intiderivatives & Indefinite Integrals (x^3-2)dx

The number 8 is not a prime number because it is divisible by the numbers other than itself such as two and four.

A prime number is that number which can only be divided either by its own or by 1.

Let us understand this by an example, assume that we are provided with the numbers 2, 4, 6 and 3.

Now let us remember the basic tables of 2 and 3 which are in an order 2, 4, 6, 8... and 3, 6, 9, 12....

Now we cannot that the number 3 and 2 are only repeated in their tables only.

But the number 4 and 6 have appeared in the table of 2 and 3 along with their own tables.

So what we can understand from here is that the numbers 2 and 3 are the prime numbers because they are not divisible by any other number then themselves but the number 4 and 6 are not prime numbers because they are divisible by the numbers other than themselves.

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Answer:

Step-by-step explanation: By using linear inequation, it can be calculated that-

After 50 hours,  Plan B be more profitable than Plan A for the painter

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation.

Here, a linear inequation needs to be solved

Let after t hours,  Plan B be more profitable than Plan A for the painter

For plan A

A painter Charges $500 plus $45 per hour

Cost after t hours = $(500 + 45t)

For plan B

A painter Charges  $55 per hour

Cost after t hours = $55t

By the problem,

55t > 500 + 45t

55t - 45t > 500

10t > 500

t >

t > 50

After 50 hours,  Plan B be more profitable than Plan A for the painter

Answer:

23.5 it is hard to see the little dashes

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the equation. In this case, the equation 2x² 5x³ 7 has the highest power of x being 3, so the degree of the polynomial is 5.

Step 1: Identify the highest power of the variable (x).

Step 2: Count the number of terms in the equation.

Step 3: The degree of the polynomial is the highest power of the variable plus the number of terms minus one.

Step 4: In this case, the highest power of x is 3 and the number of terms is 3, so the degree of the polynomial is 3 + 3 - 1 = 5.

The degree of the polynomial 2x² 5x³ 7 is 5. This can be calculated by taking the highest power of the variable (x) and adding it to the number of terms in the equation (3), and then subtracting 1.

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Answer:5x to the -4 power

Over

1x to the -9 power

Step-by-step explanation:thankssss

we can graph a linear equation using XY tables by putting the values of X we are getting the values of y

what are equation

equation is a connection of number of variables and the constant terms attached with the variables x and y

define graph

graph can be draw in the xy plane with o as the origin and draw or find out the values of y by putting value of x in the equation

we can graph a linear equation using XY tables by putting the values of X we are getting the values of Y

and we can find out the range and domain of a given function and we can draw a graph accordingly

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You need to buy 3.625 yards of fabric to have enough for your project.

To find out how many yards of fabric you need to buy, you can subtract the amount of fabric you already have from the total amount of fabric needed for the project.

Total amount of fabric needed - Fabric you already have = Fabric you need to buy

6.5 yards - 2.875 yards = 3.625 yards

so we can say that:

You need to buy 3.625 yards of fabric to have enough for your project.

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Answer:

Step-by-step explanation:

Since it is a rectangle, the vertex is easily found.

It has a width of 10, and a length of 4.

Using this, the missing vertex can be found.

Missing vertex: (6,-3)

Answer: To find the inverse of a function f(x), we need to switch the x and y variables and then solve for y.

So, the inverse function f^-1(x) of f(x) = 2x - 3 is:

f^-1(x) = (x+3)/2

This is the inverse of the function, and it can be denoted by f^-1(x) = (x+3)/2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

the first term a₁ from the table below n = 1, a₂ below n = 2 and so on

here a₁ = 100 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-50}{100}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 100 [tex](-\frac{1}{2}) ^{n-1}[/tex]

The end points of the diameter of a circle then we can easily find out the center point of the circle using the midpoint formula given by: Midpoint=(x1+x22,y1+y22).

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Answer:

Step-by-step explanation:

85

A function is a set of ordered pairs (x,y) where for each x value there is only one corresponding y value, and the relation between x and y is such that for any x value there is a unique y value.

One way to determine if a set of ordered pairs is a function is to use the vertical line test. This test involves drawing a vertical line on the coordinate plane and seeing if it intersects the graph of the ordered pairs at more than one point. If a vertical line intersects the graph of the ordered pairs at more than one point, then the set of ordered pairs is not a function. If a vertical line intersects the graph of the ordered pairs at only one point, then the set of ordered pairs is a function.

Another way to determine if a set of ordered pairs is a function is to use the rule of correspondence. If every first element of the ordered pair corresponds to one and only one second element, then the set of ordered pairs is a function, otherwise is not.

Additionally, you can also use algebraic methods like the definition of a function, where a function is a relation from a set A to a set B, such that for each element in A there is exactly one element in B.

For example, the set of ordered pairs {(1,2), (2,4), (3,6)} is a function because for each x-value (1,2,3) there is only one corresponding y-value (2,4,6) and this is unique.

In contrast, the set of ordered pairs {(1,2), (2,4), (3,6), (1,3)} is not a function because for x = 1 there are two different y values, 2 and 3.

It's important to remember that it's not enough to just check a few ordered pairs, you need to check all of them.

As per the unitary method, the number of toys ha had at first is 48.

Here we have given that  Hanif had some number of toy.

Here we also know that after selling 18 of them to the customer, then he till had 30 toy in hand.

Now, we have to find how many toy did Hanif have at first.

Let us consider that x is the number of toy he had at first.

Here we know that the following value are given,

number of toys left = 30

number of toys sold = 18

Then the total number of toys at first is calculated as,

=> x = number of toys left + number of toys sold

Apply the values on the equation, then we get

=> x = 30 + 18

=> x = 48.

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The function c(x) represents the price of the jeans after the coupon code is applied will be c(x) = 2x - 5.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Katherine receives an email with a coupon code for $5 off of a pair of jeans from her favorite store.

Let 'x' be the cost of jeans. Then the cost of pair of jeans will be given as,

⇒ 2x

The function c(x) represents the price of the jeans after the coupon code is applied and will be given as,

c(x) = 2x - 5

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We can start by using the following equation to determine the number of yards of red fabric r she will need for each costume:

1 + r = y (y represents the total number of yards of fabric for each costume)

We know that the total number of yards for all the costumes is 8 and there are 5 costumes, so we can use this information to set up another equation:

5y = 8 (y represents the total number of yards of fabric for each costume)

Now we can substitute the first equation into the second equation to get:

5(1 + r) = 8

Expanding the left side of the equation:

5 + 5r = 8

Subtracting 5 from both sides:

5r = 3

Dividing both sides by 5:

r = 3/5

So, Mrs. Byers will need 3/5 yards of red fabric for each costume.

Answer:

(a) P(exactly 3 heads) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875

(b) P(exactly 2 heads) = P(X = 2) = (2!/2^2)(1/4)^2 = 0.375

(c) P(2 or more heads) = P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - (1!/1^1)(1/4) - (0!/0^0)(1/4)^0 = 0.9375

(d) P(exactly 3 tails) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875

The hypothetical value of the sum of the geometric series is 1

The first term that we have in this progression is given as 1/2. Next we have to find the common ratio that lies between the values.

The sum of the infinite geometric series can be gotten by

a / (1 -r)

where a is the first term in the series = 1/2

r is the common ratio of the progression = 1/2

we would have to input the values. such that we would have:

1/2 / (1- 1/2)

(1/2) / (1/2)

= 1

The sum of the series is 1.

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.

A straight line that splits a measure of an angle into two equal parts is termed as an angle bisector. So that the measure of the two parts are the same.

Given in the question that MK bisects <MKL, then;

m<JKL = m<JKM + m<MKL     (definition of an angle bisector)

So that;

m<JKM = m<MKL

(3a + 20) = (2a + 26)

3a + 20 = 2a + 26

collect like terms

3a - 2a = -20 + 26

a = 6

Thus,

m<MKL = (2a + 26)

            = 2(6) + 26

            = 12 + 26

            = 38

m<MKL = 38^o

To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.

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The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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Answer:

See below

Step-by-step explanation:

The purple is the pre-image.  The orange is the image.  The green is showing that the pre-image and the image are the same difference by the y axis.

The correct option regarding the number of columns representing a percentage of 25% is given as follows:

4 columns, because 25% is One-fourth of 100%.

The percentage that represents the total of the diagram is given as follows:

100%.

The ratio between the total percentage of 100% and the percentage of 25% is given as follows:

100/25 = 4.

The ratio represents the number of columns, which is of 4, and is the justification for the correct option.

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The number of tiles that are white if there are 12 tiles in total will be 9.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement.

In this case, there are 3 times as many white tiles as there are shaded.

The number of tiles that are white if there are 12 tiles in total will be:

3x + x = 12

4x = 12

Divide

x = 3

Shaded tiles = 3

White tiles = 3x

= 3 × 3

= 9

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So, the final expression that represents the number of movie theater coupons Suresh has is 4.

Suresh has 4 coupon books, each containing 6 coupons, for a total of 4*6 = 24 coupons.

He wants to keep 1/3 of these coupons, so we can write an expression to represent this as: (1/3) * 24 = 8

So he keeps 8 coupons and gives away 24-8 = 16 coupons.

Out of the 8 coupons he keeps, 50% of them are for the movie theater, so we can write an expression to represent this as: 8 * 0.50 = 4

Therefore, the final expression that represents the number of movie theater coupons Suresh has is: 8 * 0.50 = 4

In this question, we have used the basic arithmetic operations like multiplication and subtraction to find the number of coupons Suresh keeps and gives away. And then we have used the percentage to find out how many movie theater coupons he has out of the total number of coupons he kept.

Complete Question: Suresh has 4 coupon books, each with 6 coupons. He keeps 1/3 of the coupons and gives the rest away. Fifty percent of those he keeps are for the movie theater. Write and evaluate an expression to show how many movie theater coupons he has.

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Therefore , the problem of equation comes out to be Four is the solution when transformed into an equation.

An equilibrium is a rule that shows two expressions are equal by using the equals sign.The connotations of the measures the overall and its cognates might differ slightly among languages. For example, whereas in English an equation is really any well-formed formula made up of two expressions connected by the equals sign, an equation in French is defined as comprising one or more variables.

When attempting to solve a variable equation, the first step is to identify the variables with values that lead to equality.

The equation's solutions are the values of the unknown variables that satisfy the equality as well as the unknown variables that the equation should be solved.

Here,

8N+2N-6=34

10N-6=34

10N=40

N=4

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The lengths in the scale drawing are smaller than the corresponding lengths in the original figure.

When the scale factor is less than 1, the image of a shape will be reduced in size compared to the original shape. This means that all dimensions of the shape will be scaled down by the same factor. For example, if a shape is scaled down by a factor of 0.5, its length, width, and height will all be half the size of the original shape. Additionally, the area and volume of the image shape will be scaled down by the square and cube of the scale factor respectively.

In other words, when the scale factor is between 0 and 1 it will be a reduction and if it's greater than 1 it will be an enlargement.

As can be seen from the question, the scale factor is less than one as it is 1 / 3. This means that the lengths on the scale drawing would be smaller than the lengths on the original drawing.

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All possible solutions for inequality are (-∞,-7)U(-7, ∞).

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The inequality q/7 > -1 is a mathematical statement that compares the value of q/7 to -1.

To solve the inequality, we can start by isolating q on one side of the inequality.

To do this, we need to multiply both sides of the inequality by 7:

q/7 * 7 > -1 * 7

q > -7

Now we have the inequality q > -7, this inequality states that q is greater than -7.

To find all possible solutions for the inequality, we can use interval notation. The interval notation for the solution of this inequality is (-infinity,-7)U(-7, infinity)

It means all real numbers except -7, the solution set is an open interval.

Alternatively, we can also graph the solution set of the inequality on a number line, shading the region that represents the solution. The shaded region will be all the points to the right of -7 on the number line.

Hence, all possible solutions for inequality are (-∞,-7)U(-7, ∞).

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Horizontal dilation- If x is replaced by x/A in a formula and A>1, then the effect on the graph is to expand it by a factor of A in the x-direction (away from the y-axis).

If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1/A (towards the y-axis).

We use the word "dilate'' to mean expand or contract.

For example, replacing x by x/0.5=x/(1/2)=2x has the effect of contracting toward the y-axis by a factor of 2.

If A is negative, we dilate by a factor of |A| and then flip about the y-axis. Thus, replacing x by −x has the effect of taking the mirror image of the graph with respect to the y-axis.

For example, the function y=√-x, which has domain {x∈R∣x≤0}, is obtained by taking the graph of √-x and flipping it around the y-axis into the second quadrant.

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