If f(x) = 2x + 1 and
g(x) = -(x - 1)² + 3 what is the smallest solution for f(x)=g(x)?

main answer: the ratio of the denominator quantity times the derivative of the numerator function minus the denominator quantity times the derivative of the denominator function to the square of the denominator function.

supporting answer:

what is quotient rule?

According to the Quotient Rule, the derivative of a quotient is the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square.

body of the answer :The quotient is the result of dividing one number by another. For example, in 8 4 = 2, the result of the division is 2, so the quotient is 2. The dividend is 8 and the divisor is 4.

final answer: The Quotient Rule is a method for calculating a function's derivative (differentiation) as the ratio of two differentiable functions.

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The ratio of the denominator quantity times the derivative of the numerator function minus the denominator quantity times the derivative of the denominator function to the square of the denominator function.

What is the quotient rule?

According to the Quotient Rule, the derivative of a quotient is the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square.

The quotient is the result of dividing one number by another. For example, in 8 4 = 2, the result of the division is 2, so the quotient is 2. The dividend is 8 and the divisor is 4.

The Quotient Rule is a method for calculating a function's derivative (differentiation) as the ratio of two differentiable functions.

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Answer:

x=4

Step-by-step explanation:

Answer:

\(x_{1} = \frac{7 - \sqrt{51} }{4} , x_{2} = \frac{7 + \sqrt{51} }{4} \)

Step-by-step explanation:

attachment.

Answer:

Cancellation property

Step-by-step explanation:

la propiedad es propiedad de cancelación.

Answer:

Shawn.

Step-by-step explanation:

We can solve for apples per hour and pears per hour. For Shawn, to get the apples per hour, we do 4/2 which is 2 bushels of apples per hour. For pears, we do 5/2 which is 2.5 bushels of pears per hour.

When Carla is picking, we can do:4/3 which is 1 and 1/3, which is her apple bushel picking per hour. For her pears, she picks them at 2 bushels of pears per hour.

Since Shawn picks her apples quicker per hour, and her pears quicker per hour, Shawn picks at a faster fruit pace.

Answer: (4x5) / 10 - 5 = 5

Step-by-step explanation: 20/10 = 10

10-5 = 5

The probability of a game duration of fewer than 210 minutes is 0.7486, or 74.86%.

To find the probability of a game duration of fewer than 210 minutes, we need to calculate the z-score and then use the standard normal distribution table.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation.
In this case, x = 210 minutes, mean = 180 minutes, and standard deviation = 45 minutes.

z = (210 - 180) / 45
z = 30 / 45
z = 0.67

Next, we look up the z-score of 0.67 in the standard normal distribution table. The table gives us the probability corresponding to the z-score.

From the table, we find that the probability corresponding to a z-score of 0.67 is 0.7486.

Therefore, the probability of a game duration of fewer than 210 minutes is 0.7486, or 74.86%..

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The probability of a major league baseball game lasting fewer than 210 minutes is approximately 74.86%.

The duration of major league baseball games is normally distributed with a mean of 180 minutes and a standard deviation of 45 minutes. To find the probability of a game lasting fewer than 210 minutes, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the z-score using the formula:

z = (x - mean) / standard deviation

Here, x represents the desired game duration, which is 210 minutes in this case. Plugging in the values, we get:

z = (210 - 180) / 45

z = 30 / 45

z = 0.67

Next, we look up the corresponding probability for the z-score of 0.67 in the standard normal distribution table. The table tells us that the probability associated with this z-score is 0.7486.

Therefore, the probability of a game duration of fewer than 210 minutes is 0.7486 or 74.86%.

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Answer:

Deshaun =  $590 - $35x

Isabel :  $790 - $55x

$590 - $35x = $790 - $55x

Step-by-step explanation:

For  Deshaun :

Amount in her account = $590

Amount she would have withdrawn by month x = $35 × x = $35x

The amount she would have in her account = $590 - $35x

For Isabel :

Amount in her account = $790

Amount she would have withdrawn by month x = $55 × x = $55x

The amount she would have in her account = $790 - $55x

Let x be the time when the money in their account would be equal  =

$590 - $35x = $790 - $55x

The two county libraries that charge the same penalty per week are Cumberland and Lincoln.

To determine which two county libraries charge the same penalty per week, we need to compare the coefficients of 'x' in the equations representing the late fee functions.

The equations for each county library are:

Cumberland: y = x + 1/2

Lincoln: y = x + 3

Ocean: y = (1/2)x + 3

Summit: y = 3x + 1

Comparing the coefficients of 'x':

Cumberland: 1

Lincoln: 1

Ocean: 1/2

Summit: 3

From the comparison, we can see that Cumberland and Lincoln have the same coefficient of 'x' (1), indicating that they charge the same penalty per week.

Therefore, the two county libraries that charge the same penalty per week are Cumberland and Lincoln.

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The answers to the preceding equation are, in radians, x= n and x= -/2+2n, where n is an integer constant.

Sinx(sinx+1)=0 is the provided equation.

This suggests that sinx=0 or sinx+1=0, respectively.

Any number that is x's multiple if sinx=0.

Sinx=-1 when sinx+1=0, resulting in x=-/2+2n, where n is an integer.

As a result, in radians, x= n and x= -/2+2n (where n is an integer constant) are the answers to the given equation.

We must identify the values of x that fulfill the equation sinx(sinx+1)=0 in order to get the solution. We have two scenarios to take into account because the product of two components is zero if and only if at least one of the factors is zero. We need to think about two cases. The number x can be any integer multiple of if sinx=0. Sinx=-1, on the other hand, if sinx+1=0, then x=-/2+2n, where n is an integer. As a result, in radians, x= n and x= -/2+2n (where n is an integer constant) are the answers to the given equation.

The radians equivalents of x=n and x= -/2+2n, where n is an integer constant, are the solutions to the equation sinx(sinx+1)=0. By setting each element in the given equation to zero and locating x, we were able to arrive at these solutions. While the second factor sinx+1=0 produces x= -/2+2n, the first factor sinx=0 yields n.

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The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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n(A U B) = n(A) + n(B) - n(A n B)

From the question;

n(A n B) = 7 n(A U B) = 54 n(A) = 35

substituting the values into the formular above and then solve for n(B)

54 = 35 + n(B) - 7

54 = 28 + n(B)

subtract 28 from both-side of the equation

54 - 28 = 28 - 28 + n(B)

26 = n(B)

The relative atomic mass of Interactium is 290.14 amu.


We can calculate the relative atomic mass of Interactium using the following equation:

Ar = (Ab × Mb) + (Ac × Mc) + (Ad × Md) where Ar is the relative atomic mass, Ab is the abundance of Interactium-284, Mb is the mass of Interactium-284, Ac is the abundance of Interactium-289, Mc is the mass of Interactium-289, Ad is the abundance of Interactium-294, and Md is the mass of Interactium-294.  

Substituting the given values in the equation, we get:

Ar = (0.16 × 284) + (0.27 × 289) + (0.57 × 294)
Ar = 45.44 + 77.97 + 167.43
Ar = 290.14 amu

Therefore, the relative atomic mass of Interactium is 290.14 amu.

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The probability that the motorist must stop at both signals is 0.2, at the first signal but not the second is 0.3, and at exactly one signal is 0.7.

The probability that the motorist must stop at both signals is calculated by multiplying the probability of stopping at the first signal (0.4) and the probability of stopping at the second signal (0.5). This gives a probability of 0.2 that the motorist must stop at both signals. The probability of stopping at the first signal but not the second one is calculated by subtracting the probability of stopping at the second signal (0.5) from the probability of stopping at the first signal (0.4). This gives a probability of 0.3 that the motorist must stop at the first signal but not the second one. The probability that the motorist must stop at exactly one signal is calculated by subtracting the probability of stopping at both signals (0.2) from the probability of stopping at at least one of the two signals (0.7). This gives a probability of 0.7 that the motorist must stop at exactly one signal.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Answer:

2ft

Step-by-step explanation:

The bird should fly to a point on the shoreline that is 4km from B to minimize total energy expenditure. A large W/L ratio means it's more efficient to fly over land, while a small ratio means it's more efficient to fly over water. The minimum ratio is 2.834. The W/L ratio should be 1 for the bird to fly directly to D, and 0 for the bird to fly to B and then along the shore to D. It takes a bird 1.4 times more energy to fly over water than land.

To minimize the total energy expended in returning to its nesting area, the bird should fly to the point on the shoreline that is 4 km from B. This can be found using the principle of least action, which states that the bird will choose the path that minimizes the integral of the energy expended along the path.

A large value of the ratio W/L would mean that it takes significantly more energy to fly over water than over land. A small value of the ratio would mean that there is not much difference in energy expenditure between flying over water and over land. The ratio W/L corresponding to the minimum expenditure of energy can be found using the same principle of least action as in part (a).

we are asked to determine the ratio W/L corresponding to the minimum expenditure of energy. Let x be the distance from B to C, and let y be the distance from C to D along the shoreline. Then the total energy expended in returning to its nesting area is given by

E(x, y) = L(13 - x - y) + W(√(25 - x²)) + W(√(y² + (13 - x)²))

To minimize E(x, y), we take partial derivatives with respect to x and y and set them equal to zero

dE/dx = L + Wx/√(25 - x²) - Wy/√(y² + (13 - x)²) = 0

dE/dy = L - Wy/√(y² + (13 - x)²) = 0

Solving for x and y, we get

x = 5√((W/L)/(1.4(W/L) - 1))

y = 13 - x - 5√((W/L)/(1.4(W/L) - 1))

The ratio W/L corresponding to the minimum expenditure of energy is obtained by substituting these values into the expression for E(x, y) and simplifying

W/L = 2.5(1.4 + √(1.96 + 4/25))/(4.9 - √(1.96 + 4/25))

W/L ≈ 2.834

Therefore, the ratio W/L corresponding to the minimum expenditure of energy is approximately 2.834.

To fly directly to its nesting area D, the value of W/L should be equal to 1. To fly to B and then along the shore to D, the value of W/L should be equal to 0.

If birds of a certain species reach the shore at a point 4 km from B, it takes 1.4 times more energy for the bird to fly over water than over land. This can be found by comparing the energy required to fly directly from the island to the point on the shoreline that is 4 km from B (which is entirely over water) to the energy required to fly along the shoreline from that point to D (which is entirely over land).

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The linear function graphed on the grid will be g(x) = (15/2) x + 45. Option D is correct.

First, let us understand the linear equation:

When a graph is exhibited, a relationship between a number of variables results in a linear model. The variable will be of degree one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

From the graph, we are given the x-intercept is - 6, and the y-intercept is 45.

Substitute the given values in the above formula, we will get;

x / (-6) + y / 45 = 1

- 15x + 2y = 90

y = (15/2) x + 45

g(x) = (15/2) x + 45

Thus, the linear function graphed on the grid will be g(x) = (15/2) x + 45. Option D is correct.

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The domain of this relation is the years 2001-2006 and the range is the number of inductees (8-11).

a. A mapping diagram is a visual representation of data that plots each item and its corresponding value in a diagram. The domain of this relation is the years 2001-2006, and the range is the number of inductees (8-11). A mapping diagram of this relation would look like this:
2001 | 11
2002 | 8
2003 | 9
2004 | 8
2005 | 7
2006 | 6

b. An ordered pair is a set of two values that are related in some way. For example, for the year 2001, the ordered pair would be (2001, 11) because 11 inductees were inducted in 2001. The ordered pairs for the Rock and Roll Hall of Fame and Museum inductees are (2001, 11), (2002, 8), (2003, 9), (2004, 8), (2005, 7), and (2006, 6).

c. A graph on the coordinate plane is a visual representation of data plotted on two axes. The x-axis represents the domain (the years 2001-2006) and the y-axis represents the range (the number of inductees 8-11).

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A graph that represents the linear system of inequalities is shown in the image attached below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours coaching and number of hours at the printing shop respectively, and then translate the word problem into algebraic equation as follows:

Since Mason coaches a swim team for $15 per hour, works at a printing shop for $18 per hour and wants to earn at least $125, a linear inequality to describe this situation is given by:

15x + 18y ≥ 125.

Additionally, he cannot work for more than 20 hours a week;

x + y ≤ 20

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Answer:

695 km and hour

Step-by-step explanation:

Answer:

Brad has been on the team for 8 years. Apply that and that means that Anderson has been on the soccer team for 2 years.

Step-by-step explanation:

I dont know how to explain lol i made an equation and figured it out

Step-by-step explanation:

let x be the number of years that Zach has been on the soccer team and y the number of years Anderson has been on the soccer team.

So, reading our problem it seems that

x=5y-2

x+y=10

replacing x on the second formula we take that 5y-2+y=10

6y-2=10

6y=12

y=2

so x=5y-2=5*2-2=10-2=8

The equation that represents h(x) is h(x) = (f(x))(g(x)).

To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).

Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).

Let's examine the table and compare the values:

x | f(x) | g(x) | h(x)

1 | 3 | 4 | 12

2 | 5 | 2 | 10

3 | 2 | 6 | 12

From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).

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Answer:

It's B.

Step-by-step explanation:

Edge 2020.

Answer:

1. B

2. A

3. I

4. I

These should be correct

Answer:

\(\frac{16}{6561}\)

Step-by-step explanation:

\(\frac{2x2x2x2}{9x9x9x9}\) = \(\frac{16}{6561}\)

The value of the length of the arc indicated is,

⇒ 28π/3 feet

We have to given that;

Radius of circle = 14 feet

And, Central angle = 120 degree

Hence, We can formulate;

⇒ Arc length = 14 x 120 x π /180

⇒ Arc length = 28π/3

Thus, The value of the length of the arc indicated is,

⇒ 28π/3 feet

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Check below, please.

1) Let's fill in our Possibility Tree Diagram considering that the text tells us that each day you flip a coin. Since there are two possibilities either W or T we can start out this way:

2) Day 1 Day 2

So our tree is already filled let's now enlist all the possible outcomes

3)

Each letter for one day.

4) Now let's check what is the probability of playing Water tag on both days:

Thus this is the answer.

Answer:

Add the lengths:

5x - 16 + 2x - 4 = 7x - 20

True. Boyle's law states that the volume of a gas is inversely proportional to its pressure when the temperature is held constant.

This means that when the pressure of the gas increases, its volume decreases, and when the pressure decreases, the volume increases.For example, let's say that the pressure of a certain amount of gas is 1 atmosphere and the volume is 2 liters. If the pressure is increased to 2 atmospheres, then the volume will decrease to 1 liter in order to maintain the same temperature. Mathematically, this can be expressed as PV=k, where P is the pressure, V is the volume, and k is a constant.

In conclusion, Boyle's Law states that the volume of a gas varies directly with its pressure when the temperature is held constant, meaning that when the pressure increases, the volume decreases and when the pressure decreases, the volume increases.

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Answer:

The √50 is between 7.07  and 7.08

Step-by-step explanation:

brainlyest please

Answer:

The √50 is between

✔ 7.07

and

✔ 7.08

.Step-by-step explanation:

edge 2021