Felicia is a long-distance runner. She is able to run the first 2 hours of a training run at a certain rate. The rate at which she runs after her first 2 hours decreases for the remainder of her training run. On Monday, Felicia runs x hours, where x≥2. The average rate at which Felicia runs for the entire training run is represented by 13+6(x−2)x. What is the meaning of the parts of this rational expression in the context of the situation? Select from the drop-down menus to correctly complete each statement.

Answer:

domain will be ( -∞, ∞)

Step-by-step explanation:

The given functions are f(x) = x² - 1 and g(x) = 2x - 3

We have to find domain of (fog)(x)

We will find the function (fg)(x) first.

(fog)(x) = f[g(x)]

         = (2x - 3)²

         = 4x² + 9 - 12x - 1

        = 4x² - 12x + 8

       = 4 (x² - 3x + 2)

The given function is defined for all values of x.

Therefore, domain will be ( -∞, ∞)

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a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

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Answer:

No. The correct answer would be C.

Step-by-step explanation:

AAS: The side cannot be in between the two angles.

ASA: The side is in between the two angles.

Answer:

3

Step-by-step explanation:

The pattern is dividing 4 each time.

192/4=48

48/4=12

12/4=3

Hope this helps! Plz give brainliest!

Answer:

-4

Step-by-step explanation:

That's the answer above

Answer:

(y-7) +25

Step-by-step explanation:

( y-7 ) +25

25 is added after the difference. so that's only the answer.

Answer:

x = 1

y = 30°

Step-by-step explanation:

is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':

20x-3 = 5x+12

15x = 15

x = 1

we also know that RS intersecting with TU creates a 90° angle

if 3y = 90 then y = 30

Answer:

A’ (6, -4)

B’ (-2, -1)

C’ (-5, 0)

Step-by-step explanation:

When reflecting anything across the x, the x values stay the same and the y values become opposites. When reflecting anything across the y, the x values become the opposites and the y values stay the same.

The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Reflection is the flipping of a figure. If a point A(x, y) is reflected across the y axis, the new point is at A'(x, -y). Given the vertices of the triangle at A(6,4), B(-2,1) and C(5,0).

The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).

Find out more on reflection at: https://brainly.com/question/14062035

y= -4x-5 you can find this by seeing how far it goes up/down and where it starts:)

Answer:

B and A

Step-by-step explanation:

What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).

The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…

I hope this helps :)!

Answer:

3/4 or 0.75

Step-by-step explanation:

When dividing- quotient- fractions, remember keep, change, flip

Keep- keep the first fraction

Change- change the division sign into a multiplication sign

Flip- flip the second fraction

So your problem really is:

[tex]\frac{1}{6} *\frac{9}{2}[/tex]

Which is: 9/12 or 3/4

we have that

Y - 5 = 0.5x2 + 6x - 3--------------- > y=0.5x2 + 6x -3+5=0.5x2 + 6x+2

y=0.5x2 + 6x +2

using a graphic tool

see the attached figure

the graph have two x-intercepts----------> (-11.657,0) and (0.343,0)

Answer:

4.6 feet (explanation of division)

Answer:

The length of each piece is 4.6 feet

Step-by-step explanation:

Answer:

25.5

Step-by-step explanation:

There are 12 inches in a foot and therefore...

306/12=25.5

306 inches is 25.5 feet

Answer:

Point B is

Step-by-step explanation:

Answer:

B (-2,-4)

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

The remainder of the equation is [tex]\rm x+1[/tex].

Given that,

When the equation is [tex]x^3+1[/tex]  divided by [tex]x^2-x+1[/tex].

We have to determine,

The remainder for the equation?

According to the question,

The equation [tex]x^3+1[/tex] is divided by [tex]x^2-x+1[/tex].

On the division of the polynomial, the remainder is,

[tex]\dfrac{\rm x^3+1}{x^2-x+1}[/tex]

Factorize the equation to convert this into the simplest form,

[tex]\rm = x^3+1\\\\=x^3-x^2+x + x^2-x+1\\\\= x ( x^2-x+1) + 1(x^2-x+1)\\\\= (x+1) (x^2-x+1)[/tex]

Now, the equation can be written as,

[tex]\rm = \dfrac{(x+1) (x^2-x+1) }{ x^2-x+1}\\\\= x+1[/tex]

Hence, The required remainder of the equation is [tex]\rm x+1[/tex].

For more details refer to the link given below.

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Answer: a

Step-by-step explanation:

on edge

The number of books the library holds before it received the grant is 17,312 books

Let the original number of books in the library be x

If the collection  now is five times more than the original number of books, then;

x + 69,248 = 5x

5x - x = 69,248

4x = 69,248

x = 69,248 /4

x = 17,312

Hence the number of books the library holds before it received the grant is 17,312 books

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Answer:

[tex]\sqrt{49 - x^{2}}[/tex]

Step-by-step explanation:

Pythagorean theorem  [tex]c^{2} = a^{2} + b^{2}[/tex] Then:

[tex]7^{2} = x^{2} + y^{2}\\y^{2} = 7^{2} - x^{2}\\y^{2} = 49 - x^{2}\\y = \sqrt{49 - x^{2}}[/tex]

the lenght of the third side = [tex]\sqrt{49 - x^{2}}[/tex]

Ф = [tex]sin^{-1} (\frac{x}{7} )[/tex]

Ф = [tex]cos^{-1} (\frac{y}{7} )[/tex]

Ф = [tex]tan^{-1} (\frac{x}{y} )[/tex]

Answer:

Step-by-step explanation:

Answer:

Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)

Answer:  Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size.

Step-by-step explanation: pls give brainlist

Answer:

C

Step-by-step explanation:

It does what the equation says. It multiplies x by 36

I hope this helps!

Answer:

true

Step-by-step explanation:

the less than or equal to sign (≤) means that -4 is a solution. if it was the less than sign (<) then -4 would not be included

Answer:

i believe it would be true

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Answer:

That is the answer

The answer is

Answer:3,312.50

Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 2500 is 100%, so we can write it down as 2500=100%.

4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.

5. Now we have two simple equations:

1) 2500=100%

2) x=3.25%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

2500/x=100%/3.25%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

The y intercept is the y value when x is 0 which is shown on the graph as (0,4) making the y intercept is 4

The next point given is (1,8) which shows for every 1 increase in x (1-0 = 1) the y value increases by a multiple of 2 (4 x2 = 8)

The equation would be f(x) = 4 * (2)^x

The answer is B

Answer:

question 3 is $9.99

question 4 I believe is the third option