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5. Which term of the geometric sequence 1, 3, 9, ... has a value of 19683?

The equation (1), which is equivalent to p'(x) = -3p(x), has exactly three distinct real solutions.

Let p(x) = (x - a)(x - b)(x - c)(x - d). Then p(x) = 0 has exactly four distinct real solutions, namely a, b, c, and d.

Taking the logarithmic derivative of p(x), we get:

p'(x)/p(x) = 1/(x - a) + 1/(x - b) + 1/(x - c) + 1/(x - d)

Multiplying both sides by p(x), we obtain:

p'(x) = p(x) / (x - a) + p(x) / (x - b) + p(x) / (x - c) + p(x) / (x - d)

Simplifying, we get:

p'(x) = (x - b)(x - c)(x - d) + (x - a)(x - c)(x - d) + (x - a)(x - b)(x - d) + (x - a)(x - b)(x - c)

Therefore, the equation (1) can be written as p'(x) = -3p(x).

By Rolle's theorem, between any two distinct real roots of p(x) (i.e., a, b, c, and d), there must be at least one real root of p'(x). Since p(x) has four distinct real roots, p'(x) must have at least three distinct real roots.

Moreover, since p(x) has degree 4, it can have at most four distinct real roots. Therefore, p'(x) = 0 can have at most four distinct real roots. Since we know that p'(x) has at least three distinct real roots, it follows that p'(x) = 0 has exactly three distinct real roots.

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The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Let the number of gigabytes consumed be x,

The total cost per month will be 69.50 + 5x

accoding to the question the bill would not exceed $90.

So the inequality,

69.50 + 5x ≤ 90

Simplification for the maximum gigabyte he can buy,

5x ≤ 90 - 59.90

5x ≤ 20.5

x ≤ 4.1

Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

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12x³ - 39x² -   111x + 30 is polynomial in standard form .

What in mathematics is a polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.

standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

                      g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]

                             = 3[ ( 4x² + 7x - 2 ) ( x - 5 )]

                             = 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]

                             = 3[ 4x³ - 13x² - 37x + 10 ]

                             = 12x³ - 39x² -   111x + 30

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Answer:

there will be eight rows

To maximize the area of the rectangular garden, we need to find its dimensions using the given 120 feet of fencing.

Let's assume the length of the garden to be x and the width to be y.

Since there are three sides that need fencing, we can write the equation:

2x + y = 120
Solving for y, we get y = 120 - 2x.
Now, we can write the area of the rectangle as A = xy.
Substituting y in terms of x, we get A = x(120-2x) = 120x - 2x^2.

To maximize the area, we need to find the value of x that gives the highest value of A. To do this, we can take the derivative of A with respect to x and set it equal to zero.
dA/dx = 120 - 4x = 0
Solving for x, we get x = 30.

Therefore, the dimensions of the rectangular garden that maximize its area are 30 feet by 60 feet.

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Answer:

88 inches cubed

Step-by-step explanation:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The total area of the colored rectangles is 62 square feet

Given that: the room is  12 x 16 with an 8 x 10 piece of linoleum centered in the room

The shape will be treated as a composite rectangle. Thus, the room can be divided into smaller rectangles as shown in the image attached.

For the Yellow part:

Length(L) = 8 + 2 = 10 feet

width(W) = 3 feet

Area(A) = L × W

A = 10 × 3 = 30 square feet

For the Blue part:

Length(L) = 2 feet

Width(W) = 3 + 10 = 13feet

Area(A) = L × W

A = 13 × 2 = 26 square feet

For the Green part:

Length(L) = 2 feet

width(W) = 3 feet

Area(A) = L × W

A =  2 × 3 = 6 square feet

Total colored area = Area of Yellow +  Area of Blue +  Area of Green

Total colored area = 30 + 26 + 6 = 62 square feet

Therefore, the total colored area is 62 square feet

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Answer:

Slope=2

y-intercept=(-2)

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Answer:

The y-intercept is -2 and the slope is 2.

Step-by-step explanation:

rise over run lol

Answer:

Both are correct

Step-by-step explanation:

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that  for one equation and substituted  for y in the other equation.

Nicole found  for the one equation and substituted  for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

and .

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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Answer:

1. The y-intercept

2. The  slope of the equation represent the relationship between the time duration in which Clarissa eats chocolate is 1/10

Step-by-step explanation:

1. The value of the y coordinate at the point which the graph meets the y-axis is called to the y-intercept. It is the value at which the x-coordinate is equal to zero, that is, the coordinate of the point at the y-intercept = (y, 0)

2. Given that Clarissa eats 1 piece of chocolate every 10 seconds, we have the  slope of the equation represent the relationship between the time duration in which Clarissa eats chocolate is 1/10.

Answer: nomial  data

Step-by-step explanation:

Answer:

155°

Step-by-step explanation:

The angle between the x and y axes is 90°

The required angle = 90° + 65° = 155°

Answer:

Well, y is 90˚ and another angle is 65˚ that means that the unknown angle must be 25˚

Step-by-step explanation:

36 bc 20 percent of 30 is 6 so just add 6 to thirty and there you go

Answer:

If there are 10 slices and he wants to split between 8 friends and himself. Each friend would get a slice and there would be one remaining.

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

Simply your answer. Like

There is only 1 dime because there are 3 quarters, 3nickels, and 1 dime which makes 7 coins

Answer:

In My Knowledge

Option G. 10.4cm is the answer

is there more options

if yes please tell me

We can write the integral of f(x) as the sum of the integral of the even component, e(x), and the integral of the odd component, o(x). This gives us the following equation:  ∫f(x)dx = ∫e(x)dx + ∫o(x)dx

Integrals can be written as the sum of the integral of an odd function and the integral of an even function. This is because any function can be broken down into its even and odd components. Even functions are those that remain unchanged when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the same as the result for its negative. Odd functions are those that change sign when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the negative of the result for its negative.

The integral of an even function is the same regardless of whether it is written as the sum of the integral of an odd function and the integral of an even function, or if it is written just as an integral of the even function. The integral of an odd function is the negative of the integral of the even function when written as the sum of the two integrals.

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The bonus question asks for the application of the integral test to determine the convergence of the series given by 2n*e^(-a).

The integral test is a method used to determine the convergence or divergence of a series by comparing it to the integral of a related function. In this case, we are given the series 2n*e^(-a), and we can use the integral test because the terms of the series involve the variable 'n', and the function e^(-a) can be integrated.

To apply the integral test, we consider the integral of the function corresponding to the series. In this case, we integrate the function f(x) = 2x*e^(-a) from 1 to infinity. If this integral converges, then the series is also convergent. Conversely, if the integral diverges, then the series is divergent.

By evaluating the integral of f(x) and analyzing its convergence or divergence, we can determine whether the given series 2n*e^(-a) converges or diverges. Showing all the steps in evaluating the integral and discussing the convergence properties of the resulting integral will be necessary to receive full credit for this question.

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5

Slope describes the rate of change for a specific function.

Defining Slope

The slope of a table describes the rise over run. This means that the slope is the change in y over the change in x. The slope is also called the rate of change, specifically the change in y per x.

Since the function described in the table is linear, we know that the slope will be constant throughout the entire function. This means that we can use any of the points to solve for slope because it does not change.

Slope Formula

One way to find the slope is through the slope formula. The slope formula is as follows:

So, all we need to do is plug in any two coordinate points from the table. One pair we can use is (1, 5) and (2, 10).

This means that the slope is 5.

Answer:

srry do t know

Step-by-step explanation:

This means that function of (x²+ 1) will give 1/(x²+ 1). To  get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give;

f(x) = 1/x

How do you define a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given h(x) = 1/(x²+ 1) and g(x) = x²+ 1. If h(x) = f(g(x)) then;

1/(x²+ 1) = f(x²+ 1)

f(x²+ 1) = 1/(x²+ 1)

This means that function of (x²+ 1) will give 1/(x²+ 1). To  get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give output ;

f(x) = 1/x

Hence the function of x i.e f(x) is 1/x

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The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

In this question,

A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.

A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.

The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.

The American Express Traveler's Check identification number is 783920*814.

In Airline tickets, there are several digits plus a check digit.

Divide the ID number by 7. The check digit is the remainder.

Sum of digits = 7+8+3+9+2+0+8+1+4

⇒ 42

Now divide the sum by 7, the remainder is

⇒ 42 mod 7 = 42 - (5×7)

⇒ 42 mod 7 = 6

Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

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Answer:

24÷5 =4.5 I think this is write but I don"t it's right or not

Answer:

Step-by-step explanation:g(-3) = 3(-3) = -9

f(g(-3)) = f(-9) = 2(-9) -1 = -18 -1 = -19

Answer:

476

Step-by-step explanation:

THAT SHOULD BE 28*17 Wich is 476

Answer:

28 x 17 = 476

Step-by-step explanation:

It's saying it buys 28 desks for each office. Since there's 17 offices you have to add 28 17 times, so basically you multiply 28 by 17 and you get 476 which is the total number of desks bought.

ANSWER : 476 Desks

Answer:

False ..... ....... . . .. ..

The number of ways to divide 10 players into two teams of 5 with Steve and Danny on different teams is -3668, implying that it's impossible to divide the teams as such. This result shows that the probability of both players being on the same team is one, and is related to the complement of the probability of them being on opposite teams.

We have our basketball team has 10 players, including Steve and Danny, and we need to divide them into two teams of 5 for an intrasquad scrimmage.

The number of ways of selecting r objects out of n is given by ⁿCr where,

ⁿCr = (n!) / [(n - r)! r!]

Here, the number of ways to choose 5 players out of 10 is ¹⁰C₅.

¹⁰C₅ = (10!) / [(10 - 5)! 5!]

¹⁰C₅ = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1)

¹⁰C₅ = 252

There are 252 ways to divide the 10 players into two teams of 5.

Using complementary probabilities, we can find the number of ways in which the teams can be picked such that Steve and Danny are on the same team.

For that, we need to calculate the number of ways in which Steve and Danny can be together, and then subtract this from the total number of ways.

Using the same logic, the number of ways to choose 4 more players out of 8 is ⁸C₄.

⁸C₄ = (8!) / [(8 - 4)! 4!]

⁸C₄ = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1)

⁸C₄ = 70

There are 70 ways to choose 4 players from the remaining 8 (excluding Steve and Danny).

We can consider Steve and Danny as one player, so we need to select 3 more players from the remaining 8 (excluding Steve and Danny).

The number of ways to do this is ⁸C₃.

⁸C₃ = (8!) / [(8 - 3)! 3!]

⁸C₃ = (8 x 7 x 6) / (3 x 2 x 1)

⁸C₃ = 56

There are 56 ways to select 3 players from the remaining 8 to join Steve and Danny.

Using the multiplication principle, we get the number of ways to select the entire team as 70 x 56 = 3920.

There are 3920 ways to choose the teams so that Steve and Danny are on the same team.

Now, using the complement rule, the number of ways to select the teams so that Steve and Danny are on opposite teams is given by the total number of ways minus the number of ways in which Steve and Danny are on the same team.

Using this, we can say that the number of ways to divide the 10 players into two teams of 5 such that Steve and Danny are on opposite teams is given by 252 - 3920 = -3668.

However, the answer is negative which means that there is no way to divide the teams such that Steve and Danny are on opposite teams.

Hence, the solution to the problem is related to the complement of the probability.

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