The maximal number of consecutive integers by using the expression [tex]2*sqrt(n*|a|).[/tex]
Let f(x) = ax^n + bx^{n-1} + ... + z be a polynomial with integer coefficients and degree n>1. According to the theorem of Tchebychev, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is bounded by the expression 2*sqrt(n*|a|), where a is the coefficient of the highest degree term of f(x).
For example, let f(x) = 3x^3 + 4x^2 - 5. The coefficient of the highest degree term is 3, and the degree of the polynomial is 3. Therefore, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is 2*sqrt(3*|3|) = 6.
To calculate this maximal number, we can follow these steps:
Identify the degree of the polynomial, n.
Identify the coefficient of the highest degree term, a.
Calculate the maximal number of consecutive integers by using the expression 2*sqrt(n*|a|).
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What is the solution to the equation 9(x + 2) = 27?
A. x = 2.5
B. x = 0.5
C. x = −0.5
D. x = −3.5
Jerry bought baseball cards for $5.25 each, and then sold them for $6.30 each. How much profit, in dollars, did Jerry make for selling each one of the baseball cards?
Answer: $1.05
Step-by-step explanation:
The profit made will be calculated as the difference between the selling price and the cos price. This will be:
= Selling price - Cost price
= $6.30 - $5.25
= $1.05
Therefore, Jerry will make $1.05 profit on each baseball card that's sold.
Line segment ST and point P are shown below. The live segment undergoes a stron by a scale loctor of 15 through Cera Pro produce line na ST 5 S Which of the following equations are true? Select all that apply A S'T' = 5.5 B S'T' = 6 ST с 1.5 ST ST" D 2. ST
Answer: Option B
Step-by-step explanation:
The perimeter of a square room is 80 feet. How many floor tiles 1 foot square would be needed to cover the area of the room
We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.
If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.
Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.
To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.
So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.
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A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center 0f dilation. which rule could represent this dilation?
Answer:
.
Step-by-step explanation:
......
.........................
Find the gradient between the points (1,5)
and (-4,20)
Answer:
(20-5)/(-4-1)
15/-5= -3
What is the greatest common factor of 24,40,32 A.1 B.2 C.4 D.8
Answer:
D. 8
Step-by-step explanation:
8*3=24
8*5=40
8*4=32
need help with this kinda confusing
Answer:
m/_A= 84
Step-by-step explanation:
PLEASE HELP!
Which of the following measures can have more than one value for a set of data?
-Mode
-Mean
-Median
Answer:
Mode
Step-by-step explanation:
The median and mean can only have one value for a given data set. The mode can have more than one value
Answer:
Step-by-step explanation:
Shana, who lives in Canada, and Pearl, who lives in Pennsylvania, were discussing the weather. Shana complained about the cold temperature of Negative 20 degrees Celsius. Pearl, who lives in Pennsylvania, mentioned that her temperature was the opposite of Shana’s. Which is the correct way to represent “the opposite of Shana’s temperature is equal to Pearl’s”?
Answer:
You can represent "the opposite of Shana's temperature is equal to Pearl's" as follows:
(-20 C) + (-x) = x
Where x represents Pearl's temperature.
Alternatively, you can also write it as:
20 C - x = x
Both of these equations are equivalent and mean the same thing: the opposite of Shana's temperature is equal to Pearl's temperature.
Step-by-step explanation:
20 degrees Celsius
The temperature in Pennsylvania is the opposite of the temperature in Canada, therefore -20⁰ Celsius in Canada would then be 20⁰ Celsius in Pennsylvania.
There are 14 teams in a basketball league.
Each team plays every other team twice
during the season.
a) Suppose that you want to determine
how many games, in total, are played.
Suggest a simpler problem that you
could solve first.
b) How many games, in total, are played
during the season?
Please I need deep explaining.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
Definition of combinationCombinations are operations in mathematics that count the number of possible combinations that can be created from a set of items, where the selection's direction is immaterial. You are free to select any arrangement of the parts. Permutations and combinations can be mixed up.
Here,
There still are 14 teams in all, but each team plays the other twice.
Every team plays almost every team twice, hence the total amount of games played is simply the permutations of 2 out of 14, which is determined by:
₁₄P₂
=14!/((14-2)!)
= (14×13×12!)/ 12!
= 14×13
=182
Consequently, there were 182 games played in all.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
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Find the distance represented by 4.9 inches if 1 inch = 50 miles.
OA. 4.9 miles
B. 49 miles
C. 209 miles
D. 245 miles
O E none of these
write an inequality to describe the graph below ): tysm<33
Answer:
[tex]y\leq \frac{3}{2}x+1[/tex]
Hope this helps! :)
HELP PLEASE!! really need this
Answer:
153
Step-by-step explanation:
Just plug the 9 in for every x in the equation. Your final answer should be 153.
After getting new carpet installed, Antonio noticed that the door would not close. He decided to trim 1/16 of an inch off the bottom of the door to see if it would help. After doing this three more times, the door finally closed. If the door was originally 84 5/8 inches tall, how tall was it after he trimmed it?
After he trimmed it, it was [tex]84\frac{3}{8}[/tex] inches tall. This can be solved using expression.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.
There are three different expression types:
There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.The expression becomes:
= [tex]84\frac{5}{8} - [{4 * (\frac{1}{16})][/tex]
= [tex]84\frac{5}{8} - [\frac{1}{4}][/tex]
= [tex]84\frac{3}{8}[/tex]
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make a the subject 11a = 7b
Answer:
a=7b/11
Step-by-step explanation:
11a=7b
11a/11=7b/11
a=7b/11
Answer: 11a=7b
-divide 11 from both sides
you'll end up with this result:
a=7b/11
Marius buys computers for £915.00 each and sells them for £2081.00 each. What is his total profit on the sale of 13 computers?
Answer:
£15158.00
Step-by-step explanation:
The profit on the sale of 1 computer is the difference between the selling price and the buying price.
Profit on 1 computer:
£2081.00 - £915.00 = £1166.00
The profit on 13 computers is 13 times the profit on 1 computer.
13 × £1166.00 = £15158.00
Answer: £15158.00
PLZ HELP, AM BEING TIMED
Answer:
216
Step-by-step explanation:
What ordered pairs are the solutions of the system of equations shown in the graph below?
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
Ordered pair: what is it?The term "ordered pair" refers to a pair of two variable that are shown in a way that they convey a specific order.
In an order pair, the first term denotes the x- and second term, the y-coordinates. The ordered pair is written in close brackets as shown in the example below.
Here ,
Is an equation system:
A set of equations is referred to as a system of equations when a limited set of equations is available and a common solution is sought.
The intersection of two lines, for the two equations drawn on a graph, represents the system's solution.
In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
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The perimeter of a rectangle is 84 cm. the length is 3 cm shorter than the width. find the length and width of the rectangle.
Taking into account the definition of a system of linear equations, the length and width of the rectangle is 22.5 cm and 19.5 cm respectively.
System of linear equationsSystems of linear equations are groupings of first degree equations with the same unknowns, of which a common solution must be found.
In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.
Number of sodas and hot dogs soldIn this case, a system of linear equations must be proposed taking into account that:
"x" is the length of the rectangle."y" is the width of the rectangle.You know:
The perimeter of a rectangle is 84 cm. The perimeter of a flat geometric figure is called the length of its contour. It is obtained as a result of the sum of the sides of a flat geometric figureThe length is 3 cm shorter than the width.The system of equations to be solved is
2x + 2y= 84
x= y + 3
The substitution method is a way to solve systems of equations. To use the substitution method, you choose an equation and find an expression for one of the variables in terms of the other variable. Then substitute that expression for the variable in the other equation.
In this case, substituting the second equation in the first one you get:
2×(y+3) + 2y= 84
Solving:
2y+ 2×3 + 2y= 84
2y+ 6 + 2y= 84
2y + 2y= 84 - 6
4y= 78
y= 78÷4
y= 19.5
Replacing this value in the second equation, you get:
x= 19.5 + 3
x= 22.5
Finally, the length of the rectangle is 22.5 cm and the width of the rectangle is 19.5 cm.
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the total cost of the airline ticket is $432, including an 8% tax. What was the cost of the ticket before the tax was added?
Is X² is a variable?
A is the variable and X is the coefficient term in the supplied X2 expression. An algebraic expression is used to solve a particular mathematical problem .
what is variable ?In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
given
The coefficient term is denoted as X2, and the variable is A.
An algebraic expression is used to solve a particular mathematical problem by combining words and numbers.
For instance, the numerical coefficient in the equation 5x is 5, meaning that the variable x has been multiplied by 5 times.
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160 m of fencing to enclose a quadrilateral shape pen (3 sided) for a children's play area. Determine the shape of the children's play area that gives the maximum area.
Answer:
A square of side length 40 m will give the maximum area of the play area
Step-by-step explanation:
Mathematically, it has been established that a square gives the maximum area of a quadrilateral
Hence, for us to have a maximum area of the given perimeter, we have to divide the perimeter by 4 to get the side length of the square
From what we have, we know that the perimeter of the fencing is 160 m
To get the side length, we divide the perimeter by 4
Side length of the shape would be 160/4 = 40 m
1. y=-1
y = 2x - 7
Hello, and I am confused on this question I was wondering if anyone could help!
-35PTS- what theorem can be used to prove these triangles are congruent
Answer:
Neither----------------------------
We see two sides and one angle marked as congruent on both triangles.
The congruent angle is not included.
It means we can neither state it is ASA nor SAA as both of these require two congruent angles.
Round 806,713 to the nearest thousand and 7,925,024 also 6,481,525
A gallon of gasoline carries with it about 1.3 x 108 J of energy. Given a price of $3 per gallon, how many Joules can you get for a dollar
By unitary method, you can get joules by $1.
What is the unitary percentage method?When given a percentage of an amount, the unitary method can be used to determine the full amount. For instance, if $23 represents 10% of a sum of money, then $10 times $23 equals $230. $6000 is equal to 8% of a sum of money.
Price of 1 Gallon= $3
Energy produced by 1 gallon = joules
by $1 , you can get 1/3 gallon
energy produced by 1/3 gallon = = joules
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CAN ANYONE PLEASE HELP ME ON THIS!!
Answer:
8. b
9.C
10.a
11.a
12. c
13. b
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Adrianne is reading a book. She reads 275 pages and has 155 pages to go. How many pages p is Adrianne’s book? Write and solve an equation to find the book’s length in pages
There will be a total of 430 pages in the book or the length of the book in pages = 430.
Adrianne reads 275 pages
She is left with 155 pages.
So, for converting the above in form of an equation,
Let us assume that the total pages in the book be x
Let us assume that the total number of pages she read = a
Assuming that the total remaining pages that she does not read = b
So, the total number of pages will be = total pages which she read + total remaining pages.
=> x = a+b
Now, solving the values given in the questions,
The value of a = 275 and the value of b = 155
So, the total number of pages in the book = 275+155 = 430
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Where is the quadrant 1?
The quadrant 1 of the graph is in the place of upper right quadrant.
the term graph in math is referred as a non-linear kind of data structure made up of nodes or vertices and edges
Here we have given that we have to find the place of quadrant 1.
In order to find that we must know that definition of quadrant in math that is one other than the region/part of a cartesian plane which is obtained when the two axes intersect each other and it is used to determine the position of a point in a plane.
As we all know that the first quadrant is in the upper right-hand corner of the plane.
And here we all also know that both x and y have positive values in this quadrant.
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