x²-x-6
2
x+3x² - 2x - 3*
Find a reasonable estimate of the limit lim

Starting with 110mg of a radioactive substance, after 21 hours, 55mg remains. Using the exponential decay model, after 31 hours,  39.3mg of the substance will remain.

We can use the formula for exponential decay, which is:

N(t) = N0 * e^(-λt)

where:

N0 is the initial amount of the substance

N(t) is the amount remaining after time t

λ is the decay constant

To solve for λ, we can use the fact that after 21 hours, 55 mg remains:

55 = 110 * e^(-λ*21)

Simplifying:

0.5 = e^(-λ*21)

Taking the natural logarithm of both sides:

ln(0.5) = -21λ

Solving for λ:

λ = ln(0.5) / (-21) ≈ 0.033

Now we can use this value of λ to find the amount remaining after 31 hours:

N(31) = 110 * e^(-0.033*31) ≈ 39.3 mg

Therefore, approximately 39.3 milligrams of the substance will remain after 31 hours.

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If we know that f(7) = 0, we can say that:

x - 7 is a factor of the function f(x).

This is because when we substitute x = 7 into the function, we get:

f(7) = 7^3 - 7(7)^2 + 25(7) - 175 = 0

This means that (x - 7) is one of the factors of the function.

Now we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x - 7), we obtain:

           x^2 - 4x + 25

Therefore, we can say that:

f(x) = (x - 7)(x^2 - 4x + 25)

The quadratic term, x^2 - 4x + 25, has no real roots because the discriminant is negative. Therefore, we can write the factorization of f(x) in terms of complex numbers as:

f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)

Thus, the complete factorization of f(x) is:

f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)

Si nous savons que f(7) = 0 alors,

x - 7 est un facteur de la fonction f(x).

on substitue x = 7 dans la fonction

f(7) = 7^3 - 7(7)^2 + 25(7) - 175 = 0

donc  (x - 7) est l’un des facteurs de la fonction.

Maintenant, on utilise division polynomiale ou la division synthétique pour avoir les autres facteurs. Si on divise la fonction f(x) par (x - 7), on obtient:

x^2 - 4x + 25

Du coup peut dire que :

f(x) = (x - 7)(x^2 - 4x + 25)

Le terme quadratique, x^2 - 4x + 25, n’a pas de racines réelles car le discriminant est négatif. Par conséquent, nous pouvons écrire la factorisation de f(x) en termes de nombres complexes comme:

f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)

la factorisation complète de f(x) est:

f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)

The solution is the factor 4y - 6x:. 2(2y - 3x) = 2(2y - 3x). 8 = 2• 4 =. 2(2y - 3x)

8. 2• 4

cancel the common factor: 2

= 2y - 3x. the answer is 2y - 3x

4 4

1. Ben's mistake in solving the area of circle is, he has taken the value of diameter at the place of radius in formula.

2. Luna's mistake is, he did the incorrect squaring of radius 4.5.

The formula makes use of the diameter. The units are squared at all times. When the diameter is known, the area can be calculated by first determining the radius. The radius of the circle is the area. You can use circumference to determine area.

area of circle A =  πr²

where, π = 3.14 and r is the radius of circle

r = diameter /2 = 9/2 = 4.5 cm

A = πr²

A = 3.14*(4.5)²

A = 3.14*20.25

A = 63.585 cm² (correct area)

Thus,

1. Ben's mistake in solving the area of circle is, he has taken the value of diameter at the place of radius in formula.

2. Luna's mistake is, he did the incorrect squaring of radius 4.5.

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Meg has 12 different options to choose from when it comes to buying a new pair of skates based on combinations.

Meg has three options to choose from - roller skates, figure skates, and hockey skates, and four options for the color of her skates - black, white, blue, and silver. To find the total number of different combinations, we have to multiply the number of options for each category.

Total number of combinations of skates that Meg can choose from is:

3 (types of skates) x 4 (colors of skates) = 12

Meg has 12 different options to choose from when it comes to buying a new pair of skates.

It is important to note that this calculation assumes that Meg can choose any combination of skate type and color. If certain types of skates only come in certain colors, or if certain colors are only available for certain types of skates, then the number of possible combinations will be less than 12. Additionally, other factors such as size and brand of the skates may also affect the total number of options available to Meg.

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Answer:

48

Step-by-step explanation:

first multiply 60 by 0.80 the decimal version of the percentage then you get 48.00 or 48 as your anser

Answer:

To subtract −5x² − 9x − 5 from 4x² − 5x + 3, we need to subtract the coefficients of each term with the same degree.

(4x² - 5x + 3) - (-5x² - 9x - 5)

4x² - 5x + 3 + 5x² + 9x + 5

9x² + 4x + 8

To subtract -5x² - 9x - 5 from 4x² - 5x + 3, you subtract each corresponding term, which results in 9x² + 4x + 8.

If you would like to subtract -5x² - 9x - 5 from 4x² - 5x + 3, you need to subtract every term separately. So, the steps will look like the following:

So, 4x² - 5x + 3 - (-5x² - 9x - 5) = 9x² + 4x + 8.

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Step-by-step explanation:

We can simplify each equation to determine which one is true:

61 x 5 = 305

10381 x 27 = 279,387

1143 ÷ 9854 x 63 = 0.00736 x 63 = 0.46368

562 x 42 = 23,604

Therefore, the only equation that is true is 562 x 42 = 23,604.

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

Answer:  Option A, [tex]\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}[/tex]

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

Given:  [tex]\textsf{3a + 5 and 2a}^2\textsf{ + 4a - 2}[/tex]

Find:  [tex]\textsf{The product of the two given equations}[/tex]

Solution: The first step toward solving this problem would be to distribute the 3a and 5 to each of the values in the second equation.

After doing so, we can simplify each of the expressions until we have one equation.  This can be done by both some simple algebra and combining of like terms.

Therefore, the correct answer to this question is Option A, [tex]\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}[/tex].

The interval estimate for the population mean, μ, is 65 ± 3.38 mph, or 61.62 to 68.38 mph.

The z-value for a 96.6% confidence level is 2.58. This value is used to determine the margin of error for a sample mean in a population. The formula for margin of error is ME = z*σ/√n, where σ is the population standard deviation, n is the sample size, and z is the z-value for the desired confidence level. In this case, ME = 2.58*22/√121 = 3.38 mph.Therefore, the interval estimate for the population mean, μ, is 65 ± 3.38 mph, or 61.62 to 68.38 mph.

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Using the trigonometric Identities, [tex]tan(A - B) =\frac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given

[tex]sin(A) =\dfrac{5}{13}[/tex]

[tex]\dfrac{\pi }{2} < A < \pi[/tex]

Using the trigonometric identity

[tex]sin^2A+cos^2A=1[/tex]

[tex]cosA =\sqrt{1-sin^2A}[/tex]

[tex]cosA =\sqrt{1-(\dfrac{5}{13})^2 }[/tex]

[tex]cosA =-\dfrac{12}{13}[/tex]

[tex]tanA=\dfrac{sinA}{cosA}[/tex]

[tex]tanA =\dfrac{\frac{5}{13} }{\frac{-12}{13} }[/tex]

[tex]tanA =-\dfrac{5}{12}[/tex]

[tex]tan(A-B) =\dfrac{tanA-tanB}{1+tanAtanB}[/tex]

[tex]=\dfrac{-\frac{5}{12}-(-\sqrt{13}}{1+(-\frac{5}{12})(-\sqrt{3}) }[/tex]

[tex]=\dfrac{5-12\sqrt{13}}{-12-5\sqrt{3} }[/tex]

[tex]=\dfrac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]

Option D is correct.

Hence, [tex]tan(A - B) =\dfrac{-5+12\sqrt{13} }{12+5\sqrt{13} }[/tex]

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According to the question the area of the triangle with sides of 10, 9, and 6 is 45.

Area is a term used to describe the size of a two-dimensional space. It is a measure of how much surface is contained within a two-dimensional boundary. It is usually expressed in units of square meters, square kilometers, square feet, or square miles. Area can also be used to describe the size of a three-dimensional space, such as for a volume. In this case, area is expressed in units of cubic meters, cubic feet, or cubic miles. Area is an important concept in mathematics and is used to calculate the area of shapes, such as triangles and circles, as well as to solve problems related to probability, motion, and other topics. Area is also used in physics to calculate the amount of force that an object exerts on another object.

The area of a triangle can be calculated using the formula A = 1/2 * b * h, where b is the base of the triangle and h is the height of the triangle.
Using this formula, the area of a triangle with a base of 10 and a height of 9 would be A = 1/2 * 10 * 9 = 45.
Therefore, the area of the triangle with sides of 10, 9, and 6 is 45.

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The area of the triangle with sides of lengths 10, 9, and 6 is approximately 37 square units.

What is the Pythagorean theorem?

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To find the area of a triangle, we can use the formula:

Area = 1/2 * base * height

In this case, we need to identify the base and height of the triangle.

The longest side of the triangle is 10, which is opposite to the largest angle, so we can take that as the base. Let's call it b.

To find the height, we need to draw an altitude from the vertex opposite the base. Let's call the height h.

Now, we can use the Pythagorean theorem to find the height:

h^2 = 10^2 - (9^2 + 6^2)/2^2

h^2 = 100 - 45.25

h^2 = 54.75

h = sqrt(54.75)

h = 7.4 (rounded to one decimal place)

Now that we have the base and height, we can use the formula to find the area:

Area = 1/2 * base * height

Area = 1/2 * 10 * 7.4

Area = 37 square units (rounded to the nearest whole number)

Therefore, the area of the triangle with sides of length 10, 9, and 6 is approximately 37 square units.

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The probability that the next 4 science fair winners will all be seventh grade students is approximately 0.316

Assuming that the probability of winning the science fair is independent of grade level, the probability of a seventh grade student winning the science fair is 12/16 or 3/4, and the probability of a student of any other grade level winning is 1/4.

If Mona placed 3 red marbles (representing seventh grade winners) and 1 green marble (representing winners from other grade levels) in the bag, then the probability of drawing a red marble (representing a seventh grade winner) is 3/4, and the probability of drawing a green marble (representing a winner from another grade level) is 1/4.

Since the events of each science fair winner are independent, we can apply the multiplication rule of probability to determine the probability that the next 4 winners will all be seventh grade students

P(4 seventh grade winners) = (3/4)^4 = 81/256 or approximately 0.316.

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Answer:

Step-by-step explanation:

We can solve the equation 4x+2 = 12 for x using the change of base formula by isolating x on one side of the equation:

4x + 2 = 12

Subtracting 2 from both sides:

4x = 10

Dividing both sides by 4:

x = 2.5

We do not need to use the change of base formula to solve this equation as it is a simple linear equation that can be solved by basic algebraic manipulations. Therefore, none of the given options are correct.

Check the picture below.

so the cars are 276 miles apart, let's say the southbound car is going "r" mph fast, that means the northbound car is going "r + 12" mph fast as you see in the picture, so at some time they meet, hmmm wait, we know they're 3 hours apart from passing each other, so that means by the time they meet, 3 hours have passed, so by the time that happens, the northbound car has been traveling for 3 hours and the southbound car has been traveling for 3 hours as well.

Since we know they're 276 miles apart, let's say by the time they meet the southbound car has covered "d" miles, so the northbound car has covered the slack then, that is "276 - d" miles.

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Southbound&d&r&3\\ Northbound&276-d&r+12&3 \end{array}\hspace{5em} \begin{cases} d=(r)(3)\\\\ 276-d=(r+12)(3) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{d=3r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{276-(3r)~~ = ~~3(r+12)} \\\\\\ 276-3r=3r+36\implies 240-3r=3r\implies 240=6r \\\\\\ \cfrac{240}{6}=r\implies \stackrel{ Southbound~car }{40=r}\hspace{5em}\underset{ Northbound~car }{\stackrel{ 40~~ + ~~12 }{\text{\LARGE 52}}}[/tex]

Therefore, the result of (u*v)v is a vector with components (80, -16).

In mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are used to represent physical quantities such as force, velocity, and acceleration, as well as abstract mathematical quantities such as points, lines, and planes. A vector is usually represented geometrically as an arrow in a coordinate system, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can be added, subtracted, and multiplied by scalars, and these operations follow specific rules that make them a powerful tool for solving problems in mathematics, physics, engineering, and other fields. Vectors can have any number of dimensions, but in two-dimensional space, a vector can be represented as an ordered pair of numbers (x, y), where x and y represent the horizontal and vertical components of the vector, respectively. In three-dimensional space, a vector can be represented as an ordered triplet of numbers (x, y, z), and so on for higher dimensions.

Here,

To find (u*v)v, we first need to find the dot product of u and v, which is defined as:

u · v = (4, 4) · (-5, 1)

= (4 × -5) + (4 × 1)

= -20 + 4

= -16

Next, we need to multiply the dot product of u and v by v:

(u*v)v = (-16)(-5, 1)

= (80, -16)

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Answer:

Step-by-step explanation:

[tex]\sqrt{87x} =\sqrt{29\times3\times x}[/tex]

When [tex]x=21[/tex] we get:

    [tex]\sqrt{87x} =\sqrt{29\times3\times 21}[/tex]

              [tex]=\sqrt{29\times3\times3\times7}[/tex]

              [tex]=3\sqrt{29\times7}[/tex]

               [tex]=3\sqrt{203}[/tex]

So when [tex]x=21[/tex] we can simplify [tex]\sqrt{87x}[/tex].

The area of the circle is 63.585 sq. cm.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area. Each shape's area may be calculated by counting how many unit squares will fit inside of it.

Given that the diameter of the circle is 9 cm

The radius = 9/2 = 4.5 cm

The area of the circle is:

A = πr²

Substitute the values:

A = (3.14)(4.5)²

A = 63.585 sq. cm.

Hence, the area of the circle is 63.585 sq. cm.

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The complete question is:

The perimeter of ABCDEFGH is 8s, with s = 3, so the perimeter of ABCDEFGH is 8x3 = 24 units.

The perimeter of a regular octagon can be calculated using the formula P = 8s, where s is the length of each side. To solve for the perimeter of ABCDEFGH, we need to first calculate the length of each side.We can use the distance formula to calculate the length of AH. The distance formula is [tex]d = √((x2-x1)^2 + (y2-y1)^2).[/tex] In this case, x1 = 4, y1 = 5, x2 = 7, and y2 = 5. Plugging these values into the formula, we get [tex]d = √((7-4)^2 + (5-5)^2) = √(3^2 + 0) = √9 = 3[/tex] units.Since each side of a regular octagon is equal, we can use the length of AH, 3 units, to calculate the perimeter of the octagon. The perimeter of ABCDEFGH is 8s, with s = 3, so the perimeter of ABCDEFGH is 8x3 = 24 units.

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Answer:

Step-by-step explanation:

I’m not good at explaining but basically if you do 20n - 15n it would be 5n

The system of inequalities that represents Irene's constraints is:

c + v ≥ 25 (She needs to make at least 25 dinners) 8.75c + 5.50v ≤ 250.

The problem presents two types of dinners: chicken and vegetarian. Irene needs to make at least 25 dinners, so the total number of dinners must be greater than or equal to 25. The cost of chicken dinners and vegetarian dinners is also given, along with the total budget of $250. These constraints can be translated into mathematical inequalities using variables c and v to represent the number of chicken and vegetarian dinners, respectively.

The first inequality represents the constraint that the total number of dinners must be greater than or equal to 25:

c + v ≥ 25

The second inequality represents the constraint that the cost of the dinners cannot exceed the total budget of $250:

8.75c + 5.50v ≤ 250

Together, these two inequalities form a system of inequalities that represents Irene's constraints. The solution to this system will give the possible values of c and v that satisfy both constraints.

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In conclusion there are 33 ways to distribute seven identical balls into three distinct boxes so that each box contains at least one ball.

How to solve?

This is a combinatorics problem known as distributing identical objects into distinct boxes with the condition that each box has at least one object.

There are three such cases: when the first box is empty, when the second box is empty, and when the third box is empty. Each of these cases can be represented by a single bar that is placed at the beginning or end of the line of stars. For example, the case where the first box is empty can be represented as:

|****|

There are three ways to place this single bar, so we need to subtract three from our previous count of 36 to get the final answer:

36 - 3 = 33

Therefore, there are 33 ways to distribute seven identical balls into three distinct boxes so that each box contains at least one ball.

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Part a: Model for m∠A : cos A = 200/d.

Part b: If d = 300 m,  m∠A = 48.19°.

Part c: If d = 550 m, m∠A =  68.67° .

The trigonometric functions sine, cosine, tangent, and its inverses make up these trigonometric ratios.

Given an angle measurement, so every function represents a distinct ratio in either a right triangle. Trigonometric ratios are the ratios of a right triangle's sides to one of the triangle's non-right angles. Remember that a right triangle has one right angle that is always 90 degrees in length.

In the given query:

Base  = 200 m.

Hypotenuse = d m.

Part a: Model for m∠A :

cos A = Base/ Hypotenuse

cos A = 200/d.

Thus, Model for m∠A : cos A = 200/d.

Part b: If d = 300 m,  m∠A = ?

cos A = 200/d.

cos A = 200/300

cos A = 2/3

m∠A =  48.19°

Part c: If d = 550 m, m∠A = ?

cos A = 200/d.

cos A = 200/550

cos A = 4/11

m∠A = 68.67°

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The amount of paint needed in cubic centimeters to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 30 meters is 1.413737 × 10¹⁰ cm³.

To estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 30 meters, we will use linear approximation.

The volume of a hemisphere with a diameter of 30 meters is given by:

V = (2/3)πr³Where r = 30/2 = 15 meters

We need to find the amount of paint required for a thickness of 0.03 cm.

We convert this to meters as:

0.03 cm = 0.0003 m

The linear approximation formula is given by:

ΔV ≈ dV/dx × Δx

where Δx = 0.0003 is the change in thickness, and

dV/dx is the rate of change of the volume with respect to thickness x.

We have:

V = (2/3)πr³ = (2/3)π(15)³ = 14137.2 m³

dV/dx = 4πr² = 1800π m²

Now, we can estimate the change in volume:

ΔV ≈ dV/dx × Δx = 1800π × 0.0003 = 0.1696 m³

The total amount of paint needed is:

V + ΔV = 14137.2 + 0.1696 = 14137.37 m³

We can convert this to cubic centimeters as:

1 m³ = 10⁶ cm³

So, the amount of paint needed in cubic centimeters is:

V = 14137.37 * 10⁶ cm³ = 1.413737 × 10¹⁰ cm³

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Answer:

Given :

By selling an article for rupees 144, a man loses 17

of his outlay. It is sold for rupees 189.

To do :

We have to find the gain or loss percent.

Solution :

Let the cost price of article be Rs. x

.

This implies,

SP =CP −Loss

=x−x7

=6x7

Therefore,

6x7=144

x=144×76

x=Rs. 168

If the article is sold for Rs. 189, then,

SP =Rs. 189

Profit =

SP − CP

=189−168

=Rs. 21

Gain %=GainCP×100%

=21168×100%

=12.5%

The gain percent is 12.5%

.

Step-by-step explanation:

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Answer:

Step-by-step explanation:

A) 6 inches. ( if the equation for the area of a triangle is

The answer of the given question based on the finding the area of rectangle is  QRST is approximately 116.56 square units.

Area is a measure of the size or extent of a two-dimensional surface, like a shape or a region on a flat surface. It is typically measured in square units, like square meters (m²), square feet (ft²), or square centimeters (cm²).

To calculate the area of a shape, you need to know its dimensions and shape. The formula for finding the area of a shape depends on its shape. Area is an important concept in mathematics and geometry, and it is used in many real-life applications, such as measuring the size of land, determining the amount of material needed for a project, and calculating the volume of a container or room.

To find the area of the rectangle, we can use the distance formula to find the lengths of its sides. Then, we can use the formula for the area of a rectangle, which is the product of its length and width.

Length QR = √[(6 - (-4))² + (3 - (-3))²] = √[10² + 6²] = √(136)

Length ST = √[(9 - (-1))² + (-2 - (-8))²] = √[10² + 6²] = √(136)

Width QS = √[(6 - (-1))² + (3 - (-8))²] = √[7² + 11²] = √(170)

Width RT = √[(-4 - 9)² + (-3 - (-2))²] = √[13² + 1] = √(170)

Therefore, the area of the rectangle is:

Area = Length x Width = √(136) x √(170) = 116.56 (rounded to two decimal places)

So, the area of the rectangle QRST is approximately 116.56 square units.

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The volume of the cone with radius as 9 inches and height as 11 inches is 933 cubic inches.

The formula for the volume of a cone is the product of the following multiplication, given as V = π×r²×h/3.

In this formula, π is the pie or 22/7, r is the radius, and h is the height.

The radius of the base of cone, r = 9 inches

The height of the cone, h = 11 inches

π = 22/7

The volume of the cone = πr²h/3 cubic units.

= 22/7 x 9 x 9 x 11/3

= 22/7 x 81 x 3.667

= 933 cubic inches

= 933 in³

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It will take 5.71 hours for Pam and Erin to be 14 miles apart.

If Pam and Erin start at the same point and rollerblade in different directions, then the total distance between them at any given time can be represented by the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Let x represent the number of hours it takes for Pam and Erin to be 14 miles apart. Then, the distance traveled by Pam will be 2x, and the distance traveled by Erin will be 4x.

Using the Pythagorean Theorem, the equation that represents the distance between them can be written as 2x^2 + 4x^2 = 14^2.

Solving this equation, we get 6x^2 = 196, which can be written as x^2 = 32.75. Taking the square root of both sides, we get x = 5.71.

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Answer:

ANSWER IS PROVIDED BELOW

hope this helps and good luck on your assignment