The correct choice is:
B. The rank of A is equal to the number of non-pivot columns in A. Since there are more rows than columns in an 8 times 6 matrix, the rank of an 8 times 6 matrix must be equal to the number of columns, which is 6.
Since there are 6 rows in a 6 times 8 matrix, there can be at most 6 pivot positions in A. Thus, there are 2 non-pivot columns. Therefore, the largest possible rank of a 6 times 8 matrix is 6.
The rank of a matrix represents the maximum number of linearly independent rows or columns in that matrix. It is also equal to the number of pivot positions (leading non-zero entries) in the row-echelon form of the matrix.
For an 8x6 matrix, the maximum number of pivot positions can be at most 6 because there are only 6 columns. Therefore, the largest possible rank of an 8x6 matrix is 6.
On the other hand, for a 6x8 matrix, there can be at most 6 pivot positions since there are only 6 rows. This means there are 2 non-pivot columns (total columns - pivot positions = 8 - 6 = 2). Thus, the largest possible rank of a 6x8 matrix is 6.
In summary, the rank of a matrix is determined by the number of pivot positions, and it cannot exceed the number of columns in the case of an 8x6 matrix or the number of rows in the case of a 6x8 matrix.
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sketch the strophoid shown below. r = sec() − 2 cos(), − 2 < < 2
The strophoid is a curve represented by the polar equation r = sec(θ) − 2cos(θ), where -2 < θ < 2. In Cartesian coordinates, the strophoid equation can be written as (x^2 + y^2)^2 = 4y^2(x + 2).
The strophoid has a unique shape characterized by its looped structure.
The strophoid is symmetric with respect to the y-axis, as changing θ to -θ gives the same value of r. It has two branches that intersect at the origin (0, 0). As θ increases from -2 to 2, the curve starts from the rightmost point of the loop, extends to the left, and then returns back to the rightmost point.
The loop of the strophoid is created by the interplay of the secant function, which stretches the curve away from the origin, and the cosine function, which pulls it towards the origin. The strophoid exhibits interesting geometric properties and is often used in mathematical modeling and visualization.
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From the equation, find the axis of symmetry of the parabola.
y = 2x^2 + 4 x - 1
a. x = 3
b. x = -1
c. x = -3
d. x = 1
PLEASE HURRY!!! WILL MARK AS BRAINLIEST!!!
Answer:
C
Step-by-step explanation:
Ur welcome
Arrange the following fraction from least to greatest 2/3, 5/6, 3/5
What did you do to arrange the fraction from least to greatest?
Answer:
2/3 and 3/5 is same, then 5/6
Step-by-step explanation:
you can convert the fractions to decimals to find their value and then arrange them from least to the greatest.
Answer:
3/5, 2/3, 5/6 [From Least to Greatest]
Step-by-step explanation:
First you're going to want to know which one is "the bigger piece of pie".
I made a few drawing and look at the pictures (Just in case you have a different opinion from my answer)
Circle | was dilated with the orgin as the center of dilation to create Circle ||.
Which rule best represents the dilation applied to Circle | to create Circle ||?
Step-by-step explanation:
The rule that best represents the dilation applied to Circle | to create Circle || is the scale factor. The scale factor determines the ratio of corresponding lengths between the original figure (Circle |) and the dilated figure (Circle ||).
In a dilation, all lengths in the original figure are multiplied by the scale factor to obtain the corresponding lengths in the dilated figure. This includes the radii of the circles.
For example, if the scale factor is 2, it means that every length in the original figure is doubled in the dilated figure. If the scale factor is 1/2, it means that every length is halved. The scale factor can be greater than 1, less than 1 (but greater than 0), or even negative, indicating a reflection.
In the context of the given scenario, since the origin is the center of dilation, the scale factor determines how the distances from the origin to any point on Circle | are scaled to obtain the corresponding distances on Circle ||.
Tell whether $x$ and $y$ are proportional. $x$ 0.25 0.5 0.75 $y$ 4 8 12
Answer:
x and y are proportional. Two quantities are proportional if there is a constant ratio between them. In this case, the ratio between y and x is always 16:
4/0.25=16
8/0.5=16
12/0.75=16
Since the ratio between y and x is always the same, x and y are proportional.
Step-by-step explanation:
A curve with the equation Sin(x) – y Cos(x) = y passes through two points A(nt, a) and B(a, b) (a
The equation of the curve as, (y - a) = (b - a) (x - nt) / (a - nt) which is a straight line passing through the two given points, A(nt, a) and B(a, b).
Given: Two points A (e.g., a) and B (a, b) are traversed by the curve whose equation is Sin(x) – y Cos(x) = y (a Solution: (sin x - y cos x) = y Taking y to the left, we get (sin x) = (y y cos x) Again, we can write y as (y) = (sin x) / (1 cos x) Simplifying this even further, we get (y) = (sin x / 2) / (cos x/2) Substituting the values of x = nt A( eg, a) and B( a, b), we get the condition in the structure, y - a = (b - a) (x - ex.)/( a-ex.)
Tackling the above condition, we get the condition bend which is a straight line going through two given focuses A (eg, a) and B(a, b). As a result, we obtain a curve in the form of an equation (y - a) = (b - a) (x - nt) / (a) - nt), which is a straight line that runs through the two points A(eg, a) and B(a, b) that have been given to us.
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A faraway planet is populated by creatures called Jolos. All Jolos are either
green or purple and either one-headed or two-headed.
Balan, who lives on this planet, does a survey and finds that her colony of 500
contains 100 green, one-headed Jolos: 125 purple, two-headed Jolos; and
270 one headed Jolos.
Answer:
Option B
Step-by-step explanation:
We have to complete the table given in the question,
One headed Two headed Total
Green 100 230 - 125 = 105 105 + 100 = 205
Purple 270 - 100 = 170 125 170 + 125 = 295
Total 270 500 - 270 = 230 500
By analyzing the given table,
Number of green Jolos in Balan's colony = Total of one headed green Jolos and Two headed green Jolos
= 205
Therefore, number of green Jolos in Balan's colony are 205.
Option B will be answer.
Answer:
When you put together the whole chart you will see the total is 205.
Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the corresponding eigenspaces. A = [2 -1]
[ 1 2]
λ1 = ___ has eigenspace span (__) (λ-value with smaller imaginary part) λ2 ___ has eigenspace span (__) (A-value with larger imaginary part)
An eigenvector corresponding to λ₂ = 2 - i is v₂ = [-1, 1].
To find the eigenvalues of matrix A, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.
Let's compute the determinant:
det(A - λI) = |[2 - λ -1]|
|[ 1 2 - λ]|
Expanding along the first row, we have:
(2 - λ)(2 - λ) - (-1)(1) = (2 - λ)² + 1 = λ² - 4λ + 5 = 0
To solve this quadratic equation, we can use the quadratic formula:
λ = (-(-4) ± √((-4)² - 4(1)(5))) / (2(1))
= (4 ± √(16 - 20)) / 2
= (4 ± √(-4)) / 2
Since we are working over the complex numbers, the square root of -4 is √(-4) = 2i.
λ₁ = (4 + 2i) / 2 = 2 + i
λ₂ = (4 - 2i) / 2 = 2 - i
Now, let's find the eigenvectors corresponding to each eigenvalue.
For λ₁ = 2 + i, we solve the equation (A - (2 + i)I)v = 0:
[2 - (2 + i) -1] [x] [0]
[ 1 2 - (2 + i)] [y] = [0]
Simplifying, we have:
[0 -1 -1] [x] [0]
[ 1 0 - i] [y] = [0]
From the first equation, we have -x - y = 0, which implies x = -y.
Choosing y = 1, we have x = -1.
Therefore, an eigenvector corresponding to λ₁ = 2 + i is v₁ = [-1, 1].
For λ₂ = 2 - i, we solve the equation (A - (2 - i)I)v = 0:
[2 - (2 - i) -1] [x] [0]
[ 1 2 - (2 - i)] [y] = [0]
Simplifying, we have:
[0 -1 -1] [x] [0]
[ 1 0 i] [y] = [0]
From the first equation, we have -x - y = 0, which implies x = -y.
Choosing y = 1, we have x = -1.
In summary:
λ₁ = 2 + i has eigenspace span {[-1, 1]}
λ₂ = 2 - i has eigenspace span {[-1, 1]}
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cos80°.cos10°-sin80°.sin10°
Step-by-step explanation:
The answer will be zero
here are the steps:
cos(90-10)xcos(90-80)-sin(90-10)xsin(90-10)=
(cos10xcos10)-(sin80xsin80)=
0.965111-0.965111=0
have a good day :)
I hope it will benefit you.
6th grade math plz help
8.
Find the area of the shaded region.
A. 5x2 – 11x + 16
B. 5x2 + 7x – 26
C. 5x2 + 11x – 12
D. 5x2 + 7x – 20
Area of the shaded region = area of big square minus area of little square.
Here is the set up:
Let A_s = area of shaded region.
A_s = (2x + 2)(3x - 4) - [(x - 3)(x - 6)]
Take it from here.
Answer:
B. 5x2 + 7x – 26
Step-by-step explanation: keeping in mind that the area of a rectangle is simply width * length, if we get the area of the larger rectangle, and then subtract the area of the smaller rectangle, we're in effect making a hole in the larger rectangle's area and thus what's leftover is the shaded area.
.................................................................................................................................
Answer:
Area = 5x^2 +7x -26
Step-by-step explanation:
The area of the shaded region can be found if you substruct the small rectangle from the big one. The area of any rectangle is calculated if you multiply width and height.
In other words:
A_small = (x-3)(x-6) = x^2-9x +18
A_big = (2x+2)(3x-4) = 6x^2 -2x -8
A_big - A_small = (6x^2 -2x -8) - (x^2-9x +18)
= 6x^2 -2x -8 - x^2 + 9x -18
= 5x^2 +7x -26
If difference scores begin to pile up away from a sample mean difference score of Mp= 0, which of the following statements is true? a. The critical region is small.
b. The null hypothesis will likely be rejected. c. The sample size is large. d. The null hypothesis will likely fail to be rejected.
If difference scores begin to pile up away from a sample mean difference score of Mp= 0, the null hypothesis will likely be rejected. So, correct option is B.
This suggests that there is a likely effect or relationship between the variables being compared.
Option b. The null hypothesis will likely be rejected is the correct statement in this scenario. When the observed differences are consistently far from zero, it implies that the null hypothesis, which assumes no significant difference or effect, is unlikely to be true.
Thus, based on the evidence provided by the data, we would reject the null hypothesis in favor of an alternative hypothesis that suggests the presence of a difference or effect.
The critical region refers to the region of extreme values that would lead to rejecting the null hypothesis. While the size of the critical region can vary depending on the chosen significance level, it does not directly indicate the likelihood of rejecting the null hypothesis in this context.
Similarly, the sample size (option c) does not provide information about the likelihood of rejecting the null hypothesis in this situation.
So, correct option is B.
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et k be a real number and A=[1 k 9 1 2 3 2 5 7]. Then determinant of A is ?
The determinant of A is -23 - k.
In case, we have a 3x3 submatrix starting at element (1,1) and ending at element (3,3). Therefore, we can calculate the determinant using cofactor expansion method:
| 1 k 9 |
| 1 2 3 |
| 2 5 7 |
= 1| 2 3 | - k| 1 3 | + 9| 1 2 |
| 5 7 | | 5 7 | | 5 7 |
= 1(2(7) - 3(5)) - k(1(7) - 3(2)) + 9(1(7) - 2(5))
= 1(4) - k(1) + 9(-3)
= -23 - k
Therefore, the determinant of A is -23 - k.
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The math club is selling T-shirts to raise money. Each T-shirt sold represents a profit of $2. The club has a total of 500 T-
shirts
If P() is the profit that the math club makes for selling T-shirts, a reasonable domain of this function is
<
Answer:
2 < or equal to (t) < or equal to 1000
Step-by-step explanation:
2 is the profit of the (t) amount of t shirts so the amount should be greater than or equal too 1000 because if they have 500 shirts 500 x 2 is 1000
The domain of this function will be given by the set A[1, 500].
What is the end behaviour of a function? What do you mean by domain and range of a function?The end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.
Given is the math club which is selling T-shirts to raise money. Each T-shirt sold represents a profit of $2. The club has a total of 500 T- shirts.
The function representing the profit by selling [x] T - shirts can be written as -
P(x) = 2x
or
y = 2x
Maximum value of y = 2x 500 = $1000
The domain of this function will be given by the set A[1, 500].
Hence, the domain of this function will be given by the set A[1, 500].
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The graph shown is a scatter plot:
A scatter plot is shown with the values on the x-axis in increasing units of 1 and the y-axis in increasing units of 10. The data moves in an upward cluster. Point A has coordinates 8 and 70. Point B has coordinates 1 and 20, point C has coordinates 3 and 40, point D has coordinates 7 and 30. Additional points are located at 2 and 10, 2 and 20, 3 and 30, 5 and 50, 5 and 40, 7 and 70, 7 and 60.
Which point on the scatter plot is an outlier? (4 points)
Group of answer choices
Point D
Point B
Point C
Point A
Answer:
D
Step-by-step explanation:
if we see on the graph, the point which is scattered is point D !
also took the FLVS test!!
Since the arithmetic mean of the above data is 20, what is the span?
A) 45. B) 40. C) 35. D) 30
Answer:
Step-by-step explanation:
a) SST represents the _____sum of squares.
b) SSTr represents the _____sum of squares.
c) SSE represents the _____sum of squares.
d) Which of the following statements is TRUE?
SSE = SSTr + SST
SST = SST - SSE
MSE = MST + MST
MST = MST + MSE
SST = SSTr + SSE
e) Which of the following represents the average between group variation?
σ
MSE
s
MST
a) SST represents the total sum of squares.
b) SSTr represents the treatment sum of squares.
c) SSE represents the error sum of squares.
d) The true statement is: SST = SSTr + SSE.
e) The average between-group variation is represented by MST (mean square treatment).
How to explain the informationa) SST (Total Sum of Squares) represents the total variation in the data. It measures the total deviation of each data point from the overall mean.
b) SSTr (Treatment Sum of Squares) represents the variation attributed to the treatment or factor being studied. It measures the deviation of each group mean from the overall mean.
c) SSE (Error Sum of Squares) represents the residual or unexplained variation in the data. It measures the deviation of each individual data point from its respective group mean.
d) The true statement is: SST = SSTr + SSE. This equation states that the total variation (SST) is equal to the sum of the variation attributed to the treatment (SSTr) and the residual or unexplained variation (SSE).
e) The average between-group variation is represented by MST (mean square treatment). MST is calculated by dividing the treatment sum of squares (SSTr) by the degrees of freedom associated with the treatment. It represents the average variation between the group means and provides information about the treatment effect or the differences between groups.
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The scores on a psychology exam were normally distributed with a mean of 65 and a standard deviation of 6. What is the standard score for an exam score of 74?
Answer:
z = 1.5
Step-by-step explanation:
x - mean
standard score = -----------------
6
Substituting 74 for x, 65 for mean, we get:
74 - 65
standard score = ----------------- = 9/6 = 1.5
6
The pertinent z-score (standard score) is 1.5.
Answer:
Solution :-Score = 74 - 65/6
Score = 9/6
Hence
Score is 9/6 or 1.5
[tex] \\ [/tex]
Please help me asap thanks
Answer:
x=3.5
Step-by-step explanation:
To make DEF similar to XYZ, the sides have to be in the same ratio. EF corresponds to YZ. EF=3, and YZ=4.5. The ratio 3:4.5 can be simplified to 2:3. Side DF corresponds to XZ. DF=7 and XZ=3x. So, the ratio is 7:3x.
To find x, we first find out what 3x is. In this case 3x is 3(7/2)=10.5. So, x=10.5/3=3.5.
If 491 households were surveyed out of which 343 households have internet fiber cable, what is the sample proportion of households without fiber cable is
The sample proportion of households without fiber cable can be calculated by subtracting the proportion of households with fiber cable from 1.
In this case, out of the 491 households surveyed, 343 households have internet fiber cable. To find the proportion of households without fiber cable, we subtract the proportion of households with fiber cable (343/491) from 1. The proportion of households without fiber cable is 1 - (343/491). Simplifying this expression, we get (491 - 343)/491 = 148/491.
Therefore, the sample proportion of households without fiber cable is 148/491, which is approximately 0.3012 or 30.12%. This means that in the surveyed sample, around 30.12% of households do not have internet fiber cable. It's important to note that this proportion represents the sample and not the entire population, as it is based on the households surveyed.
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6=2(y+2) i need help
Answer:
y=1
Step-by-step explanation:
6=2(y+2)
6=2y+4
2=2y
y=1
Answer:
y=1
Step-by-step explanation:
6th grade math help me pleaseeee
Answer:
3 CDs
Step-by-step explanation:
If we have $65 and buy a $23 DVD, we will have $42 left.
So how many $14 CDs can we buy with $42?
All we have to do is divide 42 into 14, so we know how many groups of $14 we can make with $42.
42 ÷ 14 = 3
Therefore, Michella can purchase 3 CDs.
can someone help??!???!?!
Answer:
download discord
Answer:
im confused-
Step-by-step explanation:
Find the general solution of the following:
dy/dt + 4/ty = e^t/t^3
The general solution of the differential equation dy/dt + 4/ty = e raised to power of t/t raised to power of 3:
y = C * e raised to power of t * t raised to power of 4
where C is an arbitrary constant.
To find this solution, we can use the following steps:
First, we can factor out e raised to power of t/t raised to power 3 from the right-hand side of the equation. This gives us:
dy/dt + 4/ty = e raised to power t/t raised to power of 3 * (1/t)
Next, we can multiply both sides of the equation by ty to get:
dy + 4 = e raised to power of t/t raised to power of 2
Now, we can integrate both sides of the equation. This gives us:
y + 4t = C * e raised to power of t
Finally, we can solve for y to get the general solution:
y = C * e raised to power of t * t raised to power of 4
where C is an arbitrary constant.
The first step of the solution is to factor out e raised to power t/t raised to power of 3 from the right-hand side of the equation. This is possible because the derivative of e raised to power of t/t raised to power of 3 is e raised to power of t/t raised to power of 3 * (1/t).
The second step of the solution is to multiply both sides of the equation by ty to get dy + 4 = e raised to power of t/t raised to power of 2. This is possible because the derivative of ty is t + y.
The third step of the solution is to integrate both sides of the equation. This gives us y + 4t = C * e raised to power of t. This is possible because the integral of dy is y and the integral of e raised to power t/t raised to power of 2 is -2e raised to power of t/t + C.
The fourth step of the solution is to solve for y to get the general solution y = C * e raised to power t * t raised to power of 4. This is possible by dividing both sides of the equation by C * e raised to power of t.
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help!!!! ^^^ due in 20 mins!
Answer:
I believe its 60cm squared
I’m not sure
Answer:
i think its 60cm
Step-by-step explanation:
Consider an upright cone that has a base radius of r and height h that has been obtained by revolving a triangular plane region (pictured below) about the y-axis. Apply the cylindrical shells method to con- Ty firm that the volume of the cone is V = arh. h + 0 r
By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
Given that,
Consider an upright cone that was generated by rotating the triangular plane region shown in the image about the y-axis. It has a base radius of r and a height of h.
We have to apply the cylindrical shells method to confirm that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h
We know that,
By using the disk method,
V = [tex]\int\limits^b_a {\pi [f(x)]^2} \, dx[/tex]
Differentiating on both the sides,
dV = π[f(x)]² dx
Integrating on both sides with the limits 0 to h
[tex]\int\limits^h_0 { dV }= \int\limits^h_0 {\pi[f(x)]^2 }dx[/tex]
V = [tex]\int\limits^h_0 {\pi \frac{r^2x^2}{h^2} } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}\int\limits^h_0 {x^2 } \, dx[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{x^3}{3}]^h_0[/tex]
V = [tex]\pi \frac{r^2}{h^2}[\frac{h^3}{3}][/tex]
V = [tex]\frac{1}{3}[/tex]πr²h
Therefore, By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.
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Two cheeseburgers and one small order of fries contain a total of 1400 calories. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Find the caloric content of each item.
Let the calories of a cheeseburger be C, and the calories of a small order of fries be F. Using this notation: Two cheeseburgers and one small order of fries contain a total of 1400 calories. Calories in 2 cheeseburgers + Calories in 1 small order of fries = 14002C + F = 1400. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Calories in 3 cheeseburgers + Calories in 2 small orders of fries = 22603C + 2F = 2260. We can solve for C and F by solving these two equations for C and F using the method of elimination.
Let's double the first equation and subtract the second equation: 4C + 2F = 2800 -(3C + 2F = 2260). 1C = 540 C = 540. Calories in a cheeseburger = C = 540. Substituting this value of C into either of the two equations and solving for F gives us:2C + F = 14002(540) + F = 1400. F = 320. Calories in a small order of fries = F = 320. Therefore, two cheeseburgers contain 2C = 2(540) = 1080 calories, and one small order of fries contains F = 320 calories. Three cheeseburgers contain 3C = 3(540) = 1620 calories, and two small orders of fries contain 2F = 2(320) = 640 calories.
Answer: Calories in a cheeseburger = C = 540Calories in a small order of fries = F = 320. Calories in two cheeseburgers = 2C = 2(540) = 1080. Calories in three cheeseburgers = 3C = 3(540) = 1620. Calories in one small order of fries = F = 320Calories in two small orders of fries = 2F = 2(320) = 640.
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A cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. What is the height of the cone?
A) 95 cm
B) 115 cm
C) 125 cm
D) 135 cm
Answer:
its d
Step-by-step explanation:
Show that the following are equivalent, for Snopea filter Fonot todological Space X 9 f is if G is G an open set in C and CnH+ 0 s G for each Hef, then CEF c) iz G is G ° open and C & F, then X-cef ?
The given statement is true (i) implies (ii) and (ii) implies (i).
The statement in the question that needs to be proven is :C & F, then X-cef = G is G an open set in C and CnH+ 0 s G for each Hef
We will prove that (i) implies (ii) and (ii) implies (i).
Proof: (i) C & F, then X-cef = G is G an open set in C and CnH+ 0 s G for each Hef
Let X \ {C & F} = U, then U is open, since C & F is closed.
Let H be any point of U.
By hypothesis, there exists an open set G such that CnH+ 0 s G.
Let x in G. If x ∈ C & F, then x ∉ H, so x ∉ U.
Thus, G ⊆ C, and so G ∩ U = ∅.
Hence, U is open(ii) G is G an open set in C and CnH+ 0 s G for each Hef
Let x ∈ X-C & F.
Then x ∉ C & F, so x ∉ C.
Since C is closed, there exists a neighborhood G of x that is disjoint from C.
Let H be any point of X-C & F.
Then H ∈ G and so CnH+ 0 s G.
Thus, C & F is closed.
Therefore, X-C & F is open, since C & F is closed.
Thus, X-C & F = G.
Hence, (ii) implies (i).
Therefore, the statement in the question is proven.
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What is the area of the shaded region?
6 units
Answer:
Step-by-step explanation: