Kara has 10 books on a shelf and decides to move 3 of them to an empty shelf. In how many different ways can the empty shelf be filled?

As per the rational root theorem, the actual root of the polynomial is  - 5/2

The term polynomial refers the algebraic expression in which the exponents of all variables should be a whole number

Here we have given that  f(x) = 6x⁴ + 5x³ – 33x² – 12x + 20.  and we need to find which is an actual root of f(x).

In order to find the root for the polynomial we have to apply each value as the replacement of x in the polynomial.

And then we have to find in which one makes the polynomial result as zero.

First we have to take the value of x as -5/2, then the polynomial equation be like,

Here we have to substitute x=-5/2, then we get

=> f(-5/2) = 6(-5/2)⁴ + 5(-5/2)³ - 33(-5/2)² - 12(-5/2) + 20

=> f(-5/2) = 6(625/16)-5(125/8)-33(25/4)+30+20

when we simplify this one then we get,

=> f(-5/2)=(1,875-625-1,650+400)/8

=>  f(-5/2)=0/8

Here we know that if we zero by any number we get the result as zero.

Therefore, f(-5/2)=0 then x=-5/2 is a root of f(x)

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Answer:

its A

Step-by-step explanation:

Just took the test

(A) Given question can be represented in the system of linear equations as x + y = 360,

      y =3x

(B) 90 tickets were sold on Friday and 270 tickets were sold on Saturday.

There will be only one solution to this question.

(C) We have drawn the graph for the solution.

(D) We have justified our answers by using the substitution method.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let x number of tickets sold on Friday and y number of tickets sold on Saturday.

By using the given condition,

x + y = 360 ----------(I)

y =3x -------(II)

Put y = 3x in equation (I), we get

x + 3x = 360

4x = 360

  x = 90

Now put x = 90 in equation (I), and we get

90 + y = 360

y = 270

Hence, 90 tickets were sold on Friday and 270 tickets were sold on Saturday.

There will be only one solution to this question.

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Range with three parameters: start, end, step.

Now, According to the question:

What are the 3 loops in Python?

The three types of loop control statements are:

What are the three parameters in range in Python?

The range() function in Python works by taking three inputs as parameters which are start_value, stop_value, and step value. The range() function returns an immutable sequence of numbers starting from the start_value, and increments the values by the value given in the step_value, and stops at the stop_value.

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You represent three consecutive odd integers with x, x + 2 and x + 4

From the question, we have the following parameters that can be used in our computation:

Three consecutive odd integers

As a general rule

Odd integers are integers that cannot be divided by 2

Consecutive odd integers have a difference of 2

This means that the three consecutive odd integers are

x, x + 2 and x + 4

Where the least of the integers is x

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We find the inverse of a 2x2 matrix on a calculator using formula

A⁻¹ = Adjoint of A / determinant of A

Where, adjoint of A = [ d  -b]

                                    [-c   a]

and, determinant of A = 1/ ad - bc

A real number's inverse is a number that, when multiplied by the inputted number, yields the multiplicative identity, which is 1, or 1. A matrix's inverse, represented by A⁻¹ in matrices, is a matrix that, when multiplied by A, yields the identity matrix I, or A.A⁻¹ = A⁻¹.A = I

The formula (adj A)/(det A) can be used to determine the inverse of a matrix A, where "adj A" stands for "adjoint of A" and "det A" for "determinant of A".

Let A is a 2x2 matrix such that, A = [a  b]

                                                          [c  d]

then, A⁻¹ = Adjoint of A / determinant of A

Where, adjoint of A = [ d  -b]

                                    [-c   a]

and, determinant of A = 1/ ad - bc

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The geometric sequence 2, −6, 18, −54, ... to represent the 9th term is

d. f(9)=f(8)+3(8)

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number, called the common ratio. In the given sequence, the common ratio is -3, so the nth term of the sequence can be found by multiplying the previous term by -3.

Using the recursive formula for a geometric sequence, the nth term can be found by multiplying the first term, f(1), by the common ratio raised to the (n-1) power, or f(n) = f(1)•(-3)^(n-1). In the given sequence, f(1) is 2, so the 9th term can be found by multiplying 2 by -3 raised to the 8th power, or f(9)=f(1)•(-3)^8.

Alternatively, the nth term can also be found by multiplying the previous term, f(n-1), by the common ratio, or f(n) = f(n-1)•(-3). Since the 8th term in the given sequence is -54, the 9th term can be found by multiplying -54 by -3, or f(9)=f(8)•(-3).

Therefore, the 9th term in the given sequence is -486 and the correct answer is d. f(9)=f(8)+3(8).

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Regional economic integration has facilitated trade among neighbors while allowing nations to concentrate on issues pertinent to their stage of development. Four forms of regional economic integration are possible. Zone of unrestricted trade. The most basic form of economic cooperation is this one.

Worldwide integration of the markets. global integration of the economy. On the financial markets, the effects of globalization are being assessed. More than ever, people, companies, and sectors are linked. This facilitates linkages, which encourages specialization, innovation, and economic expansion.

These accords have made it possible for nations to trade successfully with one another today by removing trade and financial restrictions. actions taken to lower prices for consumers in the member countries of the bloc when tariffs are decreased

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Answer:

f is negative

Answer:

4 1/3, 4.337, 35/8, 4.44

Step-by-step explanation:

4.337, 4 1/3, 35/8, 4.44

4 1/3 = 13/3 = 4.333

35/8 = 4.375

So, the order from least to greatest is: 4 1/3, 4.337, 35/8, 4.44

Answer:

4 1/3, 4.337, 35/8, 4.44

Step-by-step explanation:

"order from least to greatest" means put the smallest first and each next one bigger and the biggest one last.

Change everything to decimals to compare.

A fraction bar is just a division symbol.

1/3 means 1÷3 which is .33333...

4 1/3 = 4.33333...

35/8 means 35÷8

= 4.375

Smallest is 4.333...

So 4 1/3 goes first.

Then 4.337 and next 35/8 (bc 4.375)

Last is biggest 4.44 so it goes last.

In order from least to geatest is:

4 1/3, 4.337, 35/8, 4.44

Answer:

Rounding down to the nearest whole number, we get 5 stories. The correct answer is, therefore (A) the 5th story.

Step-by-step explanation:

To solve this problem, we need to find the number of stories the ladder can reach by dividing the length of the ladder by the height of each story.

The longest ladder on the fire truck reaches 95 feet, and each story is 18 feet high, so the highest story that the ladder can reach is:

95 feet / 18 feet/story = <<95/18=5.28>>5.28 stories

Therefore, the solution to this problem is  (x - 2)(x + 3) are the factors of p(x) (2x - 5).

An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.

Here,

Given, the polynomial in this case is 2x3 - 3x2 - 17x + 30.

It is necessary to factor the polynomial.

Let p(x) equal 2x3, 3x2, 17x, and 30.

P(xconstant )'s term is 30.

Factors of 30 are equal to 1, 2, 3, 5, 6, 10, 15, and 30.

Consider x = 2.

Replace x = 2 in p. (x),

2(2)³ - 3(2)² - 17(2) + 30 =p(2)

=> 2(8) - 34 - 3(4) + 30

= >16 - 16

= 0

So, x - 2 is a factor of 2x³ - 3x² - 17x + 30.

Now splitting the x² and x terms,

2x³ - 4x² + x² - 2x - 15x + 30= 2x³ - 3x² - 17x + 30

=> x(x - 2) - 15(x - 2) +  2x²(x - 2)

= > (x - 2)  *  (2x² + x - 15)

factoring  2[tex]x^{2}[/tex] + x - 15

= 2[tex]x^{2}[/tex] + 6x - 5x - 15

= - 5(x + 3)  +  2x(x + 3)

= (x + 3)(2x - 5)

Therefore, the solution to this problem is  (x - 2)(x + 3) are the factors of p(x) (2x - 5).

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Answer: x=2, y=-8

Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution

to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case

so we have 13x-6y=22 and x=y+6

for the x value of the first equation, plug in x=y+6 from the second equation to get:

13(y+6)-6y=22

then you solve for y,

13y+78-6y=22

7y=-56

y=-8

then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6

so you'd have x=(-8)+6 to give you x=2

hope this helps!

There are 3 methods to find the largest and smallest number in an

unsorted integer array Python.

Method 1:

Method 2:

Method 3:

There are 3 methods to find the largest and smallest number in an

unsorted integer array Python.

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The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.

What is inequality ?

If an inequality has no real solution, this means that there are no numbers that can be substituted into the inequality to make the statement true. If an inequality has all real numbers as the solution, this means that every real number can be substituted into the inequality to make a true statement.

Have given,

x > 3 and x < 5

Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .

The region of the line greater than 3 and less than 5 that number is 4.

Hence,

The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers .

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Have given,

x > 3 and x < 5

Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .

The region of the line greater than 3 and less than 5 that number is 4.

The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.

Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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Answer:

34 cm

Step-by-step explanation:

the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2

4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34

The elements in sets are separated by commas so they can be read easily.

Instead of describing the constituents of a set, a set-builder notation describes them. The elements are listed, for instance, in the set {5, 6, 7, 8, 9}. We interpret the collection of all x such that x is a counting number between 4 and 10 as the collection of all x.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets {}; for instance, A = {1, 2, 3, 4} is a set.

The sequence of elements (separated by commas) between the curly braces " and "in mathematics form an unordered group of elements known as a set. For instance, the domesticated animals {cat, cow, dog} , the odd numbers {1, 3, 5, 7, 9} and the alphabets {a, b, c, d, e} are all sets. So they can be read or interpreted easily.

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Answer:

Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:

x-6

Answer:

a. $660

b. $3660

Step-by-step explanation:

a. 1.1% = 1 years

   22% = 20 years

22% = 0.22

Take 3000 times 0.22 = $660

So, they will earn $660 interest in 20 years

b. $3000 + $660 = $3660

$3660 is their account balance after 20 years

We know that,

Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.

According to question.

Given data,

Factor of a= a

Factor of b=b× b× b× b

Factor of c=c× c× c× c× c× c× c

Therefore,

Factor of a=a× a× a× a× a ×a ×a

Factor of b4=b ×b ×b× b

Factor of c=c

Greatest common factor=ab4c

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Answer:

Para encontrar a taxa trimestral equivalente à taxa de 1,05% ao mês, basta dividir a taxa mensal por 3, pois um trimestre é composto por 3 meses. Portanto, a taxa trimestral equivalente à taxa de 1,05% ao mês é de 1,05% / 3 = 0,35%.

Para encontrar a taxa anual equivalente à taxa de 1,05% ao mês, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa anual equivalente à taxa de 1,05% ao mês é de 1,05% x 12 = 12,6%.

2)a) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre, basta multiplicar a taxa mensal por 6, pois um semestre é composto por 6 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre é de 1% x 6 = 6%.

b) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano é de 1% x 12 = 12%.

Answer: C: pay the complete balance each month

The income of whales star after 3 years and getting 19% rise every year will be  $1685159 .

Given, The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years .

To get the salary of whale star after 3 years of increment with 19%.

Salary =  $1 million

Salary after 1st increment =  $1 million +  $1 million of 19%

Salary after 1st increment = $1190000

Salary after 2nd increment =  $1190000 + $1190000 of 19%

Salary after 2nd increment = $1416100

Salary after 3rd increment =  $1416100 + $1416100 of 19%

Salary after 3rd increment = $1685159

Final salary after 3 years will be  $1685159.

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4x + 8y ≤ -24 is the example of linear inequality in two variables.

Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

For example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

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Answer:

-----------------------------------

Hypotenuse of an isosceles triangle is √2 times the leg:

Answer: f(x)= 2x+ 1

Step-by-step explanation:

Let's set up an equation

f(x)=mx+b

We know it's 3 inches tall and grows 2 inches weekly.

Our equation is

f(x)= 2x + 1

Now let's test the week is 1

f(1) = 2(1) +1

f(1) = 3

Let test the week is 2

f(2) = 2(2)+1

f(2) = 5

So we know this equation work

Answer:

one solution because when you isolate the x terms:

2x-3x=0 and you combine like terms

-x=0

and divide by negitive one because -x is (-1)(x)

you get x=0

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

It appears this problem has no solution, buttt let's look closer.

2x and 3x are like terms, meaning they can be added and subtracted because they both have x!

So let's combine these like terms and see what we get...

2x = 3x

0 = 3x -2x

0 = 1x

x = 0 / 1

x = 0

The only solution is 0! No other number is possible.

There is no input mapped into two or more outputs in the given relation:

(-3,4) (6,0),(-3,4),(-8,-2)

Thus, the relation is a function.

A relation maps elements of a set (inputs, usually defined by the variable x) into elements of another set (outputs, usually defined by the variable y).

So, for example, the coordinate pair (x, y) means that a relation is mapping the input x into the output y.

A relation is also a function if there is no input being mapped into two or more outputs.

For the case of the given relation:

(-3,4) (6,0),(-3,4),(-8,-2)

The mappings are:

-3  → 4   (this one appears twice)

6  → 0

-8  → -2

So no input is mapped into two or more outputs, then the relation is a function.

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