True Or False: (If True Prove it, If false Give Example) 1) The union of two topologies is a topology. 2) The usual topology is finer than co-finite topology. (Tco ST.) 3) Int(A) Int(B) = Int(AUB) 4) The set of integers Z is dense in (X,T.).
Answers
1) The statement "The union of two topologies is a topology" is true. 2) The statement "The usual topology is finer than co-finite topology" is false. 3) The statement "Int(A) Int(B) = Int(AUB)" is false. 4) The statement "The set of integers Z is dense in (X,T)" is false.
1) The statement "The union of two topologies is a topology" is true. If two topologies are defined on the same set X, then the union of the two topologies is also a topology on X. This is because the union of any collection of open sets is also an open set, and the intersection of any finite number of open sets is also open. Hence, the union of two topologies is a topology.
2) The statement "The usual topology is finer than co-finite topology" is false. A topology T1 is finer than another topology T2 if every set that is open in T2 is also open in T1. However, the co-finite topology has the property that the only closed sets are finite sets and the entire set. Thus, every set that is not finite is open. On the other hand, in the usual topology, there are many more open sets than in the co-finite topology. For example, in the usual topology, every singleton is open. This means that the co-finite topology is actually finer than the usual topology.
3) The statement "Int(A) Int(B) = Int(AUB)" is false. Here, Int denotes the interior of a set. The correct statement is "Int(AUB) ⊇ Int(A) ∩ Int(B)". This inequality says that the interior of the union is a superset of the intersection of the interiors. To see why this is true, note that any point in the intersection of the interiors is in both A and B, so it is also in AUB. Hence, it must be in the interior of AUB.
4) The statement "The set of integers Z is dense in (X,T)" is false.
Here, T is a topology on X. A subset A of X is said to be dense if every point in X is either in A or is a limit point of A. In other words, the closure of A is equal to X. However, the set of integers Z is not dense in any usual topology on a metric space X. For example, if X = R with the usual topology, then the closure of Z is Z ∪ {∞}, which is strictly smaller than R.
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Related Questions
Multiply polynomials
HELP I NEED THIS ASAP
Answers
Answer:
6x^3-5x^2+9x+10
Step-by-step explanation:
Use the distributive property and multiply like terms.
Are the two triangles below similar? N 259 50 5 105 50 3 01)
Answers
Answer:
I didn't get the question please explain it
Use the graph to find the following(H) The number at which of has a relative minimumE,F,G,H, I, J,K, L
Answers
Explanation:
Part (e)
f is increasing when from left to right, the function goes up. Then, the interval on which f is increasing is (5, ∞)
Part (f)
f is decreasing when from left to right the graph goes down. Then, the interval is (0, 5)
Part (g)
f is constant when the graph is a horizontal line, so the interval is (-∞, 0).
Part (h)
f has a relative minimum at point (5, -1) because it is the lowest point of the curve. So, the number at which f has a relative minimum is 5.
part (i)
Since the relative minimum is at point (5, -1), the relative minimum is -1.
Part (j)
f(-2) is the y-coordinate of the graph when x = -2. Then f(-2) = 24
Part (k)
When the y-coordinate is 3, the x-coordinate is 3 and 7, so the values of x for which f(x) = 3 are 3 and 7.
Part (l)
A graph is even if it is symmetric across the y-axis and it is odd if it is symmetric across the origin. In this case, there is no symmetry, so f is neither even nor odd
Therefore, the answers are:
e) (5, ∞)
f) (0, 5)
g) (-∞, 0)
h) 5
i) -1
j) 24
k) 3 and 7
l) neither
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The multiplicity of a root r of the characteristic equation of Ais called the algebraic multiplicity of r as an eigenvalue of A. Choose the correct answer below. O A The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. B. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. O
C. The statement is false. The multiplicity of a root r of the characteristic equation of A is the number of eigenvectors corresponding to that root. O
D. The statement is false. The multiplicity of a root r of the characteristic equation of Ais called the geometric multiplicity of r as an eigenvalue of A.
Answers
The correct option is B. The statement "The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A." is true. The statement is the definition of the algebraic multiplicity of an eigenvalue of A.
A matrix is diagonalizable if and only if each eigenvalue of the matrix has an algebraic multiplicity that is equal to its geometric multiplicity. To get the characteristic equation of a matrix, the determinant of the matrix A I is set to zero. The characteristic equation of an nn matrix A is given by AI = 0. The characteristic equation's roots are the matrix's eigenvalues.
The algebraic multiplicity of an eigenvalue is the number of times it appears as the root of the characteristic equation. The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors corresponding to that eigenvalue. So, the correct option is B.
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Question 1 Professor Plum is putting a brick border around his irregular shaped garden. Before installing the border, Professor Plum must cut the bricks to fit the angles of the garden. Use the given measures to answer the question.
What are the angle measures of each vertex of the garden? Show your work.
question 2 ⦁ In Parallelogram , diagonals and intersect at point A. Give and. What is ? Show your work.
question 3 ⦁ Quadrilateral ABCD has vertices at. Based on the properties of the diagonals, is quadrilateral ABCD a rectangle, rhombus, or square? Use the distance and slope formulas to prove your conclusion. Show your work
Answers
The angle measures of each vertex of the garden are 53.13 degrees.
In Parallelogram ABCD, diagonals AC and BD intersect at point A = √7.
What is angle?Angle is a geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360°.
1. To determine the angle measures of each vertex of the garden, we must first calculate the angles formed by each side. For example, the angle formed by sides AB and BC can be found by using the inverse tangent function. The equation would be
arctan(BC/AB) = arctan (4/3) = 53.13 degrees.
The angles for the other sides can be calculated in the same way. We can then use the sum of angles theorem to calculate the angles at each vertex. Since the garden is an irregular shape, the angles at each vertex will be different.
2. In Parallelogram ABCD, diagonals AC and BD intersect at point A. To calculate , we can use the distance formula.
The equation would be = √((x2 – x1)2 + (y2 – y1)2).
For the coordinates given, we would have
= √((2 – 5)2 + (5 – 1)2)
= √(-9 + 16)
= √7.
Answer 3: To determine whether quadrilateral ABCD is a rectangle, rhombus, or square, we must first calculate the slope.
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What is the find the value of p x 8 when p=6
Answers
6 * 8 = 48
Breaking it down into addition:
8 +8+8+8 +8+8
16+16+16
32+16
48
On 1 October 2015 Karen purchased freehold land and buildings for £480,000, of which the land element was £80,000. The buildings had a useful life of 25 years at the date of purchase. The residual value was nil.
On 1 October 2020 the land and buildings were revalued to £500,000, of which the land element was £100,000. There was no change in the useful life of the property.
According to IAS 16 Property, Plant and Equipment, what should be the depreciation charge for the year ended 30 September 2021 and the balance on the revaluation surplus as at that date?
A Depreciation charge £16,000; revaluation surplus £100,000
B Depreciation charge £20,000; revaluation surplus £100,000
C Depreciation charge £25,000; revaluation surplus £116,000
D Depreciation charge £20,000; revaluation surplus £116,000
Answers
Accoding to the calculations , the correct answer is:
A) Depreciation charge 16,000; revaluation surplus £20,000
According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.
In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).
To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:
£400,000 / 25 = £16,000
Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.
Now, let's calculate the balance on the revaluation surplus as at that date.
The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).
Revaluation surplus = Fair value - Carrying amount
Revaluation surplus = £500,000 - £480,000
Revaluation surplus = £20,000
Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.
Based on the calculations above, the correct answer is:
A) Depreciation charge £16,000; revaluation surplus £20,000
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Samuel made 31 out of 40 field goals during football practice. What percent of the field goals did Samuel make?
Answers
The percent of the field goals did Samuel make will be 77.5%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:
= 31 / 40 × 100
= 77.5%
The percentage is 77.5%.
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Please help , how do you do this ?
Answers
(-6)x (y=3x+5) 22x=-2 x=-2/22
4x+6y=28 y=3(-2/22)+5 y=52/11
-6y=-18x-30
4x+6y=28
eliminate
so -18x-30=0
4x-28=0
=-22x-2=0
*Mark Brainlist please that took me 7 minutes
a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players?
Answers
The median weight of the players on the football team is approximately 160 lbs.
The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.
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The complete question is
a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.
Write the equation of this line in point slope form the line passes through (-2,22) and (4,8)
Answers
Write the equation of this line in point slope form the line passes through (-2,22) and (4,8)
step 1
Find the slope
m=(8-22)/(4+2)
m=-14/6
m=-7/3
step 2
Find the equation in point slope form
y-y1=m(x-x1)
we have
m=-7/3
if take the point (-2,22)
the equation is
y-22=-(7/3)(x+2)If take the point (4,8)
the equation is
y-8=-(7/3)(x-4)PLEASE HELP!! WILL GIVE BRAIN AND FIVE STARS!!
Answers
20.) GH = FE
21.) <JGH = <FEK
Hope it helps ⭐⭐⭐HELP PLEASE
FR DO NOT UNDERSTAND THIS AT ALL
Answers
Answer:
x= 20
Step-by-step explanation:
hope this helps :>
x+10+2x+20=90
x=20
In the figure below, mZ1=(x +48) and m2 2=2xº.
Find the angle measures.
Answers
m < 1 + m < 2 = 90°
x° + 48° + 2x° = 90°
Combine like terms:
48° + 3x° = 90°
Subtract 48° from both sides:
48° - 48° + 3x° = 90° - 48°
3x = 42°
Divide both sides by 3 to solve for x:
3x/3 = 42/3
x = 14°
Plug in the value of x into the equation to fins m< 1 and m < 2:
m < 1 + m < 2 = 90°
(14° + 48°) + 2(14)° = 90°
62° + 28° = 90°
90° = 90° (True statement)
Therefore:
m < 1 = 62°
m < 2 = 28°
What ordered pairs satisfy the function y=2/3+1
Answers
Answer:
2345678io90
Step-by-step explanation:
Let e_1 = [1 0], e_2 = [0 1], y_1 = [2 5], and y_2 = [-1 6], and let T : R^2 rightarrow R^2 be a linear transformation that maps e_1 into y_1 and maps e_2 into y_2. Find the images of [5 -3] and [x_1 x_2].
Answers
Let T: R² → R² be a linear transformation that maps e1 = [1 0] and e2 = [0 1] into y1 = [2 5] and y2 = [-1 6] respectively.
So, T(e1) = y1 and T(e2) = y2.
Now, we need to find the images of [5 -3] and [x1 x2]. [5 -3] can be expressed as 5e1 - 3e2.
Therefore, T([5 -3]) = T(5e1 - 3e2) = 5T(e1) - 3T(e2) = 5y1 - 3y2 = [19 -7].
Similarly, let's say [x1 x2] is a vector in R².
Then [x1 x2] = x1e1 + x2e2. So, T([x1 x2]) = T(x1e1 + x2e2) = x1T(e1) + x2T(e2) = x1y1 + x2y2 = [2x1 - x2 5x1 + 6x2].
Therefore, the image of [5 -3] under T is [19 -7], and the image of [x1 x2] under T is [2x1 - x2 5x1 + 6x2].
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A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min.
At what rate is the area changing, in cm2/min, when the height is 1.5 cm?
Answers
The area of the rectangle is changing at
0.75 sq.cm/min
Let
x
and
y
be the base and height of the rectangle.
x
=
0.5
cm is constant :. dx/dt=0#. Area of the rectangle
is
A
=
x
⋅
y
. Differentiating both sides we get
d
A
d
t
=
d
x
d
t
⋅
y
+
d
y
d
t
⋅
x
;
y
=
1.5
,
d
y
d
t
=
1.5
cm /min.
∴
d
A
d
t
=
0
⋅
1.5
+
1.5
⋅
0.5
=
0.75
sq.cm/min.
The area of the rectangle is changing at
0.75
sq.cm/min
factorise 16-(5y-2)^2
Answers
The factorized form 16 - \((5y-2)^2\) is -1(5y+2)(5y-6)
The expression is
16 - \((5y-2)^2\)
The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators
The expression is
The expression is
16 - \((5y-2)^2\)
We know the identity
\((a+b)^2= a^2+2ab+b^2\)
Apply this identity on the expression
= 16 -( \(25y^2\)- 20y + 4)
Apply the distributive property
= 16 - \(25y^2\)+ 20y - 4
Subtract the like terms
= - \(25y^2\)+ 20y + 12
Take common term outside
= -1(\(25y^2\)- 20y - 12)
Split the middle term and apply factorization
= -1 (\(25y^2\)+ 10y -30y - 12)
Take common term outside
= -1 ( 5y(5y+ 2) -6(5y +2)
Take common term outside
= -1(5y+2)(5y-6)
Hence, the factorized form 16 - \((5y-2)^2\) is -1(5y+2)(5y-6)
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how many different spanning trees does each of these simple graphs have? a) k3 b) k4 c) k2,2 d) c5
Answers
The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.
a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.
b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.
c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.
d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.
Therefore, the number of different spanning trees for each graph is:
a) K3: 1
b) K4: 4
c) K2,2: 2
d) C5: 5
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What is the vortex of the quadratic function fox (x-8)(x-2)?
Answers
Answer:
Vertex is (5,-9)
Step-by-step explanation:
Answer: The vertex is (5,-9).
Step-by-step explanation:
Asmall island ist am from the nearest point on the straight shine of a large if a woman on the island cartow a boat 3 kmh and can walk where should the boot belanded in order to arrive at a town 12 km down the shore from Pintere? The boat should be aded down the shore from (Type an exacta)
Answers
To determine the landing point, we need to balance the time it takes to row the boat with the time it takes to walk.
The woman's rowing speed is 3 km/h, and her walking speed is denoted as w km/h. Let d be the distance from the island to the landing point, and x be the distance she needs to walk from the landing point to reach the town. The total time for rowing (d/3) should be equal to the total time for walking [(12 - x)/w] in order to arrive at the town.
By rearranging the equation, we find that the landing point should be 12 km minus the distance covered by walking (d * w) divided by 3.
The exact value of x depends on the specific distances involved and the woman's walking speed, which are not provided in the given information.
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Determine whether the two lines given below are Parallel, perpendicular, or neither.A) ParallelB) PerpendicularC) Neither
Answers
We can determine whether two lines are parallel, perpendicular, or neither using the slopes of the lines.
Two lines are parallel when both of the lines have the same slope, for example:
\(\begin{gathered} y=-2x+3 \\ y=-2x-4 \end{gathered}\)Two lines are perpendicular to each other when the product between the lines is equal to -1, for example:
\(\begin{gathered} y=-2x+5 \\ y=\frac{1}{2}x+3 \end{gathered}\)if none of the conditions stated before the lines are neither parallel nor perpendicular.
In the given exercise:
\(\begin{gathered} y=-\frac{1}{3}x+2 \\ y=3x-5 \end{gathered}\)both lines have different slopes, then they are not parallel.
Find the product between the slopes,
\(\begin{gathered} m_1\cdot m_2 \\ -\frac{1}{3}\cdot3 \\ -1 \end{gathered}\)Answer:
The lines shown are perpendicular to each other because the product between the slopes is equal to -1.
Which is the next step in the following construction of an equilateral triangle?
circle with center P and point A along circles edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C
Answers
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
Circle with centre P and point A along the circle's edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C.
A triangle with three sides that are all the same length and three angles that are all the same size (60°) is called an equilateral triangle.
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
Thus, connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
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As an estimation we are told 5 miles is 8 km.
Convert 37.5 miles to km.
Answers
Answer:
60.3504
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
-3(x-4)=-9(x-1) solving linear equations
Answers
-3(x-4)=-9(x-1)
-3x+12=-9x+9
-3x+9x=9-12
6x=-3
x= -3/6
x=-1/2
How do you know if a curve is positive or negative?
Answers
Positive curve graphs will be upward-sloping.
Negative curve graphs will be downward-sloping.
Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.
In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.
On a coordinate grid, line j passes through points (8, 2) and (-2,-2). On the same grid, line k
passes through points (-4, 3) and (-6, 8). Are lines j and k parallel, perpendicular, or neither?
Answers
Answer: lines j and k are perpendicular
Step-by-step explanation:
Let's find the equations of lines j and k
\(\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\)
Line j: (8,2) (-2,-2)
x₁= 8 x₂=-2 y₁=2 y₂=-2
\(\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\\)
Multiply both parts of the equation by -4:
\(\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2\)
Line k: (-4,3) (-6,8)
x₁=-4 x₂=-6 y₁=3 y₂=8
\(\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}\)
Multiply both parts of the equation by 5:
\(\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7\)
Hence, lines j and k are perpendicular
What percent of the dogs and cats sold were dogs? a 70% b 22% c 55% d 45%
Answers
Answer:
im going to say c 55%
Step-by-step explanation: please let me know if its wrong so i can fix it thanks
5. Which of the following rational numbers does not lie between (2/5 and 3/4
Answers
From the given options, the rational number that does not lie between 2/5 and 3/4 is option (d) 9/20.
We need to discover a number that is either smaller than 2/5 or greater than 3/4 in order to find a rational number that does not fall between these two numbers.
Let's contrast each choice with the range provided:
a. 17/20 does not fall between 2/5 and 3/4 because it is more than 3/4.
b. 13/20: This number falls inside the provided range and is not the solution we are seeking for because it is larger than 2/5 but smaller than 3/4.
c. 11/20: This number falls inside the provided range and is not the solution we are seeking for because it is larger than 2/5 but smaller than 3/4.
d. 9/20: Because this number is less than 2/5, it does not fall within the range.
From the given options, the rational number that does not lie between 2/5 and 3/4 is option (d) 9/20.
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Complete question =
Choose a rational number which does not lie between 2/5 and3/4.
a.17/20
b.13/20
c.11/20
d.9/20
How many answers are there in inequality?
Answers
There is no single answer to this question as there are many different types of inequalities and each one can have a different number of solutions.
Number of Solutions to InequalitiesInequalities are mathematical statements that compare two values or expressions using an inequality sign. These signs can be:
Greater than (>) Less than (<)Greater than or equal to (>=)Less than or equal to (<=)Depending on the type of inequality and the values involved, the number of solutions can vary.
For example, a linear inequality with two variables will have an infinite number of solutions as the two variables can take on any real number value.
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