(y + 1)^5 divided by (y + 1)^2

The expressions that represent the derivative of the function y = f(x) are dy/dx, l'(x), and lim h->0 [f(x+h) - f(x)]/h. These expressions show the rate of change of y with respect to x at any given point on the function.

The other expressions, such as S(x) + f(h), xth dh/dx, lim 10 f(x) + f(h) x+h, and lim 1-0 F(x +h)-f(x)/h, are not equivalent to the derivative of the function. It is important to understand and use the correct expressions for the derivative in order to accurately analyze and interpret the behavior of a given function.

The expressions that represent the derivative of the function y = f(x) are:

1. lim (x→0) [f(x + h) - f(x)] / h
2. dy/dx
3. f'(x)
4. dh/dx

These expressions are used to describe the rate of change of the function y = f(x) with respect to the variable x. They can be used to find the slope of the tangent line to the curve at any given point or to analyze the behavior of the function.

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Answer:

5374771.2

Step-by-step explanation:

Answer:

9π

Step-by-step explanation:

Area of Circle: πr²

Diameter = radius * 2

Diameter = 3 * 2 = 6

Plug into the formula πr²

(3)²π ≈ 28.274 or 9π

The area of the figure formed by the dilation is 36 square units.

Area is particularly essential in modern mathematics. In addition to its importance in geometry and calculus, area is linked to the determination of determinants in linear algebra and is an essential feature of surfaces in differential geometry.

A dilation occurs when an figure is reduced to a smaller size using a fixed center.

From the given diagram we can find the sides of the square that is the transformed image as 9 - 3 = 6 units

Area of the A'B'C'D' square = 36 square units.

Side of the original square = 18 units.

Area of the ABCD square = 18² = 324 square units

Scale factor of dilation = 324/36 = 9 times.

Hence from the figure we can calculate the area of the transformed figure to be 36 square units which is dilated by a factor of 9 times.

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Numbered meridians are semicircles.

On a map of the planet, the Prime Meridian is an illustrative line. It serves as the origin of the longitude system of measurement. Meridians, a system of fictitious north-south lines, make up longitude. The planet Earth rotates like a ball. The Earth's axis serves as the spin's focal point.

The North Pole and the South Pole are where the axis intersects the surface of the planet. The North Pole and the South Pole are the points on each meridian. Meridians are used to calculate how far away from the prime meridian you are in degrees east or west.

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Answer:

9°C

Step-by-step explanation:

Group the terms and get \(24+8-1-10-12\)

Then simplify to get \(32-23\)

Subtract and you get 9

So the answer is 9°C.

Hope this helps!

Answer:

3/7 is the correct answer

Step-by-step explanation:

Answer:

my answer is that is 3/7 because look at the question and you will see what i mean.

Step-by-step explanation:

Answer: D. 1/10

Step-by-step explanation:

With there being 5 sections on the spinner and only one number wanted to be spun, the probability of that would be 1/5.

On a dice, 3 of the numbers on a cube are prime (1, 3 and 5). So the probability would be 3/6 or 1/2.

1/5 x 1/2 = 1/10, so the probability of spinning a 4 and rolling a prime number would be 1/10, or 10%

Answer:

bahahahhahahahahahah hello

Answer: 6x+18

Step-by-step explanation: you just have to distribute so you multiply the six with whatever is inside so 6 times x is 6x + 6 times 3 is 18 so the answer is 6x+18 we cant simplify anymore

The formula for determining the area of a rectangle is expressed as

Area = length * width

From the diagram,

Length = 3x + 6

Width = 4x - 1

The expression for the area of the room would be

In standard polynomial form, the terms are arranged in decreasing order of exponents. Therefore, the expression in standard form is

number 7 is 21 people

Step-by-step explanation:

for number 7 I got 21 because if 6 pounds feeds 14 people then if you divide both by 2 then you will get 3 pounds feed 7 people and to find 9 pounds its 7×3 which is 21.

The original limit represents the derivative of f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at the point a=0, and the value of the limit is 5.

To find the function and number, we need to simplify the expression first. Using the binomial formula, we can expand \((1+h)^5\) as follows:
\((1+h)^5\) = 1 + 5h + 10h² + 10h³ + \(5h^4\) + \(h^5\)
Then, we can substitute this expansion into the original expression and simplify:
lim h→0 [(1+h)^5 - 1]/h
= lim h→0 [1 + 5h + 10h² + 10h³ + \(5h^4\) + \(h^5\) - 1]/h
= lim h→0 [5h + 10h² + 10h³ + 5h^4 + h^5]/h
= lim h→0 [5 + 10h + 10h² + 5h³ + h^4]
Now, we can see that this limit represents the derivative of the function f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at the point a=0. Taking the derivative of f(x) using the power rule, we get:
f'(x) = 4x³ + 15x² + 20x + 5
Evaluating this derivative at a=0, we get:
f'(0) = 4(0)² + 15(0)² + 20(0) + 5 = 5
Therefore, the original limit represents the derivative of f(x) = \(x^4\) + 5x³ + 10x² + 5x + 5 at point a=0, and the value of the limit is 5.

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The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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We have translated the given phrase into a variable expression as (1/9) × (x - 15).

To translate the given phrase "the product of one-ninth and the difference of a number and fifteen" into a variable expression, we can use the following:

1: Identify the unknown or variable number in the expression.

Let's say the variable number is 'x'.

2: Translate the phrase "one-ninth" to a fraction as 1/9.

3: Translate the phrase "the difference of a number and fifteen" to a mathematical expression.

As we have taken 'x' as the variable number, the difference of 'x' and fifteen can be written as (x - 15).

4: Combine the above expressions using the multiplication sign to get the variable expression.

So, the variable expression is:(1/9) × (x - 15)

The variable expression obtained is (1/9) × (x - 15). Hence, we have translated the given phrase into a variable expression using the required terms.

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Answer:

17.9 m^3

Step-by-step explanation:

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

y= 60

x= 100

Step-by-step explanation:

To find y we have to do the following steps below:

180-120= 60 degrees which is y, we do this because a straight line is 180 degrees.

Now we know the value of y is 60 and we know that all angles in a triangle add up to 180 degrees therefore, do 60+40=100 and now we do 180-100 to find the angle C which is 80 degrees. Now do the same to find x, 180-80= 100 degrees, and done you've got values for x and y.

Pls make me the brainliest pls....

Answer:

348m

Step-by-step explanation:

I took the k12 test

The required total number of pages in the dictionary are 443.

A sum equivalent to three of the four a balance of which make up something : 75%. 3/4 of the class will be going on the excursion. 3/4 of 60 minutes.

We have,

Dictionary contains 253 pages,

Then,

Total number of pages in the dictionary = 253 + \(\frac{3}{4}\) of 253

253 + approx(190)

Total pages =  443 pages

Thus, required number of pages are 443.

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Hence, the probability of being dealt a five-card hand that is all diamonds from a standard deck of cards is approximately 0.000495 or about 0.0495%.

To calculate the probability of being dealt a five-card hand that is all diamonds from a standard deck of cards, we need to determine the number of favorable outcomes (getting all diamonds) and divide it by the total number of possible outcomes (all possible five-card hands).

In a standard deck of cards, there are 52 cards, and 13 of them are diamonds (there are 13 diamonds in total).

To calculate the number of favorable outcomes, we need to select all 5 cards from the 13 diamonds. We can use the combination formula, which is given by:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items we want to select.

Using the combination formula, the number of ways to select 5 cards from 13 diamonds is:

C(13, 5) = 13! / (5!(13-5)!)

= 13! / (5! * 8!)

= (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1)

= 1287

Therefore, there are 1287 favorable outcomes (five-card hands consisting of all diamonds).

Now, let's calculate the total number of possible outcomes (all possible five-card hands). We need to select 5 cards from the total deck of 52 cards:

C(52, 5) = 52! / (5!(52-5)!)

= 52! / (5! * 47!)

= (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)

= 2,598,960

Therefore, there are 2,598,960 possible outcomes (all possible five-card hands).

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = favorable outcomes / total outcomes

= 1287 / 2,598,960

≈ 0.000495

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Answer:

z= 4-x-y

z= -1+4x-y

z= 2-x

Step-by-step explanation:

z = 2-x

y = -1-z +4x

substitute

x -1 -2+x +4x + 2 -x = 4

-1 + 5x = 4

5x = 5

x = 1

z = 1

1+y+1 = 4

y = 2

Answer: small bottles

Step-by-step explanation:

124 * 7 =868 ounces

14 * 64 = 896 ounces

Answer:

The rate of the plane is 753 km/h while the rate of the wind is 75km/h

Step-by-step explanation:

Here in this question, we are interested in calculating the rate of the plane in still air and the rate of the wind.

Since we do not know these rates, we shall be representing both using variables.

Let’s represent the rate of the plane in still air by x kmph while the rate of the wind be represented by y kmph

Now, for us to calculate the speed of the plane while it travels against the wind, that would be the speed of the plane in still air minus the speed of the wind.

Mathematically, that would be (x-y) kmph

Now the speed of the plane while it travels with the wind would be its speed in still air plus the speed of the wind.

Mathematically, that would be;

(x + y) kmph

From the question;

The plane journeyed 5424 km against the speed in 8 hours, this means that its speed will be 5424/8 = 678 kmph

Thus, that means;

x -y = 678 •••••••(i)

Now, traveling with the wind , its speed will be ;

6624/8 = 828 kmph

Thus;

x + y = 828 kmph •••••••(ii)

So we have two equations to solve simultaneously;

Let’s add both together;

x -y + x + y = 828+ 678

2x = 1,506

x = 1506/2

x = 753 kmph

From ii

x + y = 828

y = 828 - x

y = 828 - 753

y = 75 kmph

Answer:

una función aritmética es cualquier función matemática definida para enteros (..., 3, 2, 1, 0, 1, 2, 3, ...) y dependiente de esas propiedades del propio entero como un número, en contraste con las funciones que se definen para otros valores (números reales, números complejos, o incluso otras funciones) y que implican varias operaciones de álgebra y cálculo.

Answer: To solve the system of equations using substitution, we'll start by rearranging one of the equations so that one of the variables can be expressed in terms of the other. In this case, we'll rearrange the second equation to find y in terms of x.

y = 2x + 4

Next, we'll substitute this expression for y into the first equation:

+3x + 5(2x + 4) = 7

Expanding the right-hand side:

+3x + 10x + 20 = 7

Combining like terms:

13x + 20 = 7

Subtracting 20 from both sides:

13x = -13

Dividing both sides by 13:

x = -1

Finally, we'll use the expression we found for y in terms of x to find the corresponding value of y:

y = 2x + 4

y = 2(-1) + 4

y = -2 + 4

y = 2

So the solution to the system is (x, y) = (-1, 2).

Step-by-step explanation:

The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

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For a rectangular prism, the

Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

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