Perform the indicated operation and simplify the result. Leave your answer in factored form.

[tex]\frac{5x+20}{8x^{5} }[/tex]·[tex]\frac{x}{x^{2} -16}[/tex]

Answer:

B.

Step-by-step explanation:

any arithmetic operation with functions just means to do this operation with the functional expressions.

f/g is really just the expression of f divided by the expression of g.

so, this results in a fraction with the denominator (bottom part) = 2x + 1

as you know, a division by 0 is not a valid operation, and therefore we have to forbid any value for x that would create a 0 in the denominator.

so, for what x do we get

2x + 1 = 0

2x = -1

x = -1/2

therefore, we have to exclude x = -1/2.

The image of triangle DEF after the dilation with a scale factor of -1/2  is given at the end of the answer.

Transformations in the graph of a function involve operations in the vertices of the image, such as addition, subtraction, division or multiplication.

The transformation used in this problem is a dilation, in which the coordinates of the vertices of the original figure are multiplied by the scale factor.

For this problem, the vertices of the triangle are given as follows:

D(3,6), E(3,2) and F(5,4).

The dilation has a scale factor of -0.5 = -1/2, hence the coordinates of the image are given as follows:

The dilated triangle is given by the graph at the end of this answer.

More can be learned about transformations such as dilation at https://brainly.com/question/28687396

#SPJ1

The length of the pen is 2√3 feet

The formula for calculating the area of a rectangle is expressed according to the formula below:

Area of a right triangle = 1/2 * base * height

A = 1/2 bh

Given the following parameters

Area = 20 square feet

If the height is five times the length, then;

h = 5b

Substitute

A = 1/2 bh

A = 1/2(b)5b

30 = 1/2(5b²)

60 =5b²

b² = 12

b = 2√3

Hence the length of the pen is 2√3 feet

Learn more on area of triangle here: https://brainly.com/question/17335144

#SPJ1

The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27.

Interest is the sum of money paid for using someone else's funds. You must pay interest when you borrow money from lenders. You receive interest when you lend money to borrowers. It could be stated in terms of money or the rate of payment. You will learn more about interest in this article, including the different sorts of interest, what they are, and how to determine how much interest will be charged on a loan or a loan amount.

Given that,

At the beginning of each of her four years in college

Miranda took out a new Stafford loan.

Each loan had a principal of $5,500,

An interest rate of 7.5% compounded monthly

A duration of ten years.

Miranda paid off each loan by making constant monthly payments, starting with when she graduated.

All of the loans were subsidized.

The total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27

Therefore, the total lifetime cost for Miranda to pay off her 4 loans is: $31,337.27

To know more about interest visit:

https://brainly.com/question/13324776

#SPJ9

Answer: D 31,337.27

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

1 kilogram of soil will fill:

1/3 ÷ 2/5 = 5/6 (of a container)

Because 5/6 < 1

=> 1 kilogram of soil will fit in the container

The  average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.

a. Average:

Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91

Average=70.35÷0.91

Average=77.31%

b. Average

Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91

Average=66.64÷0.91

Average=73.23%

Therefore the average for both a and b is 77.31% and 73.23%.

Learn more about average here:https://brainly.com/question/20118982

#SPJ1

Answer:

For the 60-30-90 degree triangle:

x=12

y=[tex]12\sqrt{3}[/tex]

For the 30-60-90 degree triangle:

x=16

y=[tex]8\sqrt{3}[/tex]

For the 45-45-90 degree triangle:

x=7

y=[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

For 30-60-90 triangles, the side opposite the 30 degree angle is x, while the side opposite the hypotenuse is 2x, while the side opposite the 60 degree angle is [tex]x\sqrt{3}[/tex].

For 45-45-90 triangles, the sides opposite the 45 degree angles are x, while the hypotenuse is [tex]x\sqrt{2}[/tex].

Answer:

Yes it is a function

Step-by-step explanation:

There is a relationship between x and y. It is not linear but quadratic

Answer:

yes it is a function

Step-by-step explanation:

that is the answer bc I said I was

Consider the integral

[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx[/tex]

which is the negative of yours. Bit strange to integrate over [tex](\infty,-\infty)[/tex], but if that's what you actually intended, just multiply the final result by -1. Of course, I've already canceled the superfluous factors of [tex]x^2[/tex].

Expand the integrand into partial fractions.

[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \int_{-\infty}^\infty \left(2 + \frac3{1+x^2}\right) e^{-x^2} \, dx[/tex]

Recall that for [tex]\alpha>0[/tex],

[tex]\displaystyle \int_{-\infty}^\infty e^{-\alpha x^2} \, dx = \sqrt{\frac\pi\alpha}[/tex]

Now let

[tex]\displaystyle I(a) = \int_{-\infty}^\infty \frac{e^{-ax^2}}{1+x^2} \, dx[/tex]

Together, these give

[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = 2\sqrt\pi + 3I(1)[/tex]

Differentiate [tex]I(a)[/tex] under the integral sign with respect to [tex]a[/tex] to obtain a simple linear differential equation.

[tex]\displaystyle \frac{dI}{da} = -\int_{-\infty}^\infty \frac{x^2 e^{-ax^2}}{1+x^2} \, dx \\\\ ~~~~~~~~ = - \int_{-\infty}^\infty \left(1 - \frac1{1+x^2}\right) e^{-ax^2} \, dx \\\\ ~~~~~~~~ = -\sqrt{\frac\pi a} + I(a)[/tex]

Solve for [tex]I(a)[/tex] with the initial value [tex]I(1) = \sqrt\pi[/tex]. Using an integrating factor,

[tex]\displaystyle \frac{dI}{da} - I(a) = -\sqrt{\frac\pi a} \\\\ e^{-a} \frac{dI}{da} - e^{-a} I(a) = -\sqrt{\frac\pi a}\,e^{-a} \\\\ \frac{d}{da}\left[e^{-a} I(a)\right] = -\sqrt{\frac\pi a}\,e^{-a}[/tex]

By the fundamental theorem of calculus,

[tex]\displaystyle e^{-a} I(a) = e^{-a}I(a)\bigg|_{a=0} - \sqrt\pi \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi \\\\ I(a) = \pi e^a - \sqrt\pi \, e^a \int_0^a \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]

so that

[tex]\displaystyle I(1) = \pi e - \sqrt\pi\,e \int_0^1 \frac{e^{-\xi}}{\sqrt\xi} \, d\xi[/tex]

Substitute [tex]t=\sqrt\xi[/tex].

[tex]\displaystyle I(1) = \pi e - 2\sqrt\pi\,e \int_0^1 e^{-t^2} \, dt[/tex]

Recall the error function,

[tex]\mathrm{erf}(x) = \displaystyle \frac2{\sqrt\pi} \int_0^x e^{-t^2} \, dt[/tex]

which we can use to write

[tex]I(1) = \pi e - 2\sqrt\pi e \cdot \dfrac{\sqrt\pi}2\,\mathrm{erf}(1) = \pi e - \pi e \,\mathrm{erf}(1)[/tex]

Finally, we arrive at

[tex]\displaystyle \int_{-\infty}^\infty \frac{5 + 2x^2}{1 + x^2} e^{-x^2} \, dx = \boxed{2\sqrt\pi + 3\pi e - 3\pi e \, \mathrm{erf}(1)}[/tex]

i answered this one already on your other post for it

3 is the constant/slope

5 is the y intercept

The area of the shaded triangle will be 11.5 square centimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The area of the square will be given as,

A₁ = 5 x 5

A₁ = 25

The area of the triangles will be given as,

A₂ = 1/2 (1 x 5 + 4 x 3 + 2 x 5)

A₂ = 1/2 (27)

A₂ = 27/2

Then the area of the shaded triangle will be given as,

A = A₁ - A₂

A = 25 - 27/2

A = (50 - 27) / 2

A = 23/2

A = 11.5 square cm

The area of the shaded triangle will be 11.5 square centimeters.

More about the area link is given below.

https://brainly.com/question/27683633

#SPJ1

Answer:

In the graph, excluding the shaded triangle, there are three right angled triangles surrounding the shaded triangle in a square

Area of shaded triangle = area of square - area of three triangles

The limit dimensions of the part are 3.135 inches and 3.155 inches

The given parameters are

The limit dimensions of the part are calculated as

Limit = Thickness +/- Tolerance

So, we have

Limit = 3.145 inches +/- 0.010 inches

Expand the above expression

So, we have

Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)

Evaluate the sum

Limit = (3.135 inches, 3.155 inches)

Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches

Read more about dimensions at

brainly.com/question/19819849

#SPJ1

The given system has zero solutions.

Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).

In the general equation of a line, y = mx + b, m represents the slope of the line.

The general equations of parallel lines would be of the form:

(1) y = mx + b

(2) y = mx + c

where b and c are any constants.

Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.

To learn more about parallel lines, visit:

https://brainly.com/question/16701300

#SPJ10

The unit tangent vector for the parametrized curve is [tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex].

In this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:

[tex]\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}[/tex]

Where:

First, determine the first derivative of the parametrized curve:

[tex]\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}[/tex]

Second, derive the magnitude of the parametrized curve:

[tex]\|\vec R'(t)\|[/tex] = √[(- sin t)² + (cos t)² + (cos t)²]

[tex]\|\vec R'(t)\|[/tex] = √(1 + cos² t)

Third, substitute every term in the unit tangent curve formula:

[tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex]

To learn more on parametrized curves: https://brainly.com/question/15565506

#SPJ1

Answer:

the scientific notation of 83300 is 8.33*10^4

Answer:

  C.  Multiply by 5, then subtract 7.

Step-by-step explanation:

You want to know the two steps required to solve this 2-step linear equation.

The variable x has 7 added to it, and the sum is divided by 5. To find the value of x, we must undo these operations in reverse order.

To undo division by 5, we must multiply by 5.

Then, to undo the addition of 7, we must subtract 7.

Here is the "work":

  [tex]\dfrac{x+7}{5}=10\qquad\text{given}\\\\x+7 = 50\qquad\text{multiply both sides by 5}\\\\x=43\qquad\text{subtract 7 from both sides}[/tex]

The operations in order of use are ...

  Multiply both sides by 5 first, then subtract 7 from both sides.

__

Additional comment

The properties of equality tell you that you must do the same operation to both sides of the equation.

The height of the box that has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm will be 12.5cm.

It should be noted that the formula for the volume will be:

= Length × Width × Height

Therefore the height will be:

Volume = LWH

where

L = length = 20cm

W = width = 5cm

H = height = unknown

1250 = (20 × 5 × H)

1250 = 100H

Height = 1250/100

Height = 12.5 cm

Therefore, the height is 12.5cm.

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

Answer:

Hello,

Step-by-step explanation:

[tex]3y^3+20y^2-7y=y(3y^2+20y-7)\\\\=y(3y^2+21y-y-7)\\\\=y(3y(y+7)-(y+7))\\\\=y(y+7)(3y-1)\\[/tex]

Answer:

-1.

Step-by-step explanation:

Rate of change = [ f(2) - f(-1)] / [2 - (-1)]

                          = [(2)^2 - 2(2) + 3)  - ((-1)^2  - 2(-1) + 3] / 3

                           = ( 3 - 6)/3

                            = -1.

Answer: 34.3%

Step-by-step explanation:

[tex]Given:\ 12/35\ flights\ on\ time[/tex]

To find the percent, divide then multiply by 100:

[tex]\frac{12}{35} = 0.343\times100=\large\boxed{34.3}[/tex]

Answer:

See work below.

30 sold for full price and 68 sold for a discount.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because I give him and the answer is incorrect I know but I gave him believe me

Answer: TV costs $828 and DVD player costs $414.

Step-by-step explanation: let x represent the cost of tv while y represents the cost of the player. x+y = 1242. since the tv costs twice as much as the dvd player, we can say that 2y=x. now replace x with 2y in our equation and we get 2y+y= 1242,  3y = 1242. now divide both sides by 3 and y = 414. Now that we now the value of y, just sub it into our original equation, x+y = 1242. x + 414 = 1242. x = 828.

Answer:

Step-by-step explanation: