find the derivative by first principle rule f(x)=3÷x+2

The solution to the given complex number expression is; 0 + [1/(-2√6))]i

We are given the expression as;

(√-4)/[(√-8)√-12)]

Now, when it comes to complex numbers, we know that the square root of a negative number for example √-25 would result in 5i.

Similarly, i² = -1

Thus, our expression is now;

2i/(2i√2 * 2i√3)

= 2i/(-4√6)

= i/(-2√6))

= 0 + [1/(-2√6))]i

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Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to find the solutions or roots of a quadratic equation in the form of ax^2 + bx + c = 0. The goal of factoring is to rewrite the equation in the form of (x-r)(x-s) = 0, where r and s are the solutions or roots of the equation. Once the equation is in this form, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Here is an example to illustrate the process:

Example: Solve the equation x^2 + 5x - 14 = 0 using factoring.

Step 1: Rewrite the equation in standard form (ax^2 + bx + c = 0). In this case, a = 1, b = 5, and c = -14.

Step 2: Factor the equation by looking for two numbers that multiply to give c and add to give b. In this case, the two numbers are -7 and 2, since (-7)(2) = -14 and -7 + 2 = -5.

Step 3: Rewrite the equation as (x + 7)(x - 2) = 0.

Step 4: Use the zero product property to set each factor equal to zero and solve for x.

x + 7 = 0 or x - 2 = 0

x = -7 or x = 2

So the solutions or roots of the equation are x = -7 and x = 2.

It's important to note that not all quadratic equations can be factored, and in such cases, other methods like completing the square or using the quadratic formula should be used.

It's also important to understand that when factoring, it's important to make sure that you have correctly factored the equation, if not the solution will be wrong.

Answer:

100,000,000,000cm

Step-by-step explanation:

there are one hundred billion cm in one billion meters.

This is a mathematical problem that can be solved using algebra. Let P be the original amount borrowed, and R be the interest rate as a decimal (for example, 5% would be represented as 0.05).

We know that at the end of 25 years, the amount borrowed has trebled, so the total amount is 3P. We also know that the interest is calculated using simple interest, which is calculated as P x R x T, where T is the number of years.

So we can set up the equation:

3P = P + P x R x 25

To find R, we can solve for R by dividing both sides of the equation by P:

3 = 1 + 25R

Then by subtracting one from both sides we have :

2 = 25R

Then by dividing both sides by 25 we can find the rate as :

R = 2/25

Finally, to find the interest rate as a percentage, we multiply R by 100:

rate = 2/25 x 100 = 8%

So the interest rate is 8% per annum

Answer:

( - inf, 5) (9, inf )

Step-by-step explanation:

The arrow(s) at the end of the line indicate that the highlighted green line does not stop at a specific number, hence the use of infinity signs (inf). If the arrow is going to the left on a line, then the value would be negative infinity. If it is going to the right, then it would be positive.

As for the space in between the green arrows pointing separate ways, there are two points, one which is positioned at the number 5 and the other at the number 9. Because there are two separate points which are both solid green, the use of parentheses is needed. The final answer is, as mentioned, ( - inf, 5) (9, inf ).

Answer:

exponential growth

Step-by-step explanation:

Answer: C

Step-by-step explanation:

10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310

The required expression is x³ + 5x² + 6x as an expanded form.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

x(x + 2)(x + 3)

We have to expand and simplify the given factors.

As per the question, we have

⇒ x(x + 2)(x + 3)

Open the first parentheses, and distributes

⇒ (x² + 2x)(x + 3)

⇒ x²(x + 3) +  + 2x(x + 3)

Combine the likewise terms in the above expression,

⇒ x³ + 3x² +2x² + 6x

⇒ x³ + 5x² + 6x

Thus, the required expression is x³ + 5x² + 6x.

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The requried, score is given as 42, as of the given condition,

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the total score after finishing the game be x,
Receive one point for each card you played and lose two points for each card remaining in your hand. and the score is tripled.
According to the quesiton,
x =3 [1 × 18 - 2 × 2]
x = 3[ 18 -4]
x = 3 × 14
x = 42

Thus, The requried, score is given as 42, as of the given question,

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Answer: True

Step-by-step explanation: Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.

Answer: x = 1, -13

Step-by-step explanation:

      We will solve this by completing the square, as asked in the instructions. If we do this correctly, we will end up with a perfect square that will allow us to solve more easily.

Given:

      x² + 12x = 13

Set the equation equal to 0 by subtracting both sides of the equation by 13:

      x² + 12x - 13 = 0

Group the first two terms:

      (x² + 12x) - 13 = 0

Add and subtract [tex]\frac{b}{2} ^2[/tex] to the grouped terms:

      (x² + 12x + 36 - 36) - 13 = 0

Regroup the terms, move the negative out and simplify:

      (x² + 12x + 36) - 49 = 0

Factor the grouped terms (6 is our perfect square here):

      (x + 6)(x + 6) - 49 = 0

Add 49 to both sides of the equation and simplify the factors:

      (x + 6)² = 49

Square root both sides of the equation:

      x + 6 = 7           x + 6 = -7

Subtract 6 from both sides of each equation:

    x = 1           x - 13

The horizontal axis is the real axis and the vertical axis is the imaginary axis. We find the real and complex components in terms of r

and θ

where r

is the length of the vector and θ

is the angle made with the real axis.

From Pythagorean Theorem :

r2=a2+b2

By using the basic trigonometric ratios :

cosθ=ar

and sinθ=br

.

Multiplying each side by r

:

rcosθ=a  and  rsinθ=b

The rectangular form of a complex number is given by

z=a+bi

.

Substitute the values of a

and b

.

z=a+bi    =rcosθ+(rsinθ)i    =r(cosθ+isinθ)

In the case of a complex number, r

represents the absolute value or modulus and the angle θ

is called the argument of the complex number.

This can be summarized as follows:

The polar form of a complex number z=a+bi

is z=r(cosθ+isinθ)

, where r=|z|=a2+b2−−−−−−√

, a=rcosθ  and  b=rsinθ

, and θ=tan−1(ba)

for a>0

and θ=tan−1(ba)+π

or θ=tan−1(ba)+180°

for a<0

.

Example:

Express the complex number in polar form.

5+2i

The polar form of a complex number z=a+bi

is z=r(cosθ+isinθ)

.

So, first find the absolute value of r

.

r=|z|=a2+b2−−−−−−√    =52+22−−−−−−√    =25+4−−−−−√    =29−−√     ≈5.39

Now find the argument θ

.

Since a>0

, use the formula θ=tan−1(ba)

.

θ=tan−1(25)    ≈0.38

Note that here θ

is measured in radians.

Therefore, the polar form of 5+2i

is about 5.39(cos(0.38)+isin(0.38))

.

The length of the car in Ivans drawing is given as 8 cm

We are to solve for the length of this car by using the figure we have in the scale drawing. The length of car in Megan's drawing is 6 cm. The scale is 3 : 2

Ivan's drawing is in the relation of 2 : 1 cm

We would have to find the actual length of this car but by the use of Megan's ratio

This is given as

6 * 2 / 3

12 / 3

= 4 cm

Next we have to find Ivans length.

4 * (2/1)

= 8 / 1

= 8 cm

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Yes, Rob can ship all 4,056 eggs in the same shipment.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Rob lives on an egg farm with 5,287 chicken hens. Rob collects the chicken eggs every day. One day Rob collects 4,056 eggs.

The eggs are placed in egg cartons of twelve eggs per carton and are shipped to stores.

Here, number of cartons required =4,056/12

= 338 cartons

The egg cartons must be carefully placed in shipping boxes. Each shipping box holds twenty-four egg cartons.

Number of shipping boxes =338/24

= 14.08

The shipper can deliver no more than fifteen shipping boxes of eggs at a time.

Yes, Rob can ship all 4,056 eggs in the same shipment.

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The required equation modeled as of the given condition is 46x + 1 / x².

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the number be x, and its reciprocal is 1/x
According to the question, the product of 46 and a number added to the reciprocal of a number squared is given as,
= 46 × x + 1/x²
= 46x + 1/x²

Thus, the required equation modeled as of the given condition is 46x + 1 / x².

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Answer:

0.7 mile high

Step-by-step explanation:

tan 30 = height /1.2

so height =1.2 *tan30 = 1.2*0.58 = 0.7

So on solving the provided question we can say that - the function is  y = (-8x + - 74) and y = -82

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here, we have

y = (-8x + - 74)

and from data we have x = 1

so, y = (-8-74)

y = -82

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Answer:

Step-by-step explanation:

a(b - c) = de

b - c = de/a

-c = de/a - b

c = b - de/a

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The exact volume of the waffle ice cream cone is 114.75π square inches

From the question, we are to determine the volume of the waffle ice cream cone

The volume of a cone can be calculated by using the formula,

V = 1/3πr²h

Where V is the volume

r is radius

and h is the height

From the given information,

Diameter = 9 in

∴ Radius, r = 9/2 in = 4.5 in

h = 17 in

Putting the parameters into the formula, we get

V = 1/3 × π × 4.5² × 17

V = 114.75π square inches

Hence, the volume is 114.75π square inches

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Answer:

Step-by-step explanation:

Answer:

1/560

Step-by-step explanation:

So the x input which is the top row the numbers increase by 1 so that is your top number of your slope (rate of change)

And your bottom row increases by 560 so that is your bottom number of your slope

So your rate of change is 1/560

How do I know where to get these numbers?

Well if you take the first 2 numbers from the top row (in your case 1 and 2) and subtract them from each other (2-1=1) you get your first number. Then you do the same for the bottom (in your case 560 and 1120) subtract them (1120-560=560) and get your bottom....If needed you can simplify your fraction but sometimes your slope can come out as a whole number instead of a fraction but in your case you have a fraction.

That is where you get 1/560

Hope this helped!

Answer: C

Step-by-step explanation:

It's C, as they represent the same ratio.

3 of mixed cereal and 2 of tropical fruit

Step-by-step explanation:

here it is earning more money to the doctor said the

The domain of the function 5h + 2d = 15 is [0, 3].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function 5h + 2d = 15

Where h is the number of hours and d is the distance remaining after h hours.

Now,

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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Answer:

Step-by-step explanation:

Sure, here is an example of how the information provided could be organized in an Excel spreadsheet to calculate Taxable Income and Adjusted Gross Income: see in the attached e1 and e2 screenshots.

It's worth noting that the above example is a simplified version, and the actual calculations for tax purposes would depend on the specific tax laws and regulations in the relevant jurisdiction and year. Also, the numbers provided here are not the final Taxable Income, it's only the calculation of Taxable Income based on the information provided.

The required expression is 21.29 × 38 = 809.02. has an exact value of the given product.

The estimate is a process, and it includes the rough over-calculation that makes one have a close value to the exact value.

here,
Given expression,
21.29 × 38 = (21 + 0.29) 38
Using distributive property,
               = 21× 38 + 0.29 × 38

               = 798 + 11.02
               = 809.02

The required expression is 21.29 x 38 = 809.02. has an exact value of the given product.

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Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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