in Smooth or Standard, P(Rhythm/Smooth or Standard) = P(Rhythm and (Smooth or Standard))/P(Smooth or Standard)

i.e., P( A/(B or C) )= P(A and (B or C))/P(B or C)

n(B or C) = n(B) + n(C) - n( B and C)

=> n(B or C) = 14 + 5 + 10 + 15 + 12 + 14 + 5 + 6 - 5 - 14 = 62

Now, P(B or C) =n(B or C)/n(A or B or C)

=> P(B or C) = 62/74 = 0.703 = 70.3%

P(A and (B or C)) = n(A and (B or C))/n(A or B or C)

n(A and (B or C)) = n(A) + n(B or C) - n(A or B or C)

= 12 + 14 + 15 + 8 + 62 - 70 +4 = 41

P(A and (B or C)) = 37/74

So, P( A/(B or C) )= P(A and (B or C))/P(B or C)

=> P( A/(B or C) )= 41/74/62/74 = 41/62

= 0.6613 = 66.13%

Hence, the required probability is 66.13%.

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Complete question:

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories:

- Smooth

- Rhythm

- Standard

The results were then presented to the owner in the following Venn Diagram. Use the Venn Diagram to determine the following probabilities. Write your answers in percent form, rounded to the nearest tenth .If a student is chosen at random; what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth or Standard: P(Rhythm |Smooth or Standard)

we have given that

X=7

and Y=3

Step-by-step explanation:

3x-2y=15

put value

(3×7)-(2×3)=15

so we can say that the value of X and Y having different value and satisfied given given

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In the given graph with the function, x = -9 if f(x) = 7

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is actually equal to its graph. It is often helpful to think of functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output.

A codomain should be considered, for instance, when determining whether a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone. The terms "function" and "graph of a function" are frequently used because, although they refer to the same thing, they express different viewpoints on it.

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Answer:

Below

Step-by-step explanation:

6 (x-1.50) = 51        6 = number of tix     x - 1.50 = sale price     x = reg price

6x - 9 = 51

6x = 60

x = 10 dollar regular price

You can return multiple values from a function in Python.

Now, According to the question:

Can Python function return 3 values?

You can return multiple values from a function in Python. To do so, return a data structure that contains multiple values, like a list containing the number of miles to run each week. Data structures in Python are used to store collections of data, which can be returned from functions.

How do you return 4 values in Python?

In Python, you can return multiple values by simply return them separated by commas. In Python, comma-separated values are considered tuples without parentheses, except where required by syntax. For this reason, the function in the above example returns a tuple with each value as an element.

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You can find the missing number in an array without loop by counting the number of elements in the array, and then looping through the elements.

Here is a simple program to find the missing numbers in an integer array.

ArrayList<Integer> arr = new ArrayList<Integer>();

int a[] = { 1,3,4,5,6,7,10 };

int j = a[0];

for (int i=0;i<a.length;i++)

{

   if (j==a[i])

   {

       j++;

       continue;

   }

   else

   {

       arr.add(j);

       i--;

   j++;

   }

}

System.out.println("missing numbers are ");

for(int r : arr)

{

   System.out.println(" " + r);

}

You can find the missing number in an array without loop by counting the number of elements in the array, and then looping through the elements.

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By resolving these equations, we can arrive at one solution.

To find the number of solutions to a system of equations, you can solve the system either by graphing the equations or by using algebraic methods such as substitution or elimination.

If the equations are compatible (meaning that there is at least one combination of values for the variables that satisfies both equations), then the system has at least one solution. If the equations are independent (meaning that they are not related to each other and cannot be derived from each other), then the system has exactly two solutions. If the equations are dependent (meaning that one of the equations can be derived from the other), then the system has exactly one solution. If the equations are incompatible (meaning that there is no combination of values for the variables that can satisfy both equations), then the system has no solutions.

In this case, the equations are 3x + 2y = 5 and 2x - 3y = 7. To find the number of solutions to this system, you can either graph the equations or solve the system using algebraic methods.

Using algebraic methods, you can start by solving one of the equations for one of the variables in terms of the other:

3x + 2y = 5

2y = -3x + 5

y = (-3/2)x + (5/2)

Then, you can substitute this expression for y into the other equation to solve for x:

2x - 3((-3/2)x + (5/2)) = 7

2x + (9/2)x - (15/2) = 7

(11/2)x - (15/2) = 7

(11/2)x = (15/2) + 7

(11/2)x = (15 + 14)/2

(11/2)x = 29/2

x = 29/11

Substituting this value for x back into the first equation, you can solve for y:

3(29/11) + 2y = 5

87/11 + 2y = 5

2y = 5 - 87/11

2y = (55 - 87)/11

2y = -32/11

y = -32/22

Therefore, the solution to this system of equations is x = 29/11 and y = -32/22. Since there is only one solution, this system has exactly one solution.

The complete question is:-

How many solutions can we get by solving these equations 3x + 2y= 5;2x -3y =7?

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If ∠ A ≅ ∠ B then ∠ B ≅ ∠ A serves as an example of the symmetric property of congruence.

The symmetric property of equality in mathematics is actually fairly straightforward. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.

According to this principle, if a = b and b = c, then a = c.

THE CHARACTERSISTICS OF CONGRUENCE:

1. REFLEXIVE PROPERTY

CONCURRENCE TO LINE SEGMENT AB IS LINE SEGMENT AB

3. SYMMETRIC PROPERTY : Angle B is congruent with angle A if and only if angle A is congruent with angle B.

3. TRANSITIVE PROPERTY: Angle A is in accordance with Angle C if Angle A is in accordance with Angle B and Angle B is in accordance with Angle C.

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Mathematical expressions known as linear inequalities compare two expressions and used the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities.

When resolving multi-step linear inequalities, we must follow the laws of inequality.

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Therefore, the  solution of the given problem is  factors of the given equation are  [tex]x^{2}[/tex](x - 12) - 2. (x - 12).

An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.

Here,

The approach of grouping for factoring polynomials in this case is a progression from the method of identifying common factors.

In order to determine the factors of the given polynomial expression,

we are trying to find groups from the common factors in this case.

The components of [tex]x^{3}[/tex]- 12[tex]x^{2}[/tex] - 2x + 24 are hence

=> [tex]x^{2}[/tex](x - 12)  -2 (x - 12)

=> [tex]x^{2}[/tex](x - 12) - 2. (x - 12).

Therefore, the factors of the given equation are  [tex]x^{2}[/tex](x - 12) - 2. (x - 12).

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Answer:

Step-by-step explanation:

i think its b daddy

Prime factorization is the process of expressing a number as the sum of all its prime factors. In prime factorization, each and every integer is a prime number.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A component is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the final since the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be used.

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A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. so The first prime number is 2.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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The equation 22 = -13 + a gives the value a = 35.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 8 is an equation.

We have,

22 = -13 + a

Add 13 on both sides.

22 + 13 = a

a = 35

Thus,

The value of a is 35.

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