At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons

The minimum grade needed to have overall grade of 85% in the class is 90%

A percentage is a number or ratio expressed as a fraction of 100. It is represented by by the symbol %.

Percentage can also be said as per 100

For example if there are total of 100 students in a class and their are 40 girls, the percentage of girls in the class is

40/100 × 100

= 40%

For the student to have a overall grade of 85%, the minimum grade in exam is calculated as

(100+70+80+x)/4 = 85

250+x = 340

x = 340 - 250

x = 90%

Therefore the minimum graded needed is 90%

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Answer:

i think 25.019mm2 is the correct answerrrrrrrr.

Answer:

175.130 mm^2

Step-by-step explanation:

Took the test.

Answer:

----------------------

Use the compound interest formula:

Where:

Plugging in the values, we get:

We are 98% confident that the true mean amount of money spent per month on home maintenance by all homeowners is between $70.19 and $75.81.

A confidence interval is a range of values that is likely to contain the true value of the population parameter with a given level of confidence. A confidence interval for the population mean μ can be constructed as follows:

μ = sample mean ± margin of error where the margin of error is given by:margin of error = (critical value) x (standard error)

Here, we want to construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. We are given that a survey of 81 randomly selected homeowners finds that they spend a mean of $73 per month on home maintenance.

The population standard deviation is assumed to be $10 per month.

Therefore, the standard error of the mean is given by:standard error = σ / sqrt(n) = 10 / sqrt(81) = 10 / 9 = 1.11

where σ is the population standard deviation and n is the sample size.To find the critical value, we need to look up the t-distribution table with 80 degrees of freedom and a significance level of 0.01 (since we want a 98% confidence interval).

The corresponding value is 2.527.

Therefore, the margin of error is:margin of error = (critical value) x (standard error) = 2.527 x 1.11 = 2.81

Finally, we can construct the confidence interval as follows:73 ± 2.81 = (70.19, 75.81)The confidence interval is rounded to the nearest cent.

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By ASA congruency triangle KBH is congruent to triangle NWH.

Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.

From the given figure,

Consider ΔKBH and ΔNWH,

∠KHB=∠NHW (Vertically opposite angles)

∠HKB=∠HWN (Interior alternate angles parallelogram)

KH=HW (Diagonals bisect each other)

By ASA congruency ΔKBH ≅ ΔNWH

Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.

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The height h of the cylinder is 9 meters.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The surface area of a cylinder is expressed as;

Surface Area = 2πrh + 2πr²

Given that; the surface area is 104π m² and the radius as 4 m.

We need to solve for the height (h).

Plug the values into the above formula:

Surface Area = 2πrh + 2πr²

104π = 2πrh + 2πr²

104π = 2π( rh + r² )

Divide through by 2π

52 = rh + r²

52 = ( 4 × h) + ( 4² )

52 = 4h + 16

Subtract 16 from both sides

52 - 16 = 4h + 16 - 16

52 - 16 = 4h

36 = 4h

4h = 36

h = 36/4

h = 9 meters

Therefore, the height is 9 meters.

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Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

The solutions of the given inequality is: x ≥ -1 or x ≤ -5, the correct number line is 2nd.

To solve the inequality |x + 3| ≥ 2, we need to consider two cases:

Case 1: (x + 3) ≥ 2

If x + 3 is greater than or equal to 2, then the absolute value of (x + 3) will also be greater than or equal to 2. Solving this case:

x + 3 ≥ 2

x ≥ 2 - 3

x ≥ -1

So, for this case, the solution is x ≥ -1.

Case 2: -(x + 3) ≥ 2

If -(x + 3) is greater than or equal to 2, then the opposite of (x + 3) will also be greater than or equal to 2. Solving this case:

-(x + 3) ≥ 2

x + 3 ≤ -2

x ≤ -2 - 3

x ≤ -5

So, for this case, the solution is x ≤ -5.

Combining the solutions from both cases, we have the final solution:

x ≥ -1 or x ≤ -5

Hence the number line showing the given inequality is 2nd.

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Answer: To show that log5 7 = 1/(2n-1)(2mn-m-2), we'll start by using logarithmic properties and the given information.

First, let's express log9 75 in terms of the base 5 logarithm, using the change of base formula:

log9 75 = log5 75 / log5 9

Next, let's simplify the expression inside the logarithm by breaking down 75 and 9 into their prime factors:

log5 (3^2 * 5^2) / log5 (3^2)

Now, using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

log5 (3^2) + log5 (5^2) - log5 (3^2)

Simplifying further, we have:

2 log5 3 + 2 log5 5 - 2 log5 3

The 2 log5 3 and -2 log5 3 terms cancel each other out, leaving:

2 log5 5

Now, let's substitute the value of m from the given information (log5 21 = m) into the expression:

2 log5 5 = 2 (log5 (5^2)) = 2(2 log5 5) = 4 log5 5 = 4m

Now, let's substitute the value of n from the given information (log9 75 = n) into the expression:

4m = 4(log5 5) = 4(1/2 log5 (5^2)) = 4(1/2 log5 25) = 4(1/2 log5 (5^2 * 5^2))

Using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

4(1/2 (log5 5^2 + log5 5^2)) = 4(1/2 (2 log5 5 + 2 log5 5)) = 4(1/2 (4 log5 5))

Simplifying further, we have:

4(1/2) (4 log5 5) = 4(2 log5 5) = 8 log5 5 = 8n

Finally, substituting the values of m and n into the expression:

log5 7 = 1/(2n-1)(2mn-m-2) = 1/(2(8) - 1)(2(4m) - m - 2) = 1/(16 - 1)(8m - m - 2) = 1/15(7m - 2)

Therefore, we have shown that log5 7 = 1/(2n-1)(2mn-m-2) = 1/15(7m - 2), using the given values of log5 21 = m and log9 75 = n.

The sine function with a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2sin(2(x - π/4)) + 4.

To write a sine function with the given properties, we can use the general form of a sine function: y = A * sin(B(x - C)) + D, where A represents the amplitude, B represents the frequency (or inverse of the period), C represents the horizontal shift, and D represents the vertical shift (or midline).

In this case:

The midline is y = 4, so D = 4.

The amplitude is 2, so A = 2.

The period is π, so the frequency is B = 2π/π = 2.

The horizontal shift is π/4 to the right, so C = -π/4.

Plugging these values into the general form, we get the sine function:

y = 2 * sin(2(x - (-π/4))) + 4

Simplifying further:

y = 2 * sin(2(x + π/4)) + 4

Therefore, the sine function with a midline of y = 4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2 * sin(2(x + π/4)) + 4.

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Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results

To solve a system of linear equations using matrices:

Step 1: Write the system of linear equations in matrix form.

Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).

Step 2: Create the augmented matrix.

Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.

Step 3: Perform row operations to achieve row-echelon form.

Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.

Step 4: Perform back-substitution.

Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.

Step 5: Interpret the results.

Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.

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Answer:

----------------

Use midpoint equation to find each coordinate:

and

So the midpoint is (12, 16).

i) Compute the autonomous investment, government the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii) The equilibrium income is approximately 709.52.

To compute the autonomous investment (A), government expenditure (G), export (X), and tax (T) multipliers, we need to use the following formulas:

Autonomous Investment Multiplier (AI):

AI = 1 / (1 - MPC)

where MPC is the marginal propensity to consume.

Government Expenditure Multiplier (GM):

GM = 1 / (1 - MPC)

Export Multiplier (XM):

XM = 1 / (1 - MPM)

where MPX is the marginal propensity to import.

Tax Multiplier (TM):

TM = -MPC / (1 - MPC)

Now let's calculate these multipliers using the given information:

i). Compute the multipliers:

MPC = change in consumption / change in income

Here, we can see that the consumption function is given by C = 40 + 0.35Y.

So, the MPC is 0.35.

MPM = change in imports / change in income

Here, we can see that the import function is given by M = 45 + 0.4Y.

So, the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii). Find the equilibrium income:

To find the equilibrium income, we set aggregate demand (Y) equal to aggregate supply (Y) and solve for Y.

Aggregate demand (Y):

Y = C + I + G + (X - M)

Substituting the given values, we have:

Y = (40 + 0.35Y) + (70 - 2r) + 400 + (240 - (45 + 0.4Y))

Simplifying the equation:

Y = 40 + 0.35Y + 70 - 2(0.5) + 400 + 240 - 45 - 0.4Y

Combining like terms:

Y = 745 - 0.05Y

Bringing Y terms to one side:

1.05Y = 745

Dividing both sides by 1.05:

Y = 745 / 1.05 ≈ 709.52 (approximately)

Therefore, the equilibrium income is approximately 709.52.

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Answer:

x = 9

Step-by-step explanation:

6/(x - 1) = 21/(3x + 1)

21(x - 1) = 6(3x + 1)

21x - 21 = 18x + 6

3x = 27

x = 9

Answer:

Step-by-step explanation:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

This helped me when i was learning to solve for x

For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.

The amplitude of a sine function represents the maximum displacement from the midline.

The coefficient in front of the sine function is 3, so the amplitude is 3.

The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.

Here, b = 2, so the period is T = 2π/2 = π.

The phase shift of a sine function indicates a horizontal shift to the left or right.

In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.

The vertical shift indicates a shift up or down on the y-axis.

The constant term outside the sine function is 2, so the vertical shift is 2 units up.

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To find the area of a tent, including the floor, we need to measure or determine the dimensions of both the tent's floor and any additional areas such as vestibules or extensions.

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Answer:

The other sides = 5 centimeters.

Step-by-step explanation:

Let's assume the length of the other two sides of the rectangle is "x" centimeters.

A rectangle has two pairs of equal sides. Therefore, we can set up the equation for the perimeter of the rectangle:

Perimeter = 2(length + width)

Given:

Length = 6 centimeters

Perimeter = 22 centimeters

Using the equation, we can substitute the given values:

22 = 2(6 + x)

Simplifying further:

22 = 12 + 2x

Subtracting 12 from both sides:

10 = 2x

Dividing both sides by 2:

5 = x

Therefore, the length of the other two sides of the rectangle is 5 centimeters.

The new price of the pants, after the discount is applied, is the one in option B:

P = $38.40

We know that the original price of the pants is $64, and we have a discount of 40%.

Then to find the new price of the pants, we need to multiply the original price by a factor (1 - 40%/100%) = (1 - 0.4) = 0.6

Then the new price of the pants, exluding the taxes, we will get that the new price is:

P = $64*0.6

P = $38.40

Then we can see that the correct option is B.

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Between 40 and 60 minutes the target heart rate strictly increasing then strictly decreasing. Therefore, option B is the correct answer.

From the given graph, in the first curve between the interval 0-10 speed is increasing,  between the interval 10-30 speed is constant and  between the interval 30-40 speed is decreasing.

In the second curve between the interval 40-50 speed is increasing,  between the interval 50-60 speed is decreasing, between the interval 60-65 speed is increasing and between the interval 65-73 speed is constant.

In the third curve between the interval 73-85 speed is increasing,  between the interval 85-92 speed is constant and  between the interval 92-100 speed is decreasing.

Therefore, option B is the correct answer.

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Here are the steps to calculate the expression √20 + 5 - 43 :

Step 1: Simplify the square root of 20:

[tex]\sqrt{20}[/tex]

Step 2: Calculate the value of the square root:

[tex]\sqrt{20} = 2\sqrt{5}[/tex]

Step 3: Substitute the value of the square root into the expression:

[tex]2\sqrt{5} + 5 - 43[/tex]

Step 4: Perform addition:

[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]

Step 5: Perform subtraction:

[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]

Step 6: Simplify the numerator:

[tex]\frac{2\sqrt{5} - 38}{1}[/tex]

Step 7: Simplify the expression:

[tex]2\sqrt{5} - 38[/tex]

Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.

The center and radius of the circle is (5, -3), and 5 respectively.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given the equation of the circle in the question:

( x - 5 )² + ( y + 3 )² = 25

To identify the center and the radius.

Comparing this equation ( x - 5 )² + ( y + 3 )² = 25 to the standard form of a circle equation, which is (x - h)² + (y - k)² = r², we can easily identify the center and radius of the circle.

( x - 5 )² + ( y + 3 )²

(x - h)² + (y - k)² = r²

The center of the circle is given by the values (h, k), which correspond to the opposite signs of the terms inside the parentheses.

In this case, the center of the circle is (5, -3), as we have (x - 5)² and (y + 3)².

The radius of the circle is the square root of the value on the right side of the equation.

In this case, the radius is √25, which simplifies to 5.

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Answer:

43.47 feet (2 d.p.)

Step-by-step explanation:

Points A, B and C form a triangle.

We have been given sides a and b, and their included angle C.

The distance between points A and B is side c of triangle ABC.

Therefore, we can solve this problem using the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

Given values:

Substitute the given values into the Law of Cosines formula and solve for side c:

[tex]\implies c^2=72^2+54^2-2(72)(54)\cos(37^{\circ})[/tex]

[tex]\implies c^2=8100-7776\cos(37^{\circ})[/tex]

[tex]\implies c=\sqrt{8100-7776\cos(37^{\circ})}[/tex]

[tex]\implies c=43.4719481...[/tex]

[tex]\implies c=43.47\; \sf ft\;(2\; d.p.)[/tex]

Therefore, the width of the pond from point A to point B is 43.47 feet, to two decimal places.

The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²

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

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)

Open the bracket

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab

Evaluate the like terms

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²

Hence, the simplified expression is (b) -a³b - 8ab²

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No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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The volume of the quarter-sphere tank is approximately 1,387,244 cubic feet.

The volume of tank 1 is 353h cubic feet, and the volume of tank 2 is  31,416 cubic feet.

The main tank is in the shape of a quarter-sphere, which means it is a quarter of a full sphere.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Given that the radius of the main tank is 95 feet

we can substitute this value into the formula to calculate the volume:

V = (4/3)π(95³) = 1,387,244 cubic feet.

The holding tanks are in the shape of cylinders that have been cut in half vertically.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.

For tank 1, the radius is given as 15 feet. Since it is a half-cylinder, we divide the volume by 2:

V1 = (1/2)π(15²)h = 353h cubic feet.

For tank 2, the height is given as 120 feet.

V2 = (1/2)π(15²)(120) = 31,416 cubic feet.

The maximum density is 0.000021142 killer whales per cubic foot

we can calculate the maximum number of killer whales as follows:

Number of killer whales = (Volume of main show tank) / (Density of killer whales)

Number of killer whales = 1,387,244 / 0.000021142 ≈ 65,606,197.

Therefore, the maximum number of killer whales allowed in the main show tank at any given time is 65,606,197

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The surface areas and volumes of the solids are listed below:

Case 1: A = 118 cm², V = 70 cm³

Case 2: A = 121.5 in², V = 91.125 in³

Case 3: A = 192 m², V = 144 m²

Case 4: A = 480 ft², V = 576 ft³

Case 5: A = 87.965 yd², V = 62.832 yd³

In this problem we need to determine the surface area and the volume of each solid. The surface area is the sum of the areas of all faces. The area and volume formulas required to answer this question are shown below:

Area

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Circle

A = π · r²

Lateral face of a cylinder

A = 2π · r · h

Volumes

Prism

V = A · h

Where:

Now we proceed to determine the surface areas and volumes of the solids:

Case 1

A = 2 · [(5 cm) · (7 cm) + (5 cm) · (2 cm) + (7 cm) · (2 cm)]

A = 2 · (35 cm² + 10 cm² + 14 cm²)

A = 2 · 59 cm²

A = 118 cm²

V = (5 cm) · (7 cm) · (2 cm)

V = 70 cm³

Case 2

A = 6 · (4.5 in)²

A = 121.5 in²

V = (4.5 in)³

V = 91.125 in³

Case 3

A = 2 · 0.5 · (8 m) · (6 m) + (6 m) · (10 m) + (6 m)² + (8 m) · (6 m)

A = 192 m²

V = 0.5 · (8 m) · (6 m)²

V = 144 m²

Case 4

A = 2 · 0.5 · (12 ft) · (8 ft) + 2 · (10 ft) · (12 ft) + (12 ft)²

A = 480 ft²

V = 0.5 · (12 ft) · (8 ft) · (12 ft)

V = 576 ft³

Case 5

A = 2π · (2 yd)² + 2π · (2 yd) · (5 yd)

A = 87.965 yd²

V = π · (2 yd)² · (5 yd)

V = 62.832 yd³

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The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].

The exponential expression can be solved as follows:

Therefore, let's simplify the expression.

To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.

∛8x⁴y⁸ / 125

let's solve them individually,

125 = 5³ = 5 × 5 × 5

8 = 2³ = 2 × 2 × 2

Therefore,

∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]

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Descartes must be thinking of the number 0.

Now, Let's call the number Descartes is thinking of "x".

Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".

So we can write this as an equation:

⇒ 9x = x

Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:

⇒ 9x - x = 0

⇒ 8x = 0

divide both sides by 8 to get:

⇒ x = 0

Thus,  Descartes must be thinking of the number 0.

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The equations of the circles that have centers on the x-axis are;

A. (x - 2)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

The equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The radial length of the circle

The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²

The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .

The correct option is therefore;

A. (x - 4)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

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