The EPA is also interested in controlling the local population of deer. This could be done
by expanding or reducing the duration of each year's hunting season. After collecting
decades of data, a team of researchers developed a quadratic model relating the local
deer population to the duration of each year's hunting season.

P = -10h² + 30h + 237

Here P is the population of deer at the end the year while h is the length of that year's
hunting season that year, measured in months. What is the maximum amount of deer this
model predicts? What does the model predict the population of deer would be if the
government allowed year-round? What would this actually mean?

Using the given information sin(x) = 5/7 and x in quadrant 2, the exact values are:

sin(x/2) = √[(1 - √24/7)/2],

cos(x/2) = -√[(1 + √24/7)/2],

tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

To determine the exact values of sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2, we can utilize the half-angle formulas. These formulas allow us to express the trigonometric functions of an angle in terms of the trigonometric functions of half that angle.

Given sin(x) = 5/7, we can find cos(x) using the Pythagorean identity:

cos(x) = √(1 - sin^2(x)) = √(1 - (5/7)^2) = √(1 - 25/49) = √(24/49) = √24/7.

To find sin(x/2), we use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos(x))/2] = ±√[(1 - √24/7)/2].

Since x is in quadrant 2, sin(x) is positive. Therefore, sin(x/2) is also positive. Thus, we have:

sin(x/2) = √[(1 - √24/7)/2].

Similarly, we can find cos(x/2) using the half-angle formula for cosine:

cos(x/2) = ±√[(1 + cos(x))/2] = ±√[(1 + √24/7)/2].

Since x is in quadrant 2, cos(x) is negative. Therefore, cos(x/2) is also negative. Thus, we have:

cos(x/2) = -√[(1 + √24/7)/2].

Lastly, we can find tan(x/2) using the half-angle formula for tangent:

tan(x/2) = sin(x/2) / cos(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

Combining these results, the exact values for sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2 are:

sin(x/2) = √[(1 - √24/7)/2],

cos(x/2) = -√[(1 + √24/7)/2],

tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

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The angles formed by the diagonals and sides of the regular geometric figures and polygons indicates;

6. m∠1 = m∠2 = 90°

m∠4 = 39°

7. m∠3 = 52°

m∠1 = 128°, m∠2 = 128°

8. x = 30°

9. The lines drawn are the median lines of the triangle

10. 120°

A polygon is a geometric figure with three or more sides that form a loop.

6. The diagonals of a kite are perpendicular, therefore;

m∠1 = m∠2 = 90°

m∠3 = 51° (Corresponding angles of congruent triangles are congruent)

m∠4 = 90° - ∠3 (Acute angles in a right triangle)

m∠4 = 90° - 51° = 39°

Part 2

The base angles of an isosceles trapezoid are congruent, therefore;

m∠3 = 52° (Definition of congruent angles)

The angles ∠1 and ∠2 are congruent, therefore;

m∠1 + m∠2 + 52° + m∠3 = 360°

m∠1 + m∠2 = 360° - (52° + m∠3)

2 × m∠1 = 360° - (52° + 52°) = 256°

m∠1 = 256°/2 = 128°

m∠1 = m∠2 = 128°

8. The measure of an interior angle of a polygon is; θ = (n - 2) × 180/n

The polygon is a dodecagon, therefore, the measure of the interior angles of the 12 sided polygon is therefore;

θ = (12 - 2) × 180/12 = 150

The angle x and the interior angles of the dodecahedron are linear pair angles, therefore;

θ + x = 180°

x = 180° - θ

x = 180° - 150° = 30°

9. The lines drawn that bisect the facing sides are median lines, that are also the angle bisectors of the interior angles of the  triangle. The point of intersection of the lines is the incenter and the centroid of the triangle.

10. The interior angle of a regular hexagon, which is a 6 sided polygon can be found as follows;

Interior angle of a regular polygon with n sides, θ = (n - 2) × 180/n

In a regular hexagon, n = 6, therefore;

θ = (6 - 2) × 180/6 = 120°

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Therms are

5 , 4x , 8y

Variables are

x , y

coefficients are

4 , 8

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The extraneous solution for the rational expression 2 · x² - 2 = (x - 1) · (x - 2) is equal to x = 1.

In this problem we must determine whether an extraneous solution exist to a given rational expression. The procedure is now summarized. First, use algebra properties to eliminate denominators:

1 / (x - 1) = (x - 2) / (2 · x² - 2)

2 · x² - 2 = (x - 1) · (x - 2)

Second, expand and simplify the expression until a polynomial in standard form is found:

2 · x² - 2 = x² - 3 · x + 2

x² + 3 · x - 4 = 0

Third, factor the quadratic equation:

(x + 4) · (x - 1) = 0

x = - 4 or x = 1

Fifth, check in initial expression:

1 / (- 4 - 1) = (- 4 - 2) / [2 · (- 4)² - 2]

- 1 / 5 = - 6 / 30

- 1 / 5 = - 1 / 5

1 / (1 - 1) = (1 - 2) / (2 · 1² - 2)

1 / 0 = - 1 / 0 (EXTRANEOUS)

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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mode is the number or item that repeats most frequent so it's $15

Answer: 3.7 + 0.41 + 1.3 + 0.7

Step-by-step explanation: for 3.7 you see the number after 7 is 2 and that tells u to round  down

0.41 - the digit after the 4 is 1 so u round  down

1.3 - the digit after the 2 is 8 so u round up

0.7 - the digit after the 6 is 5 so u round up

The two planes are approximately 200 miles apart, rounded off to the nearest integer.

Using the Law of Cosines formula,

The distance between the two planes can be determined.

The formula for the Law of Cosines is as follows: c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C and a and b are the other two sides.

Using the formula, the distance between the two planes after one hour can be calculated as follows:

[tex]c^2[/tex] = [tex]200^2[/tex] + [tex]300^2[/tex] - 2(200)(300)cos(50°)[tex]c^2[/tex]

= 40,000 + 90,000 - 120,000cos(50°)[tex]c^2[/tex]

= 130,000 - 89,873.86c

= sqrt(40,126.14)c

= 200.315 miles

Therefore, after one hour, the two planes are approximately 200 miles apart, rounded off to the nearest integer.

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The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

[tex]5 { \times 54}^{2} [/tex]

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: [tex]\bf{A=\pi r^2}[/tex].

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}[/tex]

Plug in the data:

[tex]\sf{A=\pi\times3^2}[/tex]

[tex]\sf{A=\pi\times9}[/tex]

[tex]\sf{A=28.27\:ft^2}[/tex]

The correct answer is each comic book the individual wants to sell (S) weighs approximately 2.213 ounces.

Let's assume the weight of each comic book the individual wants to sell (S) is "x" ounces.

Given that there are 50 copies of the comic book the individual wants to sell (S) and their combined weight is 133.4 ounces, we can set up the equation:

50x + 13A = 133.4 ---(Equation 1)

Similarly, if the individual brings 35 copies of the comic book they want to sell (S) and 13 copies to be appraised (A), the combined weight would be 100.4 ounces:

35x + 13A = 100.4 ---(Equation 2)

We can solve this system of equations to find the weight of each comic book the individual wants to sell (S).

Multiplying Equation 1 by 35 and Equation 2 by 50 to eliminate the variable "A," we get:

1750x + 455A = 4679 ---(Equation 3)

1750x + 650A = 5020 ---(Equation 4)

Subtracting Equation 3 from Equation 4, we eliminate "x" and get:

195A = 341

Dividing both sides of the equation by 195, we find:

A = 341/195

A = 1.75

Now, substituting the value of A into Equation 1 or Equation 2, we can solve for "x":

50x + 13(1.75) = 133.4

50x + 22.75 = 133.4

50x = 133.4 - 22.75

50x = 110.65

x = 110.65/50

x = 2.213

Therefore, each comic book the individual wants to sell (S) weighs approximately 2.213 ounces.

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The average speed formula is given by:

[tex]\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}[/tex]

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is [tex]\displaystyle\sf 2 \times 120 = 240[/tex] miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula [tex]\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex].

For the journey from A to B:

[tex]\displaystyle\sf \text{Time}_1 = \frac{120}{30} = 4[/tex] hours

For the return journey from B to A:

[tex]\displaystyle\sf \text{Time}_2 = \frac{120}{40} = 3[/tex] hours

The total time for the round trip is the sum of the individual times:

[tex]\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7[/tex] hours

Now, we can calculate the average speed:

[tex]\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{240}{7} \approx 34.29[/tex] miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

The graph is bounded and does not extend to infinity, the range is the subset of real numbers within that constraint.

To create a table of values for the given function graph, we will identify the x-values and their corresponding y-values.
Reading the graph from left to right, the x-values in order from least to greatest are: -10, -5, 0, 5.
By looking at the graph, we can determine the corresponding y-values for each x-value.

Let's say the y-values are y1, y2, y3, and y4 respectively.
Now, we can create the table of values:
x   |   y
-10 |   y1
-5  |   y2
0   |   y3
5   |   y4
To state the domain and range of the function, we need to consider the set of all possible x-values and the set of all possible y-values.
In this case, the domain of the function is the set of x-values, which is {-10, -5, 0, 5}.
The range of the function is the set of y-values, which corresponds to {y1, y2, y3, y4}.
It is important to note that without specific values for y1, y2, y3, and y4, we cannot provide the exact range of the function.

The domain of the function is {-10, -5, 0, 5}, which is the set of all possible x-values.

Regarding the scope of the function, since you said that the y values ​​correspond to {y1, y2, y3, y4}, it i not possible to determine the exact scope of the function since there are no specific values. y4 function for y1, y2, y3.

However, based on the chart and the information given, we can say that the range will be a series of real numbers, depending on how the chart behaves.

If the graph extends infinitely in both the positive y-direction and the negative y-direction, the range consists entirely of real numbers.

However, we can say that the range will be a set of real numbers depending on the behavior of the graph.

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Answer:

1300

Step-by-step explanation:

(56 · 13) + (44 · 13)

(728) + (572)

1300

So, the answer is 1300

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Answer:

Excise tax

Step-by-step explanation:

Correct me if I'm wrong <3

sum angel measure of angles in triangle is 180° according to this rule

(n-2)180 , n is the no. of sides

so E+D+F=180

72+D+63=180

135+D=180

D=180-135

D=45°

HOPE IT HELPS

PLEASE MARK ME AS BRAINLIEST

Answer: [m and n], and [o and p]

Step-by-step explanation:

The parallel groups of lines are m and n, and the group o and p.

The correct answer is A. Yes, because the angles are congruent and the sides are proportional.

Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are proportional. In this case, we are given the triangles ABC and ADEF.

To determine if ABC is similar to ADEF, we need to compare the angles and sides of the two triangles.

If all the angles of one triangle are congruent to the corresponding angles of the other triangle, and the sides of one triangle are proportional to the corresponding sides of the other triangle, then the triangles are similar.

we can say that if the angles of ABC are congruent to the angles of ADEF and the sides of ABC are proportional to the sides of ADEF, then ABC is similar to ADEF.

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The total savings that the couple Puan Yani and her husband have now is A) RM126,000.

The total savings of the couple can be determined by addition.

Addition is one of the four basic mathematical operations, including subtraction, divsion, and multiplication.

Let the amount that Puan Yani has in her savings account, a = RM24,700

Let the amount that her husband has than Puan Yani = RM75,300

The total amount that her husband has = a + 75,300

= RM100,000 (R24,700 + RM75,300)

The additional amount that Puan Yani deposited at the end of May = RM1,300

The total amount that Puan Yani has in her savings account at the end of May = RM26,000 (RM24,700 + RM1,300)

The total savings in the couple's accounts = RM126,000 (RM100,000 + RM26,000)

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Answer: [tex](-3+18)+(i+5i)[/tex]

Step-by-step explanation:

The commutative property of addition states that the order in which numbers are added does not change the sum. In the context of complex numbers, this means that you can rearrange the real and imaginary parts separately.

So, the expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression [tex](-3+i)+(18+5i)[/tex]

would be:

[tex](-3+18)+(i+5i)[/tex]

Answer:

The room is 13 feet wide.

Step-by-step explanation:

Calculate for the Area of the room by dividing the cost by the price per square foot.

Area = $312 ÷ $2

Area = 156 ft²

Area of a rectangle = length x width

A = lw

Since we're given with 12 ft as the length then we can solve for the width 'w'

A = lw

Substitute

A = 156

l = 12

156 = 12w

Divide both sides of the equation by 12

156/12 = 12w/12

13 = w

w = 13ft

The correct option is (iii) the distance between points X and Z. Distance between points Y and Z: 2 units

We can find the distance between points on the line segment by finding the difference between their coordinates.

The correct option is the distance between points X and Z, which is equal to 6.

There are four points that partition the directed line segment from A to B.

The partition ratio at each point is as follows:

Point P partitions the directed line segment from A to B into a 3:4 ratio.

Point Q partitions the directed line segment from A to B into a 4:3 ratio.Point R partitions the directed line segment from A to B into a 2:5 ratio.

Distance between points Y and Z:

Again, the number line does not provide the exact coordinates of the points Y and Z. However, the line segment from A to B is split 5:2 at point S, so the distance can be concluded as: Between Y and Z is 2 units.

So the distance between the given points is:

Distance between points W and X: 5 units

Distance between points X and Y: 4 units

Distance between points X and Z: 5 units

Distance between points Y and Z: 2 units

Point S partitions the directed line segment from A to B into a 5:2 ratio.

Here, we have to measure the distance of each of the following:

(i) The distance between points W and X

(ii) The distance between points X and Y

(iii) The distance between points X and Z

(iv) The distance between points Y and ZThe distance between points X and Z is 6 units.

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The distances are described as follows:

The distance between points W and X is 5 units.

The distance between points X and Y is 4 units.

The distance between points X and Z is 8 units.

The distance between points Y and Z is 4 units.

The distance between points W and X is gotten:

We  subtract the coordinates of point W from the coordinates of point X to get the distance

Distance = X - W = (-3) - (-8) = 5 units.

The distance between points X and Y shown as :

we will also  subtract the coordinates of point X from the coordinates of point Y.

Distance = Y - X = 1 - (-3) = 4 units.

The distance between points X and Z is :

We also  subtract the coordinates of point X from the coordinates of point Z.

Distance = Z - X = 5 - (-3) = 8 units.

The distance between points Y and Z:

Finally, we subtract the coordinates of point Y from the coordinates of point Z.

Distance = Z - Y = 5 - 1 = 4 units.

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1. Variable: A symbol or letter that represents an unknown value or quantity in algebraic expressions and equations.

2. Equation: A mathematical statement that shows the equality between two expressions, typically represented by an equal sign (=).

3. Coefficient: The numerical factor that is multiplied by a variable in a term.

4. Expression: A mathematical phrase that may contain variables, constants, and operations, but does not have an equal sign.

5. Linear Equation: An equation in which the highest power of the variable is 1, written in the form ax + b = 0, where a and b are constants and x is the variable.

Variable: In algebra, a variable is a symbol (usually a letter) that represents an unknown value or quantity. It allows us to express mathematical relationships and solve equations.

Equation: An equation is a mathematical statement that shows the equality between two expressions.

It consists of an equal sign (=) and can include variables, constants, and operations.

Solving equations involves finding the values of the variables that make the equation true.

Coefficient: A coefficient is the numerical factor that is multiplied by a variable in a term.

It represents the scale or magnitude of the variable.

For example, in the term 3x, the coefficient is 3.

Expression:

An expression is a mathematical phrase that can contain variables, constants, and operations, but does not have an equal sign.

Expressions can be evaluated or simplified, but they cannot be solved since they lack the equality found in equations.

Linear Equation:

A linear equation is an equation where the highest power of the variable is 1.

It can be written in the form ax + b = 0,

where a and b are constants and x is the variable.

Solving linear equations involves finding the value(s) of x that satisfy the equation.

These are just a few key definitions that form the foundation of understanding introductory algebra.

Mastering these concepts will provide a solid basis for further exploration and learning in algebraic principles and problem-solving.

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