Given statement solution is :- The Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
To find the inverse function of f(x) = (x - 4)/3, we need to swap the roles of x and y and solve for y. Let's start by writing the equation with y instead of f(x):
y = (x - 4)/3
Now, let's interchange x and y:
x = (y - 4)/3
To solve for y, we can isolate it by multiplying both sides of the equation by 3:
3x = y - 4
Next, let's add 4 to both sides:
3x + 4 = y
Finally, we can write the inverse function as:
[tex]f^(-1)(x)[/tex] = 3x + 4
So, the Inverse line that represents [tex]f^(-1[/tex]) is [tex]f^(-1)[/tex] (x) = 3x + 4.
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There are 840 learners and 17 teachers at Orefile Primary school.what is the learner to teacher ratio?
Answer: 49.4 thats the answer i devided it
Cylindrical solid has a circumference of 132cm,height is 30cm.what is the area of the solid
Step-by-step explanation:
Cylinder LATERAL S.A. = circ X Height = 132 cm X 30 cm = 3960 cm^2
PLUS the two ends = two X pi r^2
the circumference = pi * d = 132 cm
then diameter = 132 / pi then radius = 1/2 132 / pi = 66/ pi
so end areas : two * pi (66/ pi)^2 = 2773.1
TOTAL = 3960 + 2773.1 = 6733.1 cm^2
The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45cm 7mm when they are born, What is the height of the average fourth grader?
The height of the average fourth grader is 135 cm 21 mm
How to determine the height of the average fourth grader?From the question, we have the following parameters that can be used in our computation:
Birth age = 45 cm 7 mm
Average fourth grader = three times as tall
using the above as a guide, we have the following:
Average fourth grader = 3 * Birth age
So, we have
Average fourth grader = 3 * 45 cm 7 mm
Evaluate
Average fourth grader = 135 cm 21 mm
Hence, the height of the average fourth grader is 135 cm 21 mm
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In the figure below, S is the center of the circle. Suppose that JK = 19, LK = 3x+ 1, SN = 12, and SP= 12. Find the
for
In the figure, applying perpendicular bisector theorem for chords in a circle, the value of JN = 9 1/2
How to find JN in the figureThe perpendicular bisector theorem for chords in a circle states that if a radius of a circle is perpendicular to a chord, then it bisects the chord.
In other words, the radius divides the chord into two equal segments.
This theorem is a direct consequence of the properties of perpendicular lines and congruent triangles.
applying this to the figure
JN = JK/2
JN = 19/2
JN = 9 1/2
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Which three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cm
Based on the Triangle Inequality Theorem the possible lengths of the sides of a triangle are:
B. 10cm, 15cm, 24cmD. 21cm, 7cm, 6cmWhat are the possible lengths of the sides of a triangle?The Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, is used to determine if three lengths can be the lengths of the sides of a triangle.
Considering each option:
A. 12cm, 5cm, 17cm:
12 + 5 > 17 (not satisfied)
5 + 17 > 12 (satisfied)
12 + 17 > 5 (satisfied)
B. 10cm, 15cm, 24cm:
10 + 15 > 24 (satisfied)
15 + 24 > 10 (satisfied)
10 + 24 > 15 (satisfied)
C. 9cm, 22cm, 11cm:
9 + 22 > 11 (satisfied)
22 + 11 > 9 (satisfied)
9 + 11 > 22 (not satisfied)
D. 21cm, 7cm, 6cm:
21 + 7 > 6 (satisfied)
7 + 6 > 21 (not satisfied)
21 + 6 > 7 (satisfied)
Hence, option B and D are correct.
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Nicole and her 3 friends bought 8 pounds of candy and shared them equally. How many pounds
of candy
?
3
Answer:
Each person will get 2 pounds of candy
Step-by-step explanation:
Nicole + 3 friends = 4 total
8 pounds of candy = total
total candy / total people
8/4 = 2
Two car services charge different rates. A charges .60 per mile plus 3.00initial charge B charges .75 per mile mile traveled . the situation is modeled bu this system where x is the number of miles traveled and y is the charge for that distance ,in cents. How many miles must each car travel for the charges to be equal and ehat is the charge for that distance
The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.
To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.
Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:
For car service A: y_A = 0.60x + 300 (in cents)
For car service B: y_B = 0.75x (in cents)
To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:
0.60x + 300 = 0.75x
Subtracting 0.60x from both sides:
300 = 0.15x
Dividing both sides by 0.15:
x = 300 / 0.15
x = 2000
Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:
y_A = 0.60(2000) + 300
y_A = 1200 + 300
y_A = 1500 cents or $15.00
So, when each car travels 2000 miles, the charges will be equal at $15.00.
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Anthony bought a house and the bank offered him a loan that so that he will pay for
it monthly for the next 20 years, with a 13.75% interest compounded monthly. How
much will Mark pay monthly if the house's original price is 15,000,000 pesos?
The amount that Mark will pay monthly if the house's original price is 15,000,000 pesos for 20 years at 13.75% monthly compounded interest is 183,810.81 pesos.
How the monthly payment is determined:The monthly payment can be computed using an online finance calculator that incorporates the compound interest system.
The compound interest system charges interest on both the principal and the accumulated interest for each period.
N (# of periods) = 240 months
I/Y (Interest per year) = 13.75%
PV (Present Value) = 15,000,000 pesos
FV (Future Value) = 0
Results:
Monthly Payment (PMT) = 183,810.81 pesos
The sum of all periodic payments = 44,114,593.72 pesos
Total Interest = 29,114,593.72 pesos
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25. Three students contributed a total of $200 towards a building for the aged. Azar contributed 50% of it, Sunil 25% and the rest was contributed by a girl Becky. How much money did Becky contribute? rice he lost 25% of its weight
Becky contributed $50 towards the building for the aged.
Let's calculate the amounts contributed by each student:
Azar contributed 50% of the total amount:
Amount contributed by Azar = 50% of $200
= (50/100) × $200
= $100
Sunil contributed 25% of the total amount:
Amount contributed by Sunil = 25% of $200
= (25/100) × $200
= $50
Now, we can calculate the amount contributed by Becky:
Total contribution by Azar and Sunil = $100 + $50 = $150
The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:
Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil
= $200 - $150
= $50
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Robert is baking a cake. He
needs 5 cups of milk, but notices that
his measuring device is only marked in
pints.
How many pints of milk will Robert
need?
What is the meaning of "it will be tacitly understood that each such formula can be written in a form that only involves ∈ and = as nonlogical symbols"?
The phrase "it will be tacitly understood that each such formula can be written in a form that only involves ∈ and = as nonlogical symbols" implies that although we may use certain symbols such as defined predicates, operations, and constants in our formulas, the underlying assumption is that these symbols can ultimately be expressed or defined using the fundamental symbols of set membership (∈) and equality (=).
What is the formulas?Symbols can always be represented using set membership and equality symbols. We simplify formulas by eliminating unnecessary symbols through this convention.
If we define predicate "P," any formula with "P" can be expressed using set membership and equality. We can translate any formula with "P" into one using only ∈ and =. By adopting this convention, we ensure clear and precise communication, with a well-defined language and logical structure for formulas.
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See text below
In practice, we shall use in formulas other symbols, namely defined pred- icates, operations, and constants, and even use formulas informally; but it will be tacitly understood that each such formula can be written in a form that only involves and as nonlogical symbols.
Concerning formulas with free variables, we adopt the notational convention that all free variables of a formula
(u1,..., Un)
are among u1, ..., un (possibly some u are not free, or even do not occur, in ). A formula without free variables is called a sentence.
What is the meaning of "it will be tacitly understood that each such formula can be written in a form that only involves ∈ and = as nonlogical symbols"?
100 Points! Geometry question. Find each measure. Photo attached. Please show as much work as possible. Thank you!
Answer:
a. 73°
b. 98°
Step-by-step explanation:
In quadrilateral EFGH
∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
11x+8+8x+1=180°
19x+9=180°
19x=180=9
19x=171
x=171/19
x=9°
similarly,
∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
6y-4+5y-3=180°
11y-7=180°
11y=180°+7
11y=187°
y=187/11
y=17°
Now
a. m∡G=8x+1=8*9+1=73°
b. m∡H=6y-4=6*17-4=98°
Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer. Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer.
The triangles are similar because they are both right triangles, so they both have an angle that is equals to 90º. They both share a common vertex, <C. So they are similar by the Angle-Angle criterion.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.For this problem, they have two equal angle measures, the right angle and < C, hence the third angle also must be equal, and they are similar by the Angle-Angle criterion.
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Geometry
Show work and number
Using the trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:
(2). x = √116
(3). x = 90
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
(1). sinA = 5/13 {opposite/hypotenuse}
cosA = 12/13 {adjacent/hypotenuse}
tanA = 5/13 {opposite/adjacent}
By Pythagoras rule
(2). x = √(4² + 10²)
x = √(16 + 100)
x = √116
(3). 106² = x² + 56²
x² = 106² - 56²
x = √(11236 - 3136)
x = √8100
x = 90
Therefore, using trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;
(2). x = √116
(3). x = 90
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Use the formula ω = (θ/t) to find the value of the missing variable. Give an exact answer unless otherwise indicated. ω = (π/8) radian per min, t = 11 min
Answer:
The missing variable θ is equal to (11π)/8.
Step-by-step explanation:
Given:
ω = π/8 radian per min
t = 11 min
Step 1: Identify the formula and the missing variable.
The formula is ω = (θ/t), and we are trying to find the value of θ.
Step 2: Rearrange the formula to solve for the missing variable.
To isolate θ, we can multiply both sides of the equation by t:
ω * t = θ
Step 3: Substitute the given values.
Substituting the given values into the rearranged formula, we have:
θ = (π/8) * 11
Step 4: Simplify the expression.
To multiply fractions, we multiply the numerators and multiply the denominators:
θ = (π * 11) / (8 * 1)
θ = (11π) / 8
Step 5: Finalize the answer.
The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.
Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.
Question: Which expression is undefined in the set of real numbers? A √-4 B 0/-4 с 0-4 D - 4x0
The expression that is undefined in the set of real numbers would be = 0/-4. That is option B.
What are real numbers?Real numbers are those numbers that can either be positive or negative and that are rational or irrational numbers which are different from complex numbers.
An expression can be said to be an undefined set of real numbers when it's numerator = 0 as seen in 0/-4.
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!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)
A) Inside the Square
B) Outside the Triangle
Answer:
A. 16.7%
B. 89.5%
Step-by-step explanation:
A) Inside the Square
length:4
The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:
(area of square)/(area of rectangle)
= 16/96
= 0.16666666666666666
This is equal to 16.7%.
B) Outside the right angles Triangle
base:4 height 5
The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:
(area of rectangle - area of triangle)/(area of rectangle)
= (96 - 10)/96
= 0.8958333333
This is equal to 89.5%.
Write a equation to calculate d for any star
The required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex].
Given that, the astronomer is finding the distance(d) of star to the sun in astronomical unit (AU) and tan [tex]\theta[/tex] = 0.000001389.
To find the equation by using the trigonometric function that is
tan a = perpendicular / base.
By using the data and the tangent trigonometric function, the equation is
tan [tex]\theta[/tex] = 1/d.
On simplifying gives,
Thus, d = 1/tan [tex]\theta[/tex].
Hence, the required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex]
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PLEASE HELP There are 30 people waiting outside in line to enter the auditorium. There are 8 times as many people already inside the auditorium. How many people are inside the auditorium?
Answer: There are 240 people inside the auditorium.
Step-by-step explanation:
30 x 8 = 240
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:
b) 17.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for the circle in this problem is given as follows:
(x + 3)² + (y - 7)² = 289.
Hence the center and the radius are obtained as follows:
Center (-3, 7).Radius of r = 17, as 17² = 289.Hence option B is the correct option for this problem.
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1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter. (2) 1.3.1 Determine the total mass of the ingredients. Give you answer in kilograms. 1.3.2 If sugar comes in 150g bags at cost of R5.95 per 150g, determine the total cost of the (2) sugar needed for this recipe.
1. The total in mass of the ingredients used is 2.35kg
2. The cost of sugar needed is R25.78.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
These statements are interpreted into mathematical equation or expression.
1. The recipes are ;
0.8kg = 800g
sugar = 650g
butter = 900000 mg = 900000/1000 = 900g
Therefore the total mass of ingredients
= 800 + 650 +900
= 2350g
in kilograms, 1000g is 1kg
2350g = 2350/1000
= 2.35kg
2. If 150g = R5.95
1g = 5.95/150
650g = 5.95 × 650/150
= R25.78.
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predict what will happen to the coordinates of a point (x,y) as the point reflects across a line to produce point (x1,y1)
The reflections are described below.
We know that,
There are two types of reflection:
Reflection with respect to X-axis:
The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.
As a result, the X-axis reflection of the point (x, y) is (x, -y).
Reflection with respect to Y- axis:
The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.
As a result, the Y-axis reflection of the point (x, y) is (-x, y).
Now the reflection is as following:
The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)
The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)
The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)
The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)
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The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)
Answer:
There are 20 blue fish in the aquarium.
Step-by-step explanation:
If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.
Fraction 1: the quantity x plus 1 over the quantity x squared minus 25; Fraction 2: the quantity x plus 5 over the quantity x squared plus 8 times x plus 7; Find Fraction 1 times by Fraction 2.
The product of the fractions is 1/[(x - 5)(x + 7)]
How to evaluate the product of the fractionsFrom the question, we have the following parameters that can be used in our computation:
Fraction 1 = (x + 1)/(x² - 25)
Also, we have
Fraction 2 = (x + 5)/(x² + 8x + 7)
So, we have
Product = (x + 1)/(x² - 25) * (x + 5)/(x² + 8x + 7)
When factored, we have
Product = (x + 1)/(x - 5)(x + 5) * (x + 5)/(x + 1)(x + 7)
Evaluate the products
Product = 1/(x - 5) * 1/(x + 7)
This gives
Product = 1/[(x - 5)(x + 7)]
Hence, the product of the fractions is 1/[(x - 5)(x + 7)]
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the expression 2x+4 is equal to what for x = 3
Answer:10
Step-by-step explanation: You plug in 3 for x so you get the equation 2(3)+4
Which becomes 6+4
Which equals 10
Which two points could be removed to make this relation a function?
A. Points R and S
B. Points Q and T
C. Points P and Q
D. Points Q and R
Option (D) D. Points Q and R is used to removed to make this relation a function.
To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.
Let's analyze the given options:
A. Points R and S: (R, 3), (S, 5)
B. Points Q and T: (Q, 2), (T, 5)
C. Points P and Q: (P, 1), (Q, 2)
D. Points Q and R: (Q, 2), (R, 3)
In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:
D. Points Q and R.
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What did Li’s crush give his Girl Friend and why was his mother upset later about the gift? Provide evidence from the text to support your response.
In the excerpt, Li's crush gave his girl friend a rose. The text states: Li's crush gave his girl friend a rose. She was so happy!
Li's mother was upset about the gift later because she thought it was too expensive.
How to explain the excerptThe text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.
Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.
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Help with this question pls?
The image of point A after the reflection is A'(3, -4).
The image of point B after the reflection is B'(2, -3).
To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.
For point A(3, 4):
After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.
Therefore, the image of point A after the reflection is A'(3, -4).
To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
For point B(-2, -3):
After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.
Therefore, the image of point B after the reflection is B'(2, -3).
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Erica bought a road bike using the store’s payment plan. She made a $320 down payment and makes monthly payments of $91. If the total cost is $1,867, how many months will Erica be paying for the bike?
Answer: 17 months
Step-by-step explanation:
Total cost of the bike = $1,867
Down payment = $320
so $1,867 - $320 = $1,547
$91 * 17 = 1,547
(17 = months) so $91 * 17 months = 1,547
The equation T^2=A^3 shows the relationship between a planets orbital period, T, and the planets mean distance from the sun, A in astronomical units, AU. If planet y is twice the mean distance from the sun as planet x. by what fsctor is the orbital period increased?
Answer:
2 * A^(3/2).
Step-by-step explanation:
Given that planet y is twice the mean distance from the sun as planet x, we can denote the mean distance of planet x as "A" and the mean distance of planet y as "2A".
The equation T^2 = A^3 represents the relationship between the orbital period (T) and the mean distance from the sun (A) for a planet.
Let's compare the orbital periods of planet x and planet y using the equation:
For planet x:
T_x^2 = A^3
For planet y:
T_y^2 = (2A)^3 = 8A^3
To find the factor by which the orbital period is increased from planet x to planet y, we can take the square root of both sides of the equation for planet y:
T_y = √(8A^3)
Simplifying the square root:
T_y = √(2^3 * A^3)
= √(2^3) * √(A^3)
= 2 * A^(3/2)
Now, we can express the ratio of the orbital periods as:
T_y / T_x = (2 * A^(3/2)) / T_x
As we can see, the orbital period of planet y is increased by a factor of 2 * A^(3/2) compared to the orbital period of planet x.
Therefore, the factor by which the orbital period is increased from planet x to planet y depends on the value of A (the mean distance from the sun of planet x), specifically, it is 2 * A^(3/2).