When given a problem such as (5 + 3i)(7 – 4i), what are 2 important processes to remember to simplify your answer?

Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

18 hours / 3 lawns = 6 hours per lawn

     Then, we can fill out the other values using this unit rate.

1 lawn * 6 hours = 6

12 hours / 6 hours = 2

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

Answer:

70

Step-by-step explanation:

-70 / -1

= 70 / 1

= 70

Answer:

Step-by-step explanation:

x + 4 + 2x + 23 = 90

3x + 27 = 90

3x = 63

x = 21

x + 4 = 21 + 4 = 25 for <1

2(21) + 23  = 42 + 23 = 65 for <2

The polynomial function has zeros of x=-2 with a multiplicity of 2, x=1 with a multiplicity of 1 , and a y-intercept of 2 is y = (x+2)^2(x-1) + 2.

To find out which polynomial function has zeros of x=-2 with a multiplicity of 2, x=1 with a multiplicity of 1, and a y-intercept of 2, we can use the factored form of a polynomial function.

This is given by:

f(x) = a(x - r₁)^n₁(x - r₂)^n₂ ... (x - rₖ)^nₖ where a is a constant, r₁, r₂, ..., rₖ are the zeros of the function, and n₁, n₂, ..., nₖ are their respective multiplicities.

Using the given zeros and multiplicities, we can write the factored form of the polynomial as:

f(x) = a(x + 2)²(x - 1) where the y-intercept is 2. To find the value of a, we can substitute the y-intercept, (0, 2), into the function:

f(0) = a(0 + 2)²(0 - 1) = -4a

Since the y-intercept is 2, we have:

f(0) = 2-4a = 2 => -4a = 0 => a = 0

Therefore, the polynomial function is:

f(x) = a(x + 2)²(x - 1) = 0(x + 2)²(x - 1) = 0

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$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

To solve this system of equations, first use the array method to organize the equations.

Array Method:

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 1 & 17 & 13 & 20 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, use row operations to solve the system. Begin by combining the first and third equations by adding them together.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Next, combine the second and fourth equations by subtracting the fourth equation from the second equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 7 & 2 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Then, combine the second and third equations by adding the second equation to the third equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Now, combine the first and third equations by subtracting the third equation from the first equation.

\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 0 & -2 & -9 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]

Finally, use back substitution to solve for the variables. Starting with $x_4$, use the fourth equation to solve for it:

$x_4 = \frac{9}{2}$

Then, use the third equation to solve for $x_3$:

$x_3 = -\frac{1}{2}$

Continuing this process, we can also solve for $x_2 = \frac{11}{2}$ and $x_1 = \frac{7}{2}$.

Therefore, the solution to the system is:

$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.

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Answer:

Step-by-step explanation:

Answer: Triangle 1: -6x + 105      Triangle 2: 20x - 30        Triangle 1 would have a greater perimeter if x = 5

Step-by-step explanation:

The perimeter of a shape is the sum of all the sides. (Add them together)

Triangle 1:

17 + 6x + 4(-3x + 22)

Simplify:

17 + 6x -12x + 88

Perimeter = -6x + 105

Triangle 2:

24 + 5x + 3(5x - 18)

Simplify:

24 + 5x + 15x - 54

Perimeter = 20x - 30

If x = 5: (Plug in 5 for x)

Triangle 1:

If x = 5: (Plug in 5 for x)

-6(5) + 105

-30 + 105 = 75

Triangle 2:

20(5) - 30

100 - 30 = 70

75 > 70

Triangle 1 would have a greater perimeter if x = 5

Hope this helps!

(3w/55c6w2)*(11c4/6w2) = 33c4/330c6w4.

To multiply fractions, we first need to express the fractions in the same denominator. To do this, we need to find the least common denominator (LCD) of the two fractions. In this case, the LCD is 55c6w2. Once we have the LCD, we can then rewrite the fractions with that as the denominator.

So the first fraction will be (3w/55c6w2) and the second fraction will be (11c4/6w2). Now that the fractions have the same denominator, we can multiply the numerators of the fractions and keep the same denominator.

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The values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

To find the values of x such that the angle between the vectors < 2, 1, -1 > and < l,x,0 > is 45 degrees, we can use the formula for the dot product of two vectors:

= |u||v|cos(theta)

Where  is the dot product of the vectors u and v, |u| and |v| are the magnitudes of the vectors, and theta is the angle between them. Plugging in the values from the question, we get:

< 2, 1, -1 > . < l,x,0 > = |< 2, 1, -1 >||< l,x,0 >|cos(45)

Simplifying the dot product, we get:

2l + x = sqrt(6)sqrt(l^2 + x^2)/sqrt(2)

Squaring both sides and rearranging, we get:

4l^2 + 4lx + x^2 = 6l^2 + 6x^2

2l^2 + 2lx - 5x^2 = 0

Using the quadratic formula, we can solve for x:

x = (-2l +/- sqrt(4l^2 - 4(2l^2)(-5)))/(2(-5))

x = (-l +/- sqrt(l^2 + 10l^2))/(-10)

x = (-l +/- sqrt(11)l)/(-10)

x = (l +/- sqrt(11)l)/10

Therefore, the values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

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If G is a non-Abelian group, it has an automorphism that is not the identity. This is proven by constructing a map φ that is a bijective homomorphism but not the identity, using an element a that is not in the center of G.

An automorphism is a bijective homomorphism of a group onto itself. If G is a non-Abelian group, we need to prove that there is an automorphism that is not the identity.

To prove this, we can use the following steps:

1. Let G be a non-Abelian group.
2. Choose an element a ∈ G that is not in the center of G. This means that there exists an element b ∈ G such that ab ≠ ba.
3. Define a map φ: G → G by φ(x) = axa⁻¹ for all x ∈ G.
4. We can prove that φ is a homomorphism by showing that φ(xy) = φ(x)φ(y) for all x, y ∈ G.
5. We can also prove that φ is bijective by showing that it has an inverse map φ⁻¹: G → G defined by φ⁻¹(x) = a⁻¹xa for all x ∈ G.
6. Since φ is a bijective homomorphism, it is an automorphism of G.
7. However, φ is not the identity, because φ(b) = aba⁻¹ ≠ b.
8. Therefore, G has an automorphism that is not the identity.

In conclusion, if G is a non-Abelian group, it has an automorphism that is not the identity. This is proven by constructing a map φ that is a bijective homomorphism but not the identity, using an element a that is not in the center of G.

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The first step in solving by elimination is (4) Multiply top equation by 2

From the question, we have the following parameters that can be used in our computation:

5x + y = 9

10x - 7y = -18

To eliminate x the coefficient of x in both equations muet be the same i.e 10

Using the above as a guide, we have the following:

Multiply (1) by 2

So, we have

10x + 2y = 18

10x - 7y = -18

Hence, the first step is (4)

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For an expression 2(3a+2b−7), an equivalent expression is 6a + 4b - 14

The correct answer is an option (D)

Consider an expression 2(3a+2b−7)

We simplify this expression.

2(3a+2b−7)

To simplfy this expression, multiply each term of (3a+2b−7) by 2

2(3a+2b−7)

= 2 × (3a + 2b - 7)

= (2 × 3a) + (2 × 2b) - (2 × 7)

= 6a + 4b - 14

So, we get 2(3a+2b−7) = 6a + 4b - 14

Therefore, 6a + 4b - 14 is an equivalent expression to 2(3a+2b−7)

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The complete question is:

Which expression is equivalent to the given expression? 2(3a+2b−7) ​

A 5a+4b−5

B 6a+2b−7

C 6a+4b−7

D 6a+4b−14

z3 = 6 - 2xz3x + 4 in the form a + b i, where a,b in R.

=> z3 + (2z3 + i)x = 4 - 6i

Expand the bracket:

z3 + 2xz3x + ix = 4 - 6i

Subtract 4 from both sides:

z3 + 2xz3x + ix - 4 = - 6i

Rearrange and set ix = -1:

z3 + 2xz3x - 4 = 6

Subtract 2xz3x from both sides:

z3 - 4 = 6 - 2xz3x

Solve for z3:

z3 = 6 - 2xz3x + 4

Therefore, z3 = 6 - 2xz3x + 4 in the form a + b i, where a,b in R.

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The number of means is 13. Option B

We can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.

Then we have:

a + (n-1)d = 125 (1)

a + nd = -113 (2)

Subtracting equation (2) from equation (1), we get:

(n-1)d + 238 = 0

Solving for d, we get:

d = -238/(n-1)

Using the formula for the twelfth term, we have:

a + 11d = -113

Substituting the expression for d, we get:

a - 11(238/(n-1)) = -113

Multiplying both sides by n-1, we get:

a(n-1) - 11(238) = -113(n-1)

Substituting a = -65 and simplifying, we get:

n = 13

Therefore, the number of means is 13

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ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).

First, we can find the prime factorization of 144:

[tex]144 = 2^4 * 3^2[/tex]

Using the property above, we can rewrite ln(144) as:

[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]

Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):

ln(144) = 4 ln(2) + 2 ln(3)

Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

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Cylinders X and Y have the same lateral surface area in square inches.

The next time when a train and a bus leave the station together is 4:30pm.

The next time when a train and a bus leave the station together will be the least common multiple (LCM) of the two intervals, 8 minutes and 10 minutes.

To find the LCM of 8 and 10, we can list the multiples of each number until we find a common multiple:
8: 8, 16, 24, 32, 40
10: 10, 20, 30, 40

The LCM of 8 and 10 is 40. This means that a train and a bus will leave the station together every 40 minutes.

Since the train and bus both leave the station at 3:50pm, the next time they will leave together will be 40 minutes later, at 4:30pm.

Therefore, the next time when a train and a bus leave the station together is 4:30pm.

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Answer: C (17)

Step-by-step explanation: We need to make the equation true so we take

2x times 17 to get 34  and so 34-22=12

The statement, "Only datasets having a linear relationship between variables can be assessed using regression analyses" is False, because Non-Linear relationships also can be assessed, the correct option is (b)False.

The Regression Analysis can be used to assess the relationship between variables, including non-linear relationships.

There are various types of regression models that can capture non-linear relationships, such as polynomial regression, exponential regression, and logarithmic regression.

The interpretation of the regression coefficients and other statistics may be different in non-linear regression models compared to linear regression models.

Therefore, the given statement is (b)False.

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The solution is:  standard deviation. So, correct option is C.

Here, we have,

Explanation:

However, note that the mean of a sample from a normal population (that is, a type of "standard deviation" known as "standard deviation from a sample mean", is an "unbiased estimator" of the "population mean".

We shall represent the "sample mean" as:  X  ;

              (pronounced: "x-bar"; that is; "ex-bar"); this is the usual symbol                                                                                                              used;

We shall represent the sample size as "n" ;

                                                (This is the usual variable used; note that

                                                                               "n" is a numeric value).

The standard deviant from the sample mean:

(n *  X)  / (n + 1) is a "biased estimator of the mean" that becomes "unbiased" as the sample size increases; since as "n" increases in values; the value of the entire entire expression becomes smaller (i.e the standard deviation becomes smaller.

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Complete question:

Which biased estimator will have a reduced bias based on an increased sample size? mean median standard deviation range

There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

To perform long division, we need to follow these steps:

Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.

For the first problem, 32.156 / 100, we can set it up like this:

```
100 | 32.156
```

Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:

```
100 | 3215.6
```

100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:

```
32
100 | 3215.6
  -3200
   -----
     15.6
```

Now we bring down the next group of digits, which is 6:

```
32.1
100 | 3215.6
  -3200
   -----
     156
```

100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:

```
32.16
100 | 3215.6
  -3200
   -----
     156
    -100
   -----
      56
```

Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.

For the second problem, 174.787 / 0.01, we can set it up like this:

```
0.01 | 174.787
```

Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:

```
0.01 | 17478.7
```

0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:

```
1747800
0.01 | 17478.7
   -17478
    -----
        0.7
```

Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.

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The correct option is A. Yes, λ=4 is an eigenvalue of the matrix.

To find the corresponding eigenvector, we need to solve the equation (A - λI)x = 0, where A is the given matrix, λ is the eigenvalue, I is the identity matrix, and x is the eigenvector.
First, we subtract λI from A:
A - λI = 3-4 -4 0 0 3-4 3 2-4 -2 6
= -1 -4 0 0 -1 3 2 -2 2
Next, we set the equation (A - λI)x = 0 and solve for x:
(-1 -4 0) (x1) = 0
(0 -1 3) (x2) = 0
(2 -2 2) (x3) = 0
Simplifying the equations gives us:
-x1 - 4x2 = 0
-x2 + 3x3 = 0
2x1 - 2x2 + 2x3 = 0
We can solve this system of equations to find the eigenvector. One possible solution is x1 = 2, x2 = 1, x3 = 1/3. Therefore, one corresponding eigenvector is (2, 1, 1/3).
So the correct answer is A. Yes, λ=4 is an eigenvalue of the matrix. One corresponding eigenvector is (2, 1, 1/3).

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Using the scale factors obtained the values are -

The value of k is 8, since g(−2) = 8.

The value of k is 8, since g(−2) = 8.

The value of k is 8, since g(−2) = 1.

The value of k is 4, since g(−2) = 2.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

For each part, we can use the given table to determine how the transformation affects the function values -

g(x) = f(2x)

This transformation is a horizontal compression by a factor of 2.

To see this, notice that when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.

Similarly, when we evaluate g at x = 0, we get the same value as f evaluated at x = 0.

And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -2).

So, g(x) is a compressed version of f(x) horizontally by a factor of 2.

Therefore, the value of k is 8, since g(−2) = 8 = f(2×(-2)).

g(x) = 2f(x)

This transformation is a vertical stretch by a factor of 2.

To see this, notice that every value of g(x) is twice the corresponding value of f(x).

So, g(x) is a stretched version of f(x) vertically by a factor of 2.

Therefore, the value of k is 8, since g(−2) = 2f(−2) = 2×4 = 8.

g(x) = f(x/2)

This transformation is a horizontal stretch by a factor of 2.

To see this, notice that when we evaluate g at x = -2, we get the same value as f evaluated at x = -4.

Similarly, when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.

And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -4).

So, g(x) is a stretched version of f(x) horizontally by a factor of 2.

Therefore, the value of k is 8, since g(−2) = f(−1) = 1.

g(x) = (1/2)f(x)

This transformation is a vertical compression by a factor of 2.

To see this, notice that every value of g(x) is half the corresponding value of f(x).

So, g(x) is a compressed version of f(x) vertically by a factor of 2.

Therefore, the value of k is 4, since g(−2) = (1/2)f(−2) = (1/2)×4 = 2.

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15000 rational numbers from (-1,1) interval using black

Answer: Code for the given mathematical function# Python code for plotting sine and cosine functions import matplotlib.py plot as plt import numpy as npa = [0.25, 1, 3] # given set of valuesx = np.linspace(-15, 1, 15000) # from (-1, 1) interval and 15000 rational numbersb = 2.5c = 1.6fig, ax = plt.subplots()# Plotting the graph with different colorsplt.plot(x, a[0]*np.cos(b*x)+ (1-a[0])*np.sin(c*x), color='black', label='a=0.25')plt.plot(x, a[1]*np.cos(b*x)+ (1-a[1])*np.sin(c*x), color='red', label='a=1')plt.plot(x, a[2]*np.cos(b*x)+ (1-a[2])*np.sin(c*x), color='blue', label='a=3')# Adding labels and titlesplt.xlabel('x-axis')plt.ylabel('y-axis')plt.title('Plot of given mathematical function')plt.legend()# Displaying the plotplt.show()Graphical output for the given mathematical function:Here, the above code gives a line plot of the given mathematical function for all a € (0.25k: 1 ks 3,k e Z+), and x € {x € R:-15x 1), where b=2.5, C = 1.6 by creating 15000 rational numbers from (-1,1) interval using black, red, and blue colors for respective k values.

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The equation for the exponential function is f(x) = (4.5)((0.5/4.5)-1/2)x. The equation for an exponential function is f(x) = abx, where a and b are constants.

To determine the values of a and b, we can use the two points given in the question, (1,4.5) and (-1,0.5).

Let's substitute the point (1,4.5) into the equation.

f(1) = a*b1
4.5 = a*b

Now let's substitute the point (-1,0.5) into the equation.

f(-1) = a*b-1
0.5 = a*b-1

We can now solve for a and b.

a = 4.5 / b
b-1 = 0.5 / a
b-1 = 0.5 / (4.5/b)
b-1 = 0.5b/4.5
b-2 = 0.5/4.5
b = (0.5/4.5)-1/2

Thus, the equation for the exponential function is f(x) = (4.5)((0.5/4.5)-1/2)x

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Answer: The flat rate cost is $25.70 and the cost per item is $2.30, so the total cost (y) can be represented as:

y = 2.30x + 25.70

This is in slope-intercept form, where the slope is 2.30 and the y-intercept is 25.70.

Step-by-step explanation:

a. The variable is the type of communication preference: postal service or email.

b. The population is the adult population in Puerto Rico.

c. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

d. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.

e. The sample is the 600 adults that the graduate student surveyed.

a. The variable in this research project is the preferred method of communication for adults in Puerto Rico (postal mail or email).

b. The population in this research project is the adult population in Puerto Rico.

c. The sample in this research project is the 600 adults that the graduate student surveyed.

d. The parameter in this research project is the percentage of adults in Puerto Rico who prefer postal mail to email.

e. The statistic in this research project is the 250 adults who indicated their preference for the postal service out of the 600 adults surveyed. This statistic was used to estimate the parameter of 48% of adults in Puerto Rico preferring the postal service to email.

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Answer:

There are two situations involving rational exponents or radicals that will never result in a negative real solution:

Even-indexed roots: If we take the square root, fourth root, sixth root, etc. of a non-negative real number, the result will always be non-negative. For example, the square root of 9 is 3, and the fourth root of 16 is 2, both of which are non-negative. This is because even-indexed roots always produce a non-negative result, regardless of the sign of the original number.

Exponents with even denominators: If we raise a non-negative real number to an exponent with an even denominator, the result will always be non-negative. For example, (4^2/4) is equal to 4, which is non-negative. This is because any negative base raised to an even power results in a positive number, and any positive base raised to an even power also results in a positive number. Therefore, any exponent with an even denominator will always produce a non-negative result, regardless of the sign of the original number.

In response to the supplied query, we may state that Therefore, the area of the circle is approximately 113.1 cm² (rounded to one decimal place).

A circle is created in the plane by each point that is a specific distance from another point (center). Hence, it is a curve made up of points that are separated from one another by a defined distance in the plane. Moreover, it is rotationally symmetric about the centre at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "centre." A circular symmetry line is made by drawing a line through the circle. Moreover, it is rotationally symmetric about the centre at every angle.

We must make certain assumptions because the diagram was not created precisely. Assume that the quarter circle is a perfect quarter circle and that its radius is 12 cm (as given in the question).

A = r2, where r is the radius, is the formula for calculating a circle's surface area. Due to the fact that we only have a quarter of a circle, we must divide the outcome by 4. Hence, the quarter circle's area is:

[tex]A = (1/4)\pi r^2\\A = (1/4))\pi(12^2)\\A = (1/4))\pi(144)\\A = 36)\pi[/tex]

Therefore, the area of the shape is approximately 113.1 cm² (rounded to one decimal place).

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