The geometric sequence has an explicit equation of f(n) = 3^(n - 1)
How to determine the explicit equation of the function?The given parameters are
r = 3
f(1) = 1
The above means that we have the following parameters:
Type of sequence: Geometric sequenceFirst term: f(1) = 1Common ratio: r = 3The explicit equation of the geometric sequence is represented as
f(n) = f(1) * r^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(n) = 1 * 3^(n - 1)
Evaluate the products
So, we have the following equation
f(n) = 3^(n - 1)
Hence, the explicit equation of the function is f(n) = 3^(n - 1)
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Write the equation of a Circle with the given information.Center: (-4,7) Point on the Circle: (8,-4)
Given:
Center of circle: (-4, 7)
Endpoint on the circle: (8, -4)
Let's write the equation of the circle with the given information.
Apply the equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
Center of circle: (h, k) ==> (-4, 7)
Radius = r
Substitute the values of (h, k) in the equation:
[tex]\begin{gathered} (x-(-4))^2+(y-7)^2=r^2 \\ \\ (x+4)^2+(y-7)^2=r^2 \end{gathered}[/tex]To find the radius, let's find the distance between the points (-4, 7) and (8, -4).
Apply the distance formula:
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]Given:
(x1, y1) ==> (-4, 7)
(x2, y2) ==> (8, -4)
Thus, we have:
[tex]\begin{gathered} d=\sqrt[]{(-4-7)^2+(8-(-4))^2} \\ \\ d=\sqrt[]{(-4-7)^2+(8+4)^2} \\ \\ d=\sqrt[]{(11)^2+(12)^2} \\ \\ d=\sqrt[]{121+144} \\ \\ d=\sqrt[]{265} \\ \\ d=16.3 \end{gathered}[/tex]Therefore, the radius is 16.3
Therefore, we have the equation of the circle as:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]ANSWER:
[tex](x+4)^2+(y-7)^2=16.3^2[/tex]please show all work
Domain and Range of Functions
Given a function y = f(x), the domain of f is
The range of f is the
We are given the function:
[tex]f(x)=\frac{1}{2x}-3[/tex]It's required to find the domain and range of the inverse function.
We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.
Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.
Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.
This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.
Now let's find the inverse function. We must solve for x the equation:
[tex]y=\frac{1}{2x}-3[/tex]Adding 3:
[tex]y+3=\frac{1}{2x}[/tex]Multiplying by x and dividing by y+3:
[tex]x=\frac{1}{2(y+3)}[/tex]Swapping letters:
[tex]y=\frac{1}{2(x+3)}[/tex]This is the inverse function of f.
Thus the domain of the inverse is:
-3-3
And the range:
Answer: Choice d
A herd of 52 horses has 12 appaloosas and the rest are mustang and its most simplified form. What is the ratio of appaloosa to mustang horses?
The ratio of appaloosa to mustang horses is 12:40
The total number of horses is given as 52.
Number of white horses =12
Let the number of black horses be x
This means that ratio of white: black horses is 12 : x
Using the ratio above, we can find the number of black horses as follows:
[tex]\frac{x}{12+x} of 52 = x[/tex]
[tex]\frac{52x}{12+x} = x[/tex]
52x = x(12 + x)
[tex](12x + x^{2} ) = 52x[/tex]
[tex]x^{2}[/tex] + 12x - 52x = 0
[tex]x^{2}[/tex] - 40x = 0
Taking out the common factor x from equation we have:
x(x - 40) = 0
This gives us with two solution:
x = 0 and x = 40
Since the question said there are some black horses, the x=0 value can be ignored. So we have x = 40
Hence, The ratio of appaloosa to mustang horses is 12:40
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Jared lost a total of $56.00 on his investment over 7 months. He lost an equal amount of money each month. Jared used this equation to figure out how much money he lost each money. -56.00/7=-8.00 what does -56.00/7=-8.00 tell us?
Answer:
I'm not so very sure but I really need points
where we can use Adding and Subtracting Polynomials in real life??
Polynomials are utilized in management, business, farming, computer science, and math-related fields.Expressions defining known and unknown numbers are created using variables and constants in all professions that need proficiency with polynomials.
where we can use Adding and Subtracting Polynomials in real life?
Finance Loan computations and firm valuation utilize an assessment of present value.In order to determine an equal liquid value (present, cash, or in-hand), it uses polynomials that back interest accumulation out of hypothetical future liquid transactions.Fortunately, if the payment schedule is regular, many payments can be rewritten in a straightforward manner.Economic and tax calculations can frequently be expressed as polynomials as well.Electronics
Polynomials are widely used in electronics.The polynomial V=IR, which defines resistance, connects the resistance of a resistor to the current flowing through it and the potential drop across it.While many conductors (but not all) abide by Ohm's law, this is comparable to that law but not the same.It claims that on a graph, the relationship between voltage drop and current flowing through a resistor is linear.In the equation V=IR, resistance is therefore constant.Electronics also uses other polynomials, such as P=IV=IR2, which describes the relationship between voltage drop and power loss.Kirchhoff's loop rule and the Kirchhoff's junction rule, which both describe voltage drop around closed circuits and the current at junctions, respectively, are polynomials.Curve Fitting
In both regression and interpolation, polynomials are fitted to data points.Regression is the process of fitting a large set of data points with a function, typically a line: y=mx+b.Numerous linear regression is used when there are multiple dependent variables (or "x"s) in the equation.Chemistry
In chemistry, polynomials are frequently used.The ideal gas law, PV=nRT (where n is the mole count and R is a proportionality constant), is an example of a gas equation linking diagnostic parameters that can typically be represented as a polynomial.Molecule concentration equations at equilibrium can alternatively be expressed as polynomials.For instance, the equilibrium concentration equation can be stated in terms of the related equilibrium constant K: KC=AB if A, B, and C are the concentrations of OH-, H3O+, and H2O in solution, respectively.Engineering and physics
Proportionality is a key study in both physics and engineering.How much does the beam deflect when a stress is raised?How far will a trajectory land if it is shot at a specific angle?F=ma (from Newton's laws of motion), E=mc2, and F—-r2=Gm1—-m2 (from Newton's law of gravitation, though typically the r2 is put in the denominator) are well-known examples from physics.To learn more about polynomials refer
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please help me solve this
Answer:
a: undefined
b: -15
c: 20
d: 25
Step-by-step explanation:
a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined
b: look at x 0 on graph, there is open dot at -15 meaning the limit is there
c: look at x -7 on graph, there is open dot at 20 meaning the limit is there
d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)
The following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes 36.1% 1.9% 38%
Do not have diabetes 5.2% 56.8% 62%
What percent of those who do not have diabetes test negative for the disease?
A 10.9%
B 56.8%
C 91.6%
D 96.8%
If the following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease. The percent of those who do not have diabetes test negative for the disease is: B. 56.8%.
ProbabilityProbability can be defined as the tendency or likelihood that something will happen.
Hence,
Percentage of people do not have diabetes and test positive is 5.2%
Percentage of people do not have diabetes and test negative is 56.8%
Total percentage of people who tested positive and negative is 62%
Based on the above analysis for people who does not have a diabetes we can see that the Percentage of people do not have diabetes and test negative is 56.8%.
Therefore the correct option is B.
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Let A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)} what type of function is this? Give reason
It is observed that f is a subset of A×B
What is subset ?A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.
Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}
A={1,2,3}
B={7,8,9,10}
A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}
f={(1,7),(2,9),(3,8)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
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Identify the Vertex. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of. (Show Work)
The g graph exhibits a four-fold vertical stretch.
The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.
The rule for g.
Identify the vertex
The g graph exhibits a four-fold vertical stretch.
=> g = 4f(x) (x)
an X-axis reflection
=> g = - 4f(x) (x)
(X-axis reflection of (X, Y) is (x , - y)
a conversion two units higher
=> g = -4f(x) + 2
f(x) = x²
=> g = - 4x² + 2
Vertex is at ( 2, 0)
What is a vertical stretch?
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
How to vertically stretch a function?
When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:
Ensure that the values for x remain the same, so the base of the curve will not change.
This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.
Take note of the new critical points, such as the new maximum point of the graph.
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DEEPER The scales shown are used to compare the weights of apples, tangerines, grapefruits, and bananas. How many tangerines
will balance one apple?
Justify your answer using a linear system. Let the weights of apples, tangerines, grapefruits, and bananas be represented by a, t,
g, and b respectively.
Equation for first picture:
Equation for second picture:
Equation for third picture:
4 Tangerines will balance 1 apple.
Given that
Weight of Apple is represented by: a
Weight of tangerine is represented by: t
Weight of Grapefruit is represented by: g
Weight of Banana is represented by: b
Consider 1st picture:
1 apple and 1 tangerine balance 1 grapefruit.
⇒ a+t = g ...(1)
Consider 2nd picture:
1 banana and 1 tangerine balance 1 apple.
⇒ b+t = a ...(2)
Consider 3rd picture:
2 grapefruits balance 3 bananas.
⇒ 2g = 3b
g = 1.5b ...(3)
The system of equations are:
First balance: a+t = g
Second balance: b+t = a
Third balance: g = 1.5b
Putting the value of g from equation (3) to equation (1), we get
a+t = 1.5b ...(4)
Now, putting the value of b from equation (2) to equation (4), we get
a+t = 1.5(a-t)
1.5a - 1.5t = a+t
0.5a = 2t
a = 4t
Hence, one apple is balanced by 4 tangerines.
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I need to find the c intercept and write the equation
The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.
As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.
We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:
[tex]C=m\cdot t+b[/tex]Where (t,C) is any point on the line, m is the slope and b is the C-intercept.
By replacing the know values we can solve for b:
[tex]\begin{gathered} 0=-4\cdot30+b \\ 0=-120+b \\ \text{Add 120 to both sides} \\ 0+120=-120+b+120 \\ 120=b \end{gathered}[/tex]Therefore,
Maggie has space in her yard for a garden. A scale drawing of the garden is shown below. The scale of the drawing is 1 cm - 2.5 ft.6 cm!616 cmWhat is the area of Maggie's actual garden?
Units change translation from cm to feets
1 cm is equivalent to 2.5 feets
triangle is a rectangular triangle suported with the bigger side
this means the height of triangle is 6cm
the base is 16 cm
the area is (base x height)/2
so then area= 16x 6/2= 48cm ^2
BUT because 1cm is equivalent to 2.5 feets then
multiply 48 x 2.5 x 2.5 = 48 x 6.25 = 300 ft^2
triangle DEF and triangle CBD are similar right triangles which statement is slopes is DF and CDs true
We can calculate the slope of a line segment by using the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are two points of the line.
In this case the side DF goes from the point D(-2,-2) to the point F(1,7), then its slope is:
[tex]m=\frac{7-(-2)}{1-(-2)}=\frac{7+2}{1+2}=\frac{9}{3}=3[/tex]For the side, CD, it goes from D(-2,-2) to C(0,4), then its slope is:
[tex]undefined[/tex]Factor each of the following completely:
y² + 7y +6
I
y² - 7y + 6
Answer: 31y2 + 6
Step-by-step explanation:
61 y2 + 1 y2 = 62 y2
7y + -7y = 0
6+6 =12
62y2 + 12 then divide by 2 and it's 31y2 + 6
4(5x - 2) = 2(9x + 3)
Answer: x = 7
Explanation - 4(5x-2)=2(9x+3)
20x-8=18x+6
20x-18x=6+8
2x=14
x=14÷2
x=7
Hello there!
Here we need to solve for x.
The first thing that we're going to do is this:
Expand both sides by using the distributive property.[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]
[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]
Next, add 8 to both sides.[tex]\implies\boldsymbol{20x=18x+14}[/tex]
Then, subtract 18 from both sides.[tex]\implies\boldsymbol{20x-18x=14}[/tex]
[tex]\implies\boldsymbol{2x=14}[/tex]
Lastly, divide both sides by 2.[tex]\implies\boldsymbol{x=7}[/tex]
Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)
What is the value of −5 + (−18) + 32? −45 −19 9 55
Answer:
9
Step-by-step explanation:
[tex]-5+(-18)+32 \\ \\ =-5-18+32 \\ \\ =-23+32 \\ \\ =9[/tex]
(-4, 2) and (5, 6) slope
In order to find the slope between those two points, we can use the following formula for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope between the points (x1, y1) and (x2, y2).
So using the points (-4, 2) and (5, 6), we have:
[tex]m=\frac{6-2}{5-(-4)}=\frac{4}{9}[/tex]So the slope is 4/9
the formula for finding the area of a rectangle is A=LWSolve this formula for LL=______if the length of a rectangle is 18 feet qnd the width is 9 inches. what is the area of the rectangle in units of square feet? _______ ft^2
1) Dividing the given formula by W we get:
[tex]\begin{gathered} \frac{A}{W}=\frac{LW}{W}, \\ \frac{A}{W}=L. \end{gathered}[/tex]2) We know that:
[tex]1in=\frac{1}{12}ft.[/tex]Therefore:
[tex]9in=9*\frac{1}{12}ft=\frac{3}{4}ft.[/tex]Then:
[tex]W=\frac{3}{4}ft.[/tex]Substituting W=3/4ft and L=18ft in the given formula we get:
[tex]A=(18ft)(\frac{3}{4}ft)=13.5ft^2[/tex]Answer:
1)
[tex]L=\frac{A}{W}.[/tex]2)
[tex]13.5ft^2.[/tex]Name the line of reflection used to map the preimage to its image.
Option E, the x-axis is the line of reflection used to map the preimage to its image.
The graph represents that if the graph is folded by an x-axis,
Point Y will cross-point Y', which is two coordinates away from the x-axis.
Point X will cross point X', which is five coordinates away from the x-axis.
Points W will cross-point W', which is eight coordinates away from the x-axis.
Points V will cross-point V', which is five coordinates away from the x-axis.
A mirror image is symmetric about the x or y-axis. Reflection is called "inverse geometry". A mirror reflector is a type of reflector. When the line reflects the image, the reflection line appears. A shape is said to reflect a different shape if a point on a shape is equidistant from a point on another shape.
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Answer asap what’s the correct answer answer now for brainlis5?
Answer: Smooth muscle contractions
Multiply 4(Q+2) what's the answer
Given the expression:
[tex]4(Q+2)[/tex]Let's multiply the expression.
To multiply apply the distributive property of multiplication.
Distribute 4 to the values in the parentheses:
[tex]\begin{gathered} 4(Q)+4(2) \\ \\ =4Q+8 \end{gathered}[/tex]ANSWER:
[tex]4Q+8[/tex]What is the probability of theft occurring in a room if it is left unlocked if 0.75 of dorm rooms are left unlocked, 3% of dorm rooms are affected by theft, and 84.2% of thefts occur in unlocked rooms
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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Use a linear approximation to estimate 3√28 write your exact answer with fractions
The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.
What is linear approximation?A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.
We need to find the approximate value of ∛28 using linear approximation
Let f(a) = ∛a
then F(27) = ∛27 = 3
We compute the derivative of f(a) as being
[tex]f(a)=a^{\frac{1}{3}}[/tex] ⇒ [tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex]
Hence,
[tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex] = [tex]\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}[/tex]
Recall the equation of a line is given by
⇒ y - b = m(x - a)
⇒ [tex]y-3=\frac{1}{27}(x-27)[/tex]
⇒ [tex]y=\frac{1}{27}x-1+3[/tex]
⇒ [tex]y=\frac{1}{27}x+2[/tex]
So the approximation at x= 27.5 would be
⇒ [tex]y=\frac{1}{27}(28)+2[/tex]
⇒ y = 82/27
⇒ y = 3.037
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Answer both questions if possible or just the main questions if that's all you can do,
ASAP
Step-by-step explanation:
domain = width
range = height
closed point (filled in) means the number is included and we use ()'s.
set builder nation format: (x,y)
domain: (-5, -1)
range: (3,3)
f(1) means what does y equal when x equals 1:
locate on the graph where y is when x = 1:
f(1) = 2
why is 25 a compiste number
Answer: 25 is divisible by 5, so it is composite
Step-by-step explanation:
The first four terms of a sequence are given below.
11, 9, 7, 5, ...
What is the seventh term of the sequence?
A. 5
B. -3
C. 1
D. -1
Answer: D:-1
Step-by-step explanation: 11,9,7,5,3,-1,-3,... => dãy số trên có quy luật là số lẻ
A square swimming pool is surrounded by a cement walkway with a uniform width. The swimming poa
has a side length of (x - 5) feet. The side length of the entire square area including the pool and the
walkway is (x+4) feet.
Enter an expression for the area of the walkway. Then find the area of the cement walkway when
x = 8 feet.
The area of the walkway is
ft².
When x = 8 feet, the area of the cement walkway
The expression of the square walkway is (x + 4)² - (x - 5)² and the area of the square cement walkway is 135ft².
Area of square:
The area of a square is refers the place covered by the square.
The formula to calculate the area of square is,
Area = s²,
where, 's' refers the side of the square.
Given,
A square swimming pool is covered by a cement walkway with a uniform width.
Length of swimming pool = (x-5) feet.
Length of square walkway including the swimming pool = (x+4) feet
Here we need to find the area of the cement walkway and when the value of x is 8 then the value of the cement walkway.
1) Here we have to write an expression for the area of the entire square minus area of the pool.
Remember the equation for the area of a square is , where
A = area of square and
s = side value of the square.
We are given that the side of the entire square including walkway and pool is s = (x+4)ft.
Apply the value of the side into the formula for the area of the square, then we get,
A = s²
A = (x + 4)² --------------(1)
We are also given that the side length of the swimming pool is s = (x-5)ft. Apply that into the equation for the area of a square to get the expression for the area of the pool:
A = s²
A = (x - 5)² --------------(2)
Now subtract the area of the pool (x - 5)² from the area of the entire square (x + 4)² to get your expression for the area of the walkway.
Expression for the area of the walkway:
=> (x + 4)² - (x - 5)²
2) Since you know that x = 8ft, you can solve your expression for the area of the walkway. Plug x into your expression:
=> (8 + 4)² - (8 - 5)²
=> (12)² - (3)²
=> 144 - 9
=> 135
The area of your walkway is 135ft².
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K
Solve.
(8v+5)(3v-9) = 0
When 3x² + 7x - 6 + 2x³ is written in
standard form, the leading coefficient is
(1) 7
(2) 2
(3) 3
(4) -6
Answer:
Your leading coefficient is 2
I will give brainliest, like and rating if u solve this right
which of the following is not true?
As per the given matrix [tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex], Option (C) is not true.
Matrix:
The matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Given,
[tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex]
Here we need to find which of the option is not true.
To find the incorrect options first we have to calculate the |A| and A⁻¹.
And we have also check whether is matrix has inverse or skew symmetric matrix.
First, we have to calculate the value of |A|,
|A| = (2 x 1) - (-1 x 2)
|A| = 2 - (-2)
|A| = 2 + 2 = 4
Therefore, option (A) is true.
Now we have to check this matrix has inverse,
It can be calculated using the formula,
[tex]A^{-1} =\frac{1}{|A|} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]
So, the inverse of the matrix is,
[tex]A^{-1} =\frac{1}{4} \left[\begin{array}{ccc}1&-2\\-(-1)&2\end{array}\right][/tex]
Which is equal to,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-2/4\\1/4&2/4\end{array}\right][/tex]
When we simplify it then we get,
[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-1/2\\1/4&1/2\end{array}\right][/tex]
Through this we have conclude that Option (B) and (D) are true.
We know that,
In the skew-symmetric matrix, a matrix whose transpose is equal to its negative.
So, the transpose of the given matrix is,
[tex]A^{T}=\left[\begin{array}{ccc}2&-1\\2&1\end{array}\right][/tex]
So, the given matrix is not a skew-symmetric matrix.
Therefore, the incorrect option is (c).
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