An equation in which the highest power of the variable is 1 is known as a linear equation. It is also termed a one-degree equation.
There are two types of linear equations, linear equations in one variable and linear equations in two variables. The standard form of a linear equation in one variable is Ax + B = 0. Where x = variable, A = coefficient and B = constant.
The standard form of a linear equation in two variables is Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always formed in a straight line. That is why it is named a 'linear equation'.
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Let f be a polynomial with integer coefficients, of degree n>1. What is the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),...
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 are the values of trigonometric ratios?
three main trigonometry ratios are sin ,cos and tan.
1- Sine or sin θ = perpendicular / Hypotenuse .
2- Cosines or cos θ = base of triangle / Hypotenuse .
3- Tangent or tan θ = perpendicular of triangle / base of triangle.
Trigonometry
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Trigonometric values are based on the angle theta and the values of the sides of triangle in which the theta angle is made.
for example - value of sin theta is equal to the side opposite to the theta angle divided by hypotenuse of the triangle and we will get the values of the sin trigonometric ratio.
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What does 8 mean in math?
The number 8 (eight) is represented by a number and numeral.
It is the natural number that follows seven and precedes nine. Given that it is an integer and a cardinal number, it can be counted. It is distinguished from imaginary numbers by being categorised as a real number.
Eight is a composite number, and its proper divisors are 1, 2, and 4. Eight can be written as 23, which when said aloud sounds like two cubed. It has a 7 aliquot total. All powers of two add up to an aliquot that is one less than their own.
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Anna's hair has grown
2
3
of an inch in the 6 weeks since her last haircut. How fast does her hair grow?
Answer:
Her hair grows 1/9th of an inch. Hope this helped you
Step-by-step explanation:
How do you plot a graph step by step?
Plotting a graph step by step is mentioned below.
Define Graph.In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
What is Bar graph?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
There are a few steps to follow when plotting a graph:
Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.To know more about graph visit:
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In 2010, the population of a city was 191,000. From 2010 to 2015, the population grew by 3.9%. From 2015 to 2020, it fell by 3.3%. To the nearest 100 people, what was the population in 2020?
Answer:
The population by 2020 is 191,900
Step-by-step explanation:
Given that;
population 2010 (population in 2010): 191000
the population grew from 2010 to 2015: by 3.9%
so, population by 2015 = [tex]191000(1 + \frac{3.9}{100})[/tex]
= [tex]191000(1 + 0.039)[/tex]
= [tex]191000(1.039)[/tex]
= [tex]198449[/tex]
the population drop from 2015 to 2020: 3.3%
so, population by 2015 = [tex]198449(1 - \frac{3.3}{100})[/tex]
= [tex]198449(1 - 0.033)[/tex]
= [tex]198449(0.967)[/tex]
= [tex]191,900.183[/tex]
help anyone or somebody please o^o
Answer:
27 degrees
Step-by-step explanation:
Sum of angles in a triangle is 180 degrees.
x + 40 + 113 = 180
x + 153 = 180
x = 180 - 153
x = 27 degrees
Solve the quadratic by factoring. 3x^{2}+7=-8x+3 3x 2 +7=−8x+3
The roots of the given quadratic equation are x = -2/3 and x = -2.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is a quadratic equation as follows -
3x² + 7 = - 8x + 3
The given quadratic equations are -
3x² + 7 = - 8x + 3
3x² + 8x = 3 - 7
3x² + 8x + 4 = 0
(x + 2/3)(x + 2) = 0
(x + 2/3) = 0 and (x + 2) = 0
x = -2/3 and x = -2
Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.
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Which ordered pair is not a solution to the inequality 2x+4y<9
Answer:
2x+4y,9
Step-by-step explanation:
A triangle has side lengths of (4b−5c) centimeters, (9b+10d) centimeters, and (6d−8c) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
need help asap!!!! will give brainliest!
Answer:
Y = 3 [tex]\sqrt{2}/2[/tex] And x = 3
Step-by-step explanation:
Because this is a 45 to 45 degree triangle, the 3 * (square root of 2 )/2 is y as well. Because this is a 45-45 triangle, x should be y (Square root of 2). Therefore, replacing y with 3 * (square root of 2 )/2 and multiply the square root of 2, the answer for x is 3. If I got something wrong please tell me, thanks.
guess what answer correcly its a classic ill give you brailynes
Answer:
Um.. Hello there. You haven't added any links to this post so we cannot see what the question was. Sorry to bother you!
What is the value of x in this equation?
−4x+8=42
Answer:
x = -8.5
Step-by-step explanation:
-4x+8=42
first subtract both sides by 8
-4x = 34
divide both sides by negative 4
x = -8.5
which value in the set {5,6,7,8,9} is a solution of the equation 21 - f = 13? Show your work.
Answer:
f=8
Step-by-step explanation:
Other way is to rest 21 by 13 that will give you 8.
Identify the function that is exponential
Answer:
d. y=-3(0.5)^x
Step-by-step explanation:
since all other functions are ^ of a number, whereas the odd one out is d with an x as an exponent
therefore y = -3(0.5)^x is exponential
hope this helps:)
Find the volume of the prism.
1.2 cm
1.8 cm
2 cm
2.3 cm
The volume is
cubic centimeters.
Answer:
Volume of prism = 6.3 cm³
Step-by-step explanation:
Given:
Dimensions of parallels line = 2.3 and 1.2 cm
Height of prism = 1.8 cm
Width of prism = 2 cm
Find:
Volume of prism
Computation:
Volume of prism = Area of base x Width
Volume of prism = [(1/2)(sum of parallels line)(Height)]Width
Volume of prism = [(1/2)(2.3 + 1.2)(1.8)]2
Volume of prism = [(1/2)(3.5)(1.8)]2
Volume of prism = [(3.5)(1.8)]
Volume of prism = 6.3 cm³
Ason is organizing the silverware drawer. He has 8 spoons. There are twice as many forks as spoons. There are 34 as many knives as forks. How many knives does Jason have
The result of two Newton's technique iterations to approximation a function's zero using the provided starting guess is 1.5262!
What is a formula that is iterative?Iteration describes carrying out a process repeatedly. To get a new value, start with an initial value and enter it into the iteration formula. To solve an equation using iteration, apply the new value for the subsequent substitution after that, and so on.
By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1, and by using the previous guess, xn, like so-
xn+1 = xn - f(xn)/f'(xn)
and herethe case is [tex]f(x) = cos(x), and so f'(x) = -sin(x).[/tex]
Also, furthermore, [tex]cos(x)/(-sin(x)) = -cot(x).[/tex]
here, we have to simplify the formula to get a better guess for a zero to: xn+1 = xn + cot(xn)
[tex]x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...\\And x3 = 2.06170... + cot(2.06170...) = 1.52615...\\Ans = 1.5262![/tex]
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NEED ANSWER ASAP GIVING 15 PTS!!! TEST DUE IN 5 MINS!!!
Given the rule y=12x−4 complete the table below.
Answer:
(-4,-52)
(1/12,-3)
(1/3,0)
(0,-4)
(3,32)
Step-by-step explanation
i think thats right
What is the largest prime factor of 999?
Answer:
37
Hope this helps :)
what is 1 half of 2 thirds
Is the second side “LK and HI” or the other way around?
Answer:
They aare both the same
Step-by-step explanation:
please help I'll give a crown if you answer correctly.
Answer:
2) 1. 73
2. 107
3. 73
4. 107
5. 73
6. 107
7. 73
8. 107
4) 1. 46
2. 134
3. 46
4. 134
5. 46
6. 134
7. 46
8. 134
Step-by-step explanation:
Vertical, corresponding, alternate exterior, and alternate interior angles are all congruent (equal).Angles such as same side exterior and same-side interior are supplementary; meaning these angles add up to 180°.i need help plz and thanks
Answer:
[tex]\pi{r}^{2} [/tex]
[tex]\pi {(13.5)}^{2} [/tex]
27 is the diameter so u divide it by 2 to get the radius which is 13.5
equals 572.56
HELP HELP HELP I NEED HELP ASAP
How Do I answer this question
Answer:
You say help is no more
Step-by-step explanation:
is triangle ABC similar to CDE?
Answer:Yes
?=6
Step-by-step explanation:
they sare the same angle 55 and angle
Answer:
Triangle ABC is similar to triangle CDE
?=8
Step-by-step explanation:
We can set up a proportion: x/12=8/12. We can use cross multiplication to get 12x=96 which would x=8.
The triangles are similar since both of them have 55 degrees as one of the angle measures.
A solid metal sphere with diameter 6cm needs to be covered with a protective
material which costs £0.25 per cm2.
How much will it cost to cover the sphere with the material?
Give your answer rounded to 2 DP.
Answer:
It will cost: £28.28
Step-by-step explanation:
Area of sphere = 4 x π x r2
Area of Circle = 4 x π x 3^2 = 113.097 (radius is half of diameter)
113.097 / 0.25 = 28.28
What is the axis of symmetry of the function f x =-( x 9 )( x 21?
The axis of symmetry of the function f(x) = -( x 9 )( x 21) is x = 15.
The axis of symmetry of a parabola is a line that divides the parabola into two exact mirror images. In this case, the parabola is defined by the quadratic function f(x) = -(x-9)(x-21). To find the axis of symmetry, we can take the average of the x-coordinates of the two solutions, which are 9 and 21. The average of 9 and 21 is 15, so the axis of symmetry is x = 15. This means that the parabola is symmetrical about the line x = 15, and the vertex of the parabola is located at the point (15,0).
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Are machines faster and better at calculating a math equation than mans?
Answer:
MIT economics professor Richard Bookstaber put it simply in his book “The End of Theory”: “No man is better than a machine, and no machine is better than a man with a machine.” ... Humans are too emotion-driven and susceptible cognitive biases, while machines lack an understanding of human thinking.
Answer:
yesThe Liverpool researchers estimate that the robot is able to work 1,000 times faster than a human scientist, and highlight that it is “unlikely a human researcher would have persevered with this multivariate experiment using manual approaches given that it might have taken 50 experiments or 25 days
The sum of 5 times a number and 3 is 7.
Use the variable y for the unknown number.
PLEASE HELP!!!
Answer:
5y+3=7
Step-by-step explanation:
What is the perimeter?
Help plz...
And No links!! I repeat No links!!
Answer:
b=4
perimeter=12
Step-by-step explanation:
frist find b by using pythagory theorm
the a+b+c=perimeter