y=6/7x+11/7 in standard form

The expression y = 4.998 · [tex]e^{1.098\cdot x}[/tex] is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).

Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:

[tex]y = A \cdot e^{B \cdot x}[/tex]

Where:

Which is equivalent to the following logarithmic expression:

㏑ y = ㏑ A + B · x

If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:

㏑ (5 / 3) = ㏑ A - B

㏑ 135 = ln A + 3 · B

Then, we solve the system by numerical methods:

㏑ A = 1.609 (A = 4.998), B = 1.098

And the exponential function is equal to y = 4.998 · [tex]e^{1.098\cdot x}[/tex].

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1. The following transactions fully comply with the revenue recognition principle of generally accepted accounting principles and should be included in the 20X5 revenue of Revgression Corporation:

(3) Goods were delivered to customers during early 20X5, ...

(4) Customers purchased goods and services during late 20X5, ...

(6) Goods were purchased and paid for by customers during 20X5, ...

2. The following transactions do not comply with the revenue recognition principle of generally accepted accounting principles and should not be included in the 20X5 revenue of Revgression Corporation:

(1) Goods were sold and shipped in late 20X5 ...

(2) Goods were produced according to ...

(5) Advance payment from a customer in...

ASC 606 of generally accepted accounting principles or IFRS 15 states that companies should recognize revenue when the service or product is delivered to the customer, not when cash is received.

Ordinarily following the five-step revenue recognition process, the goods sold and shipped in late 20X5 may be recognized in 20x5, while the installation service is recognized when completed in 20X6.

However, the contract requires substantial installation and setup services, and Revgression Corporation needs to comply before recognizing revenue.

Thus, revenue items 3, 4, and 6 should be recognized in 20X5 while revenue items 1, 2, and 5 should be recognized in 20X6.

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After using the subtraction method 49 rose bushes the workers plant today.

What do mean by the subtraction method?
A method of estimating how long a psychological process will take by measuring how long it takes to react to an activity that involves the process in question and how long it takes to react to a task that doesn't, then subtracting the second from the first.

total rose bushes are 31

total bushes to be finished in the park, 80

rose bushes planted today =(80-31)

                                             =49

Hence, the rose bushes in the worker's plant today are 49

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Answer:37

Step-by-step explanation:

Answer:

21/2 or 10.5

Step-by-step explanation:

7 = 7/1

When dividing fractions we use KFC :

K - Keep the first fraction :

7/1

F - Flip the second fraction :

2/3 ⇒ 3/2

C - Change the sign :

÷ ⇒ ×

Now we have :

7/1 × 3/2 =

Now we multiply the first numerator with the second numerator and the first denominator with the second denominator :

7×3 = 21

1×2 = 2

So our final answer is 21/2 or 10.5

Hope this helped and have a good day

According to the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ⁿ

Population function:

The term population function refers the effective population served over the course of a time

Given,

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.

Now, we need to determine the population of mosquitoes in the area at any time.

Here we have given that we have two time frames in the information given; weeks and days.

Now, we need the population after predation lets choose time in days.

And we also know that the population doubles every seven days (ignoring predation) so if P(a) is the population function we have IVP

For one week, the population function of the given situation is written as

=> dP/dt = rP

Then the value of P is P(0) = 200000

And through the given question we know that,

=> P(7) = 2P(0)

While we solving the function then we get

P = Ceⁿᵃ

When we apply the values of P(0) = 200,000 then we get the value of C = 200,000

Then, the function is rewritten as

P = 200000eⁿᵃ

Now, we have to apply the value of P(7) = 2P(0), then we get,

400000 = 200000e⁷ⁿ

When we simplify it then we get,

e⁷ⁿ = 1/2

When we apply the number of days on these function, then we can get the number of mosquitoes in the city.

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Step-by-step explanation:

Given, [tex]{ \green{ \sf{y = A {e}^{mx} + B {e}^{nx}}}} [/tex]

differentiate with respect to x

this is in the form of [tex]{ \tt{ \frac{dy}{dx} ( { {e}^{a} }^{x}) = {ae}^{ax}}} [/tex]

[tex]{ \red{ \sf{ \frac{dy}{dx} = A {me}^{mx} + B {ne}^{nx}}}} [/tex]

[tex]{ \red{ \sf{ \frac{{d}^{2} y}{d{x}^{2} } = Am.{me}^{mx} + Bn. {ne}^{nx}}}} [/tex]

[tex]{ \red{ \sf{ \frac{{d}^{2} y}{d{x}^{2} } = A {m}^{2} {e}^{mx} + B {n}^{2} {e}^{nx}}}} [/tex]

L.H.S.[tex]{ = \purple{ \sf{ \frac{ {d}^{2} y}{d {x}^{2} } - (m + n) \frac{dy}{dx} + mny}}}[/tex]

[tex]{ \purple{ \sf{A {m}^{2} {e}^{mx} + B {n}^{2} {e}^{nx} - (m + n)( A {me}^{mx} + B {ne}^{nx}) \\ \\ + mn(A {e}^{mx} + B {e}^{nx})}}}[/tex]

[tex]{ \purple{ \sf{ \cancel{A {m}^{2} {e}^{mx} }} + { \cancel{B {n}^{2} {e}^{nx} }- \cancel {A{m}^{2}{e}^{mx}}} { \cancel{-B {mne}^{nx} }} - { \cancel{A {mne}^{mx}}} - { \cancel{B{n}^2 {e}^{nx}}+{ \cancel{Amn{e}^{mx}}+{ \cancel{Bmn{e}^{nx}}}}}}}[/tex]

= 0 → R.H.S

Step-by-step explanation:

I'm assuming "A" and "B" are some constants that are coefficients as well as "m" and "n". Under this assumption we can take the derivative and then take the derivative once more to find the 2nd derivative which is denoted as: [tex]\frac{d^2y}{dx^2}[/tex]

The chain rule can be denoted as: [tex]\frac{dy}{dx}=\frac{dy}{du}*\frac{du}{dx}[/tex]

It can also be denoted in function notation as: [tex]h(x)=f(g(x)) \implies h'(x)=f'(g(x))*g'(x)[/tex]

and in general it deals with composite functions and it it's going to help us take the derivative of the exponentials.

So take for example: [tex]Ae^{mx}[/tex], we can rewrite this as a composite function where: [tex]u=mx\implies Ae^{mx}=Ae^u[/tex]

So from here we can just take the derivative of [tex]Ae^u[/tex] and then multiply it by the derivative of "u". We can also apply the same thing to [tex]Be^{nx}[/tex]

So let's first take the derivative of both sides, with respect to x

[tex]\frac{d}{dx}[y]=\frac{d}{dx}[Ae^{mx} + Be^{nx}][/tex]

From here we can take the derivative of [tex]Ae^{mx} \text{ and }Be^{nx}[/tex] and then add them after taking the derivative individually.

[tex]\frac{dy}{dx}=\frac{d}{dx}[Ae^{mx}]+\frac{d}{dx}[Be^{nx}][/tex]

Assuming that "A" and "B" are constants, we can just take the derivative of: [tex]e^{mx}\text{ and }e^{nx}[/tex] and then multiply by "A" and "B" after.

[tex]\frac{dy}{dx}=A\frac{d}{dx}[e^{mx}]+B\frac{d}{dx}[e^{nx}][/tex]

now from here we apply the chain rule. I'll start with: [tex]e^{mx}[/tex]. First let's rewrite the equation so that we have a composite function: [tex]u=mx\implies e^{mx}=e^u[/tex] now from here, we can apply the chain rule: [tex]\frac{d}{dx}[e^{mx}]=\frac{d}{dx}[e^u]*\frac{d}{dx}[u][/tex]

You may know that the derivative of e to the x is just going to be e to the x, so the derivative of e^u is just e^u. Now substitute mx back in as u, and you get e^(mx). Now take the derivative of "u" which is just mx, and you get "m" since the derivative of any linear equation is just the slope (since this is constant): [tex]\frac{d}{dx}[e^{mx}]=e^{mx}*m[/tex]

Now from here we can apply the same logic to e^(nx) to get: [tex]\frac{d}{dx}[e^{nx}]=e^{nx}*n[/tex]

So now we have the following expression:

[tex]\frac{dy}{dx}=A[e^{mx}*m]+B[e^{nx}*n][/tex]

[tex]\frac{d}{dx}[\frac{dy}{dx}]=\frac{d}{dx}[A(e^{mx}*m)+B(e^{nx}*n)][/tex]

we can apply some of the rules we used before like taking each individual derivative then adding them after, and "factoring out" the A and B (because they're constants). This gives us the following expression:

[tex]\frac{d^2y}{dx^2}=A\frac{d}{dx}[e^{mx}*m]+B\frac{d}{dx}[e^{nx}*n][/tex]

From here we can also think of "factoring out" the m and n because they're constants, so we get the following:

[tex]\frac{d^2y}{dx^2}=Am*\frac{d}{dx}[e^{mx}]+Bn*\frac{d}{dx}[e^{nx}][/tex]

From here we can apply the chain rule... except we already did this work (taking the derivative of e to the mx and e to the nx) so we can just put that here

[tex]\frac{d^2y}{dx^2}=Am*[e^{mx}*m]+Bn*[e^{nx}*n][/tex]

We can further simplify this to:

[tex]\frac{d^2y}{dx^2}=Am^2*[e^{mx}]+Bn^2*[e^{nx}][/tex]

So we know that: [tex]\frac{d^2y}{dx^2}=Am^2*[e^{mx}]+Bn^2*[e^{nx}][/tex]

and that: [tex]\frac{dy}{dx}=A[e^{mx}*m]+B[e^{nx}*n][/tex] or [tex]\frac{dy}{dx}=Am[e^{mx}]+Bn[e^{nx}][/tex]

Plugging these into the expression: [tex]\frac{d^2y}{dx^2} - (m+n)(\frac{dy}{dx}})+mny=0[/tex]

we get the following: [tex]Am^2e^{mx}+Bn^2e^{nx}-(m+n)(Ame^{mx}+Bne^{nx})+mny=0[/tex]

First let's distribute the (m+n) to the first derivative to get:

[tex](m+n)(Ame^{mx}+Bne^{nx}) =(Am^2e^{mx} +Bnme^{nx} + Anme^{mx} + Bn^2e^{nx})[/tex]

so plugging this in we get:

[tex]Am^2e^{mx}+Bn^2e^{nx}-(Am^2e^{mx} +Bnme^{nx} + Anme^{mx} + Bn^2e^{nx})+mny=0[/tex]

from here we can distribute the negative sign and cancel out values to get:

[tex]-Bnme^{nx} -Anme^{mx}+mny=0[/tex]

So we're almost done and it may look a bit weird in this situation since none of the variables look like they align to cancel them out... but notice how there is a "y" variable? We know what that is equal to! We started with that expression: [tex]y=Ae^{mx}+Be^{nx}[/tex]

So let's plug this in to our expression:

[tex]-Bnme^{nx} -Anme^{mx}+mn(Ae^{nx}+Be^{nx})=0[/tex]

Let's distribute the "mn" using the distributive property:

[tex]-Bnme^{nx} -Anme^{mx}+(Anme^{nx}+Bnme^{nx})=0[/tex]

and from here we can finally cancel out all the values! and this simplifies to zero.

[tex]0=0[/tex]

so we have proven that this expression is always equal to zero!

The triangle with sides length of  35 km , 83 km and 86 km cannot form a right triangle.

A right triangle is a triangle that has one angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides of a triangle can be found using Pythagoras's theorem. Right triangle obeys  Pythagoras's theorem.

The  Pythagoras's theorem can be represented as follows:

c² = a² + b²

where

The hypotenuse is the longest side of the right triangle.

Hence, let's check if the side length of 35 km 83 km 86 km is a right triangle.

35² + 83² = 86²

1225 + 6889  ≠ 7396

Therefore, it is not a right triangle.

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The value of s in the point (s,-3) after using slope formula is -4.

What is slope?

Slope is a term used to define how steep a line is. The rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction, is the definition of slope (x). The slope is the angle at which one is moving forward or backward when skiing down a hill or climbing a mountain. Depending on what it is, the slope may occasionally be fairly flat or extremely steep. The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. 

Using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Now the given point  is ,

[tex](x_1,y_1)=(s,-3) \\(x_2,y_2)=(-8,-4)[/tex]

=> slope m= 1/4

=> [tex]\frac{1}{4}= \frac{-4+3}{-8-s}[/tex]

=> [tex]\frac{1}{4} = \frac{-1}{-8-s}[/tex]

=> -8-s=-4

=>-s=-4+8

=> -s=4

=> s =-4.

Hence the value of s is -4.

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1) The yearly depreciation expense under the straight-line method is $2,000.

2) If the car was bought on April 3, the depreciation expense for the first year is approximately $1,500.

Under the straight-line depreciation method, the depreciation expense is the quotient of the depreciable amount (cost - residual value) divided by the estimated useful life of the asset.

The depreciation expense is prorated if it does not cover the full year.

Cost of car = $12,000

Estimated useful life = 5 years

Residual value = $2,000

Depreciable amount = $10,000 ($12,000 - $2,000)

Straight-line Depreciation (annual) = $2,000 ($10,000/5)

Depreciation for first year (April 3) = $1,496 ($2,000 x 273/365)

≈ $1,500

Thus, using the straight-line method, the depreciation expense for the car in each year is $2,000.

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The area of the triangle is 8 unit².

The amount of space a shape takes up is called the area of that space.

Here,

The given vertices are

A= (-4,1)

B= (-7,5)

C= (0,1)

Now, as we know the x and y coordinates of three vertices of triangle.

So, we will use the coordinate geometry formula.

The general formula of the area of triangle is

If the triangle have a vertices (Ax,Ay ),(Bx,By ) and (Cx,Cy ) then the area is

Area=1/2×|Ax (By-Cy )+Bx (Cy-Ay )+Cx (Ay-By )|

Now, we will put the given coordinates values in above equation

Then we will get

Area=(1/2)×|(-4)(5-1)+(-7)(1-1)+0(1-5)|

Area=(1/2)×|(-4)(4)+(-7)(0)+0(-4)|

Area=(1/2)×|-16|

Remove the mode bracket.

Area=1/2×16

Area=8

Thus, the area of the triangle is 8 unit².

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Using the given information, Billy's grade in his Math class will be 94.85%

From the question, we are to determine what the grade of Billy should be.

From the given information,
Billy had 100% in his Math class and he got 27/34 on his midterm

Also,

The midterm is 25%

This means the exam is 75%

Billy's grade will be

100% of 75 + 27/34 of 25

= 75 + 19.85

= 94.85

Hence, Billy's grade will be 94.85%

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Answer:

Carmelita Jeter 10.64

Step-by-step explanation:

Because the first is Kerron Stewart,the second is Merlene Ottey and the third is Shelley-Ann Fraster

Answer:

Determine whether the equation is half or double the given number, then solve for x.

Step-by-step explanation:

The hash marks on the sides of the triangles tell you that the pieces of the triangles are the same length. The piece with one mark is the same length as the other piece with one mark. The piece with two marks is the same length as the other piece with two marks.

This is important because it tells you that the place where the triangle is divided is at its halfway point — so, the triangles are cut right in half. The line that cuts the triangle in half will always be half the length of the line that is the bottom of the triangle. You can use this to solve for x in each of these problems.

12) We are trying to solve for x along the length of the longer line. The halfway-point line is seven.

Seven is half of fourteen (7*2=14). So, the longer line is 14.

Since the longer line has the equation 2x, we must determine what times two is fourteen. To find that, we would divide fourteen by two (division and multiplication are inverse operations). 14/2=7.

x=7.

15) We are trying to solve for x along the length of the shorter line. The longer line is 35.

The shorter line is half of the longer line, so in this case it is half of 35, which is 17.5.

However, in the equation, we subtract 8 from x. So, we have to find the number that becomes 17.5 only after you subtract 8. To do this, you simply add 8 to 17.5 (addition and subtraction are inverse operations). 25.5 - 8 = 17.5.

x = 25.5.

Answer:

x-18=x4=-36 is the answer

The rate of change for the given graph is 10.

Rate of change

Rate of change describes how one quantity changes in relation to another quantity.

The formula for the rate of change is,

R = Δx/Δy

where

Δx = x₂ - x₁

Δy = y₂ - y₁

where (x₁, y₁) and (x₂, y₂) refers the points given.

Given,

Here we have the graph that shows the distance, d, meters, travelled by Jaden on her bicycle as a function of the number of wheel revolutions, n, as she rode from Whitehorse to the Grey Mountain Road lookout in the Yukon.

And we need to determine the rate of change of the graph.

In order to find the rate of change , we have to select the points from the given graph.

So, here we have select the following point. (2400, 5000) and (2500, 6000)

Now, as per the rate of change formula, it can be calculated as,

Δx = 2500 - 2400

Δx = 100

And the next one is,

Δy = 6000 - 5000

Δy = 1000

Then the rate of change is,

R = 1000/100

R = 10

Therefore, the rate of change is 10.

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The expression that can be used to represent this situation is 5p

Expression:

Expression refers the mathematical equation that consists of variables, numbers and mathematical operator.

Given,

Bre'Asia wanted to buy 5 pizzas. She used a coupon for $7 off the entire order. Let p represent the cost of 1 pizza.

Here we need to find the expression that represents the situation.

In the given question, let us consider p represent the cost of 1 pizza and the n refers the number of pizza.

So, the expression to calculate the price of the pizza based on the number of pizza is written as,

=> np

Here Bre'Asia brought 5 pizzas, then the expression is

=> 5p.

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Answer:the answer is 12x+12=7x+56 got it right on plato

Step-by-step explanation:

12 (x+1) = 7 (x+8)

12x+ 12 = 7x+ 56

Answer:

[tex]\frac{5}{4} y^1^1[/tex]

Step-by-step explanation:

Simplify...

[tex]\frac{45y^7}{36y^4}[/tex]

[tex]\frac{5}{4} y^1^1[/tex]

Hope this helps! :)

The amount in the fund immediately after the last deposit is $1148830.185

Given,

The amount deposited by Steve annually =  $53,700

Interest rate of the fund = 15%

Time period of the investment = 10 years

We have to find the amount in the fund immediately after the last deposit.

Here,

To calculate the future value after the last deposit, we need to use the following formula:

Future Value = {A[(1+i)^n-1]}/i

A = Annual deposit

Then,

FV = {53,700[(1.15)^9 - 1]}  / 0.15 + 53,700

FV= 1095130.185 + 53,700

FV= $1148830.185

Therefore,

The amount in the fund immediately after the last deposit is $1148830.185

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Answer:

8 %

Step-by-step explanation:

To find the tax rate, we first have to find the tax

4.32 - 4 = .32

The tax rate is found by the tax / total

.32 /4 =.08

To change this to a percent multiply by 100

.08 * 100% = 8 %

Answer:

A

Step-by-step explanation:

The families of solutions (variable x) for the square root of the trigonometric expression 2 · cos x - 1  equal to 0 are x₁ = π / 6 + i · 2π and x₂ = 11π / 6 + i · 2π, where i is an integer.

In this question we find the following trigonometric expression:

√(2 · cos x - 1) = 0

Where x is measured in radians.

By algebra properties and trigonometric formulas we must solve the trigonometric expression for x. First, use algebra properties until the trigonometric function is cleared:

√(2 · cos x - 1) = 0

2 · cos x - 1 = 0

2 · cos x = 1

cos x = 1 / 2

Second, find the family of solutions for the square root of the trigonometric function:

x₁ = π / 6 + i · 2π, where i is an integer.

x₂ = 11π / 6 + i · 2π, where i is an integer.

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The zero of the function in the given table is -1, indicating that the function provided has an x-intercept.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, which is the location or coordinates from where the line crosses.

The table is given in the question,

If the value of x is -1, then the value of y is zero, according to the table. This is the function's x-intercept. The zero of the function depicted in this table is -1, which signifies that the supplied function has an x-intercept.

Therefore, the zero of the function given in this table is -1, indicating that the function provided has an x-intercept.

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The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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Answer:

See below

Step-by-step explanation:

Read across the x-axis to '5' then go up to intersect the graph.....then read to the LEFT to find the price on the y-axis

The value of x is 18.8m

Given:

θ = 48°

Y = 17m

The law of tangent which is also called as tangent formula or tangent rule is the ratio of the sine of the angle to the cos of the angle.

tan θ = Opposite / Adjacent.

Here,

Sum of triangle = 180°

90° + 48° + x° = 180°

x° = 42°

tan θ = opposite/ adjacent.

Substituting the values

tan 42° = 17/x  (∴tan 42° = 0.9004)

0.9004 = 17/x

So we get,

x = 17/0.9004

x = 18,8m

Therefore, the value of x is 18.8m.

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