Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?

Answer:

[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]

[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]

Step-by-step explanation:

we want to figure out the domain of the following function:

[tex] \displaystyle g(a) = \sqrt{1 + {a}^{2} } [/tex]

remember that, the domain of an even root function are all values of x for which the redicand is positive or 0 that is being said the domain of the function g(a) belong to [tex]\mathbb{R}[/tex] . another way to think about it, the domain of square root function f(x) belong to x≥0. In this case we have square variable in the redical so when we input a negative number, it yields a positive number with that said the domain of the function g(a) belong to all the real numbers.Thus,

[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]

we'd like to find the domain of the following function:

[tex] \displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]

in order to do so we need to simplify it further,so simplify addition in order to do so the first step is to figure out the LCM of the denominator i.e x(x+1) ⇒ x²+x, secondly divide the denominator of every fraction by the LCM and multiply the result by the numerator of very fraction ,then finally add them therefore,

[tex] \displaystyle f(x)=\frac{2x + 2+4x}{ {x}^{2} + x } \\ \displaystyle \boxed{\frac{6x + 2}{ {x}^{2} + x }} [/tex]

we know that the domain of a rational function are all the values of x for which the denominator is different than 0.

the denominator of the function would be 0 when x=0 and -1 thus,

[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]

and we're done!

By the chain rule, if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then

[tex]\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

We have [tex]f(x,y)=(x+y)e^y[/tex], for which

• [tex]\dfrac{\partial f}{\partial x} = e^y[/tex]

• [tex]\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y[/tex]

and [tex]x(t)=5t[/tex] and [tex]y(t)=1-t^2[/tex], so that

• [tex]\dfrac{\mathrm dx}{\mathrm dt} = 5[/tex]

• [tex]\dfrac{\mathrm dy}{\mathrm dt} = -2t[/tex]

Putting everything together, we get

[tex]\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}[/tex]

The solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].

The chain rule explains how to calculate a composite function's derivative.

If you may write [tex]f(g(x))[/tex] , a function is composite. It's a function within a function, or a function of a function, in other words.

By the chain rule, we can write if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then,

[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]

As it is given to us, [tex]f(x,y)=(x+y)e^y[/tex], therefore, we can write,

And x(t)=5t, while y(t)=1-t², So,

Now, Substitute all the values together, in the equation,

[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]

Substituting the values we will get,

[tex]\dfrac{dz}{dt} &=(5 \times e^y)+[-2t(x+y+1)e^y]\\\\[/tex]

     [tex]=5e^{1-t^2}-2t(5t-t^2+2)e^{1-t^2}\\\\=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex]

Hence, the solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].

Learn more about Chain Rule:

https://brainly.com/question/2285262

Answer:

2.2 % per minute

35 minutes

Step-by-step explanation:

(0,23%) and (30, 89%)

We can find the slope

m = ( y2-y1)/(x2-x1)

    = (89-23)/(30-0)

   66/30

   =2.2 % per minute

To get to full change we need 100-23 = 77 %

77% * 1 minute/ 2.2 % =35 minutes

Answer:

Baton Rouge is 19 meters higher that New Orleans.

Answer:

0.04

Step-by-step explanation:

first we change 1/5 into a decimal which is 0.2

the we just multiply it by itself which is

0.04

Answer:

D.

Step-by-step explanation:

Mean : 7 + 5 + 6 + 4 + 7 + 8 + 12 = 12 + 10 + 7 + 20 = 30 + 19 = 49. 49/7= 7

Mode : 7.

Median 4 , 4, 6, 7, 7, 8, 12.    7 is the middle number

There are not just "the two ways" to represent this expression. There are two ways, surely, but they are not the only ways as implied.

You could expose 4 and get something like [tex]4(\frac{3}{4}-n)[/tex] or expose 3 and get something like [tex]3(1-\frac{4}{3}n)[/tex].

But you could also say something like [tex]3-(1+3)n=3-n-3n=-3(n-1)-n[/tex]... in fact there are a lot of ways to write any expression.

Hope this helps :)

Answer:

1/3

Step-by-step explanation:

Answer:

x = - 6, y = - 29

Step-by-step explanation:

Elimination:

2*(-5x + y = 1) = -10x + 2y = 2

9x - 2y = 4 = + (9x - 2y = 4) =

-x = 6

x = -6

9(-6)-2y=4

-54-2y=4

-2y=58

y=-29

Answer:

0.300 + 0.030 + 0.004

or

0.100 x 3  +  0.01 x 3  +  0.001 x 4

Answer:

the answer is-2p-3

hope is helpful

Answer:

2p – 10 – 4p –7

–2p –17

I hope I helped you^_^

Answer:

let side be t

t + x + y +x + y = 4x + 3y

t + 2x + 2y = 4x + 3y

t = 2x +y

so missing side length is 2x + y

Answer:

[tex] \frac{85}{9} [/tex]

Step-by-step explanation:

hopefully the picture is clear and understandable!

:)

Answer:

The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p = s + dgh,

9514 1404 393

Answer:

  A. 32

Step-by-step explanation:

The relationship between segment lengths is ...

  WT·WU = WC·WV

  14(2x +2) = 12(2x +5)

  28x +28 = 24x +60

  4x = 32

  2x = 16

Then the measure we're after is ...

  UT = WT +WU = 14 +(16 +2)

  UT = 32

Answer:

Here is the answer . hope this helps.

Answer:

Step-by-step explanation:

In such cases use the vertical line test. If the graph is intersected at more than one point, it is not  a function.

Both the given graphs represent a function as both pass the vertical line test.

Answer:

Yes

Step-by-step explanation:

Whenever you are given a problem that's asking to see if a graph is a function or not, always use the vetical line test to determine that. In short, you draw a line accross each y axis point and if the line only goes accross one point throughout the graph then it's a function. Following the test we will see that both graphs are indeed functions.

Best of Luck!

Answer:

you could have a 6 and then a -6

or a 3 and a -3

or 0 and 0

have 2 cards with the same number but one is negative

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

$230 + $360 = $590

$590 - $253* = $337

$337

*( total sum of all the bills )

Answer:

x< -4/1 or x > 6/5

If our answers are different, just say so :)

Answer:

47

Step-by-step explanation:

x is one of the three angles of a triangle. The other two are given as 95 and 38.

Together all three have to make 180 degrees.

x + 95 + 38 = 180

x + 133 = 180

x = 180 - 133

x = 47

Answer:

47

Step-by-step explanation:

as we know that sum of a triangle is always=180°

so x+38°+95°=180

so x+133=180

and x=180-133

so x= 47

Answer:

troop number and activity preference or b

Step-by-step explanation:

Answer:

Formula = base x height

10 x 4 = 40

Area = 40cm

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

so 2x1=2 so -2x-1=2

if its wrong i dont now cause im silly

she share it to thirty seven people

Answer:

2nd option is correct

∠AEF and ∠FED , ∠AEG and ∠CEG

Step-by-step explanation:

1st option is a supplementary and even 3rd and 4th options

The dimensions of the rectangle will be 3 cm. and 16 cm..

Solution:

First, calculating the area of the rectangle, based on these dimensions,

Formula for the area of a rectangle:

A=LW

A=(3)(16), or A=(16)(3)

A=48 cm²✔

So, now we know that these dimensions satisfy the area of the rectangle, but do they satisfy the perimeter of the rectangle?

Now, calculating the perimeter of the rectangle, based on these dimensions,

Formula for the perimeter of a rectangle:

P=2(L+W)

P=2(3+16), or 2(16+3)

P=2(19)

P=38 cm ✔

Now, we know that both of these dimensions satisfy both of the given conditions. So, the final answer is that the two dimensions of the rectangle are 3 cm. and 16 cm.. I hope that this answer helped you find what you were looking for. Enjoy your day, and take care.

Answer:

the slope is -2/1

You can find it by using the equation [tex]\frac{y_{1}- y_{2} }{x_{1}- x_{2} }[/tex]

so 3-1/1-2= 2/-1, which is also written as -2/1

Answer:

m=79

t=54

Step-by-step explanation:

yes these are the answers

Answer:

angle  t =  54 degrees

angle m=79(alternate angles)

Step-by-step explanation:

angle p=126 degrees

angle z=79 degrees

angle p + angle t=180(allied angles)

      126 + t           =180

                t           =180-126

                        t =  54 degrees

u=79(vertically opposite angles)

therefore;

    angle m=79(alternate angles)