The perimeter of Aaron’s rectangular bedroom is 368 inches. His room is 8 feet wide. What is the area of Aaron’s bedroom?

the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

The relationship between the diameter of the pizza and its cost per square inch is non-proportional.

If the relationship were proportional, then the cost per square inch of the pizza would remain constant as the diameter changes. However, in this case, we see that as the diameter of the pizza increases, the cost per square inch decreases. This is because the area of a circle increases more rapidly than its diameter, so the cost must be spread out over a larger area, resulting in a lower cost per square inch.

Therefore, the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

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would relationship between the dilation factor k and the resulting volume of a solid best be described as proportional or non proportional? justify your answer

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Answer:

If the shopkeeper sold the radio for 336 rs and gained a 5% profit, then the cost price (c.p.) of the radio can be calculated as follows:

Let x be the cost price of the radio. Since the shopkeeper gained a 5% profit, we can write the equation: x + 0.05x = 336 Solving for x, we get: x(1 + 0.05) = 336 x = 336/1.05 x = 320

So, the cost price (c.p.) of the radio is 320 rs.

Step-by-step explanation:

Step-by-step explanation:

12 lemons   / 4 people      *     30 people =   90 lemons

1 liter/ 12 lemons   *  90 lemons =  7.5 liters of water

The length of the second arc is 8 feet.

The rope is swinging in such a way that the length of the arc is decreasing geometrically.

If the first arc is 18 feet long and the third arc is 8 feet long,

The length of the second arc :

In order to find the second arc length, we need to use the formula of the geometric sequence.

We have to understand what is given and what is required.

Given : First arc = 18 feet

Third arc = 8 feet.

To Find : Length of the second arc.

The formula of the geometric sequence is :

[tex]a_n[/tex] = [tex]a_1[/tex] × rn − 1

where, r = Common ratio [tex]a_1[/tex] = First term [tex]a_n[/tex] = [tex]n^{th}[/tex] term

Here, the length of the first arc is [tex]a_1[/tex] = 18.

The length of the third arc is [tex]a_3[/tex] = 8.

We have to find the length of the second arc, which is [tex]a_2[/tex]

Using the formula of the geometric sequence, we can find the [tex]a_1[/tex]: r= [tex]a_3[/tex] / [tex]a_2[/tex]

We know that [tex]a_1[/tex]= 18 and [tex]a_3[/tex]= 8

Substitute the values: r= 8 / [tex]a_2[/tex]

Now, we can rewrite the formula of the geometric sequence: an=[tex]a_1[/tex]×rn−1an= [tex]a_1[/tex] x r(n-1)

The length of the first arc is [tex]a_1[/tex] = 18 feet.

Substituting the value of r, we get:

8 / [tex]a_2[/tex] = r18 x r(n-1) = [tex]a_2[/tex]

We are given that the length of the third arc is 8 feet,

thus : 8 = 18 x r(3-1)8

= 18 x [tex]r_2[/tex][tex]r_2[/tex]

= 8 / 18[tex]r_2[/tex]

= 4 / 9r

= √(4/9)

Using this value of r, we can find the length of the second arc :

[tex]a_2[/tex] = 18 x (4/9) (2-1) [tex]a_2[/tex]

= 18 x (4/9)[tex]a_2[/tex]

= 8

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Step-by-step explanation:

La première baisse de prix est de 30%, ce qui signifie que le prix du vêtement est maintenant de 70% de son prix initial :

Prix après la première baisse = 100€ - (30% x 100€) = 70€

Ensuite, le prix est réduit à nouveau de 20%. Cela signifie que le prix final est de 80% du prix après la première baisse :

Prix après la deuxième baisse = 70€ - (20% x 70€) = 56€

Le pourcentage de réduction totale correspond donc à la différence entre le prix initial et le prix final, exprimé en pourcentage du prix initial :

Pourcentage de réduction totale = ((100€ - 56€) / 100€) x 100% = 44%

Le vêtement a donc subi une réduction de 44% au total après les deux baisses successives de prix.

The number of horizontal square of D over the number of vertical

squares  = 3 : 2

What is square in math?

A planar shape with four equal sides and four right (90°) angles is referred to as a square in geometry. An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one). All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees apart from each other or at right angles. The square's diagonals are also equal and split at an angle of 90 degrees.

the number of horizontal squares of A, B , and C over the number of vertical square = 2 : 3

  the number of horizontal square of D over the number of vertical

squares  = 3 : 2

                       6 : 4 = 3 : 2

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Answer:

2.1

Step-by-step explanation:all side lengths are the same (duh) use 4 and 3 (4 bc there is 4 sides). 4 as the diagonal support

4²=16

3²=9

16-9=7 then use square root for 7 the square root of 7 is 2.6457513111 or 2.1

The expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

3-methylheptane dial is a 7-carbon compound with two carbonyl groups, one at each end of the molecule. Intramolecular aldol condensation occurs when one carbonyl group reacts with the other within the same molecule. The carbonyl group acts as an electrophile, while the enolate formed from the other carbonyl group acts as a nucleophile.

In the case of 3-methylheptane dial, intramolecular aldol condensation can occur between the carbonyl group at the 3-position and the enolate formed from the carbonyl group at the 6-position. The resulting intermediate undergoes dehydration to form a cyclic α,β-unsaturated ketone.

The product of the reaction will have a cyclic structure with a double bond between the α and β carbons. The exact structure of the product will depend on the stereochemistry of the starting material and the reaction conditions. However, the product is expected to have a seven-membered ring and to be an α,β-unsaturated ketone.

Therefore, the expected product from the intramolecular aldol condensation of 3-methylheptane dial is a cyclic α,β-unsaturated ketone with a seven-membered ring.

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The two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.

It is given to us that the two shorter sides of a right triangle measure 15 inches and 3 feet.

Let us say that side a is 3 feet and side b is 15 inches and we need to find side c, that is the longest side also known as the hypotenuse,

A right-angled triangle is one in which only one angle is precisely 90 degrees. Since the total of all the angles in a triangle is always 180°, the other two angles will be obviously smaller than the right angle.

We define the sides of a right-angled triangle in a unique manner. The hypotenuse of a triangle is the edge that faces the right angle and is always the largest.

Pythagorean formula. Pythagoras' theorem says that: a² + b² = c². in a right triangle with cathetus a and b and with hypotenuse c.

Take the square root of both sides to find c = √(b²+a²). This Pythagorean theorem expansion can be thought of as a "hypotenuse formula."

Therefore, with this formula we can solve for hypotenuse:

side a = 15 inches = 1.3 feet

side b = 3 feet

a² + b² = c²

1.3² + 3² = c²

1.69 + 9 = c²

10.69 = c²

c = 3.269557 feet

Therefore, we can say that the two shorter sides of a right triangle measure 15 inches and 3 feet and the length of the longest side also known as the hypotenuse is 3.269557 feet.

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(a) The distance that the tip of the hour hand covers in twelve hours is 28.29 cm.

(b)The distance that the tip of the minute hand covers in one hour is 34.57 cm.

(c) The tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.

(a) To find the distance that the tip of the hour hand covers in twelve hours, we need to calculate the circumference of the circle that the tip of the hour hand traces in twelve hours. The circumference is given by:

C = 2πr

where r is the length of the hour hand

C = 2 x 22/7 x 4.5

C = 28.29 cm

(b) Also, the distance that the tip of the minute hand covers in one hour is:

C = 2 x 22/7 x 5.5

C = 34.57 cm

(c) We can see that the distance covered by the minute hand in one hour (34.57 cm) is greater than the distance covered by the hour hand in twelve hours (28.29 cm).

difference = 34.57 cm - 28.29 cm = 6.28 cm

Thus, the tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.

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Answer:

Commutative property of addition

Step-by-step explanation:

The property being used in this equation is the commutative property of addition. This property states that when two numbers are added, the order in which they are added does not change the sum. So, in this case, we can rearrange the terms 5/6 and 7/12 and still get the same result.

Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm

Procedure 2 (proportions)

Create a proportion first.

We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.

1cm x cm

——— ———

100m 60m

Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.

Thus, your response is 6.

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Answer:22.1%

Step-by-step explanation:

I remember doing this but I don’t seem to remember sorry

Answer:

220-8pi

Step-by-step explanation:

The value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

The process of integrating two or more functions into one function is known as composition of functions. A function is an example of labour. Take making bread as an example. Let x be the flour, let g(x) be the function that the food processor performs to prepare the dough using the flour, and let f(x) be the function that the oven does to bake the bread. The output of g(x) should be sent into the function f(x) to make bread (i.e., the prepared dough should be placed in the oven). The outcome is represented by the symbol f(g(x)), and it is made up of the functions f(x) and g. (x).

The function q and r are as follows:

q(x) = x² + 6

r(x) = √(x + 9)

The value of:

(q ° r )(x) = q(r(x))

Here, substitute the value of x in q(x) with the value of r(x):

q(r(x)) = (√(x + 9))² + 6

q(r(x)) = x + 9 + 6

Substitute x = 7:

q(r(7)) = 7 + 9 + 6 = 22

Now, (r ° q) = r(q(x))

r(q(x)) = √(x² + 6 + 9)

= √(x² + 15)

Substitute x = 7:

r(q(7)) = √(7² + 15) = √(49 + 15) = √64 = 8

Hence, the value of the function q and r are as follows (q ° r )(7) = 22 and (r ° q)(7) = 8.

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The average rate of change of the function f(x) over the interval [-2, -9] is -6.

To determine the average rate of change of the function f(x) over the interval [-2, -9], we need to find the slope of the secant line that connects the points (-2, f(-2)) and (-9, f(-9)).

We first find the values of f(-2) and f(-9):

f(-2) = (-2)² + 5(-2) + 14 = 4 - 10 + 14 = 8

f(-9) = (-9)² + 5(-9) + 14 = 81 - 45 + 14 = 50

So, the two points are (-2, 8) and (-9, 50).

The slope of the secant line between these two points is:

slope = (f(-9) - f(-2)) / (-9 - (-2)) = (50 - 8) / (-9 + 2) = 42 / -7 = -6

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(7)  The two polygons are congruent since we can obtain a congruent image of DEF by applying a translation or a rotation.

(8) The two polygons are congruent since we can obtain a congruent image of JKLM by applying a translation or a rotation.

To determine whether the two polygons are congruent, we can apply a series of transformations to one of them to see if it can be mapped onto the other.

(7) Let's first label the polygons: ABCD is the first polygon and DEF is the second polygon.

Translation: We can translate DEF four units to the right and two units down to obtain the image of DEF, which is congruent to ABCD.

Rotation: We can rotate DEF about the point (0, 1) by 180 degrees to obtain the image of DEF, which is congruent to ABCD.

Since we can obtain a congruent image of DEF by applying a translation or a rotation, we can conclude that the two polygons are congruent.

(8) Let's label the two polygons: JKLM is the first polygon and NOPQ is the second polygon.

Translation: We can translate JKLM six units to the right and three units down to obtain the image of JKLM, which is congruent to NOPQ.

Rotation: We can rotate JKLM about the point (-4, 4) by 180 degrees to obtain the image of JKLM, which is congruent to NOPQ.

Since we can obtain a congruent image of JKLM by applying a translation or a rotation, we can conclude that the two polygons are congruent.

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These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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Answer:

yes

Step-by-step explanation:

The coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The mapping of reflection over the x-axis is depicted as follows:

(x, y) to (x, -y)

The coordinates of A and B are:

A (7, 8)

B (2, 3)

After the reflection over x-axis the coordinates are transformed as follows:

A' = (7, -8)

B' = (2, -3)

Hence, the coordinates of the graph when reflected over x-axis is given as A' (7, -8) and B' (2, -3).

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Three equations that can be seen in the graph for each type of function are x = -6, y = 1.5x  -2.5 and y = x² + 6x + 10

Function 1: Constant

A constant function is a mathematical function that always returns the same output value regardless of its input.

A constant function with the equation x = -6 exist on the graph with the following features: x = -6 as domain and [0, 4] as the range

Function 2: Linear

A linear function is a type of mathematical function where the output varies linearly with the input.

From the graph, we have the points

(4, 3.5) and (5, 5)

Using a graphing tool, the equation is

y = 1.5x  -2.5

And the identities are [4, 5] as the domain and [3.5, 5] as the range

Function 3: Quadratic

This is a function of the form y = a(x - h)² + k or y = ax² + bx + c

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

Using a graphing tool, the equation is

y = x² + 6x + 10

And the identities are [-4, -2] as the domain and [1, 2] as the range

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The volume of the sphere is increasing at a rate of 209,439.51 mm³/s when the diameter is 100 mm

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (Round your answer to two decimal places).Formula to calculate the volume of a sphere = (4/3) × π × r³where r = radius of the sphere, π = pi = 3.14, d = diameter of the sphere. The diameter of the sphere, d = 100 mm.So, the radius of the sphere, r = d/2 = 100/2 = 50 mm.

Now, we need to find the rate of change of the volume of the sphere when the radius of the sphere is increasing at a rate of 4 mm/s.We know that the volume of the sphere is given by V = (4/3) × π × r³.We have to differentiate the above formula with respect to time (t).dV/dt = d/dt [(4/3) × π × r³]dV/dt = (4/3) × π × 3r² × dr/dt, substitute r = 50 mm and dr/dt = 4 mm/s in the above equation to find dV/dt.dV/dt = (4/3) × π × 3(50)² × 4dV/dt = 209,439.51 mm³/sTherefore, the volume of the sphere is increasing at a rate of 209,439.51 mm³/s .

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Based on the table provided, the statement that is true is of all the cats adopted, about 66% were adopted in a month or less.

To calculate a percentage, you need to divide a part by the whole and then multiply the result by 100. The formula for calculating a percentage is:

Percentage = (Part / Whole) x 100

Alternatively, if you have the percentage and the whole, you can use the following formula to find the part:

Part = (Percentage / 100) x Whole

Based on this, let's prove the true statement:

Total of animals: 58 cats

Total of cats adopted in a month or less: 38

Percentage = 38/ 58 x 100 = 65.5% which can be rounded as 66%

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The cheaper price for the 12 orchid is the 8.60 pounds for 4 orchid.

The cheaper price for the 12 orchid can be calculated as follows;

Therefore, for the first Orchid:

4 orchid = 8.60 pounds

12 orchid = ?

cross multiply

cost for 12 orchid = 8.60 × 12 / 4

cost for 12 orchid = 103.2 / 4

cost for 12 orchid = 25.8 pounds

For the second orchid:

5.40 pounds for each.

Now, 1 / 3 off,

Therefore,

1 / 3 ×5.40 = 1.8

Therefore,

5.40 - 1.8 = 3.6 pounds for each

Therefore,

12 orchid = 12 × 3.6 = 43.2 pounds

Therefore, the cheaper price is 8.60 pounds for 4 orchid.

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196 children's tickets and 328 adult tickets were sold.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in.

Let the amount of the child's ticket be x

Let the amount of adults tickets be y

If the total number of tickets sold is 524 movie tickets, then;

x + y  = 524

x = 524 - y...(1)

If an adult ticket cost $6.50 and a child’s ticket cost $3.5 with a total of $2881 in all, then;

3.5x +  6.5 y = 2881

35x + 65y = 28810 ...(2)

Substitute equation 1 into 2:

35x + 65y = 2881

35(542-y) + 65y = 28810

18970 - 35y + 65y = 28810

30y = 9840

y = 328

Put the value of y in equation (1) and we get

x = 524 - 328

x = 196

Hence,  196 children's tickets and 328 adult tickets were sold.

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To determine the approximate length of the underground pipeline needed from the lake to the water level in Apache Durham Park, we would know the distance between the lake and park, as well as the specific path that the pipeline would take from the lake to the park.

Length is a physical or conceptual measurement of the extent of something from one end to the other.

It refers to the distance between two points or the size of an object or entity in the direction of its longest dimension. In mathematics and geometry, length is a fundamental concept used to describe the size and shape of geometric figures and objects.

It is measured in units such as meters, feet, inches, or centimeters

Assuming that we have this information, we can use the distance between the two points as the approximate length of the pipeline. To calculate this distance, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) represents the coordinates of the lake and (x2, y2) represents the coordinates of Apache Durham Park.

Once we have the distance between the two points, we can round it to the nearest meter to get the approximate length of the pipeline needed.

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We would know the distance between the lake and park, as well as the precise route that the pipeline would travel from the lake to the park, if we knew the approximate length of the underground pipeline required from the lake to the water level in Apache Durham Park.

A gauge of length is one that shows how far something extends from one end to the other.

It describes the separation of two points or the size of an item or entity measured along its longest axis. Length is a basic notion in mathematics and geometry that is used to describe the size and shape of geometric figures and objects.

Its dimensions are expressed in terms of meters, feet, inches, or millimeters.

Assuming we have this knowledge, we can use the distance between the two locations to estimate the pipeline's length. We can use the following algorithm to determine this distance:

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]

where [tex](x_{1},y_{1} )[/tex] stands for the lake's coordinates and [tex](x_{2} ,y_{2} )[/tex] for Apache Durham Park's coordinates.

Once we know how far apart the two locations are, we can round it to the closest meter to determine how long the pipeline should be roughly.

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The complete question is as follows:

The Solutions to 12m ² - 4mn-5n² are:

m = n/3 or m = -5n/3

To solve the quadratic equation 12m² - 4mn - 5n² = 0, we can use the quadratic formula:

m = (-b ± √(b^2 - 4ac)) / 2a

where a = 12, b = -4n, and c = -5n².

Substituting these values into the formula, we get:

m = (-(-4n) ± √((-4n)^2 - 4(12)(-5n²))) / 2(12)

Simplifying:

m = (4n ± √(16n² + 240n²)) / 24

m = (4n ± √(256n²)) / 24

m = (4n ± 16n) / 24

So the solutions are:

m = n/3 or m = -5n/3

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The length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.  

Let's call the distance between the poles "d" and the height of the poles "h". We can use the Pythagorean theorem to find the length of the ropes:

If we draw a diagram, we can see that the four ropes form the hypotenuses of four right triangles. Each right triangle has a base of d/2 and a height of h - (banner height)/2.

Therefore, we have:

[tex]x^2[/tex] = [tex](d/2)^2[/tex] + [tex](h - (banner height)/2)^2[/tex]

Substituting the given values, we get:

[tex]x^{2}[/tex] = [tex](20/2)^2[/tex]+ [tex](16 - (8/2))/2)^2[/tex]

[tex]x^{2}[/tex]= 100 + [tex](8/2)^2[/tex]

[tex]x^{2}[/tex] = 100 + 16

[tex]x^{2}[/tex] = 116

Taking the square root of both sides, we get:

x = [tex]\sqrt{116}[/tex]

x ≈ 10.77

Therefore, the length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.  

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Answer:20.25

Step-by-step explanation: