A set of all rational and irrational numbers is called the real numbers. All real numbers can be plotted on the number line. It is not imaginary number which cannot be quantified. It is denoted by capital Latin letter R.
Rational numbers are number that can be expressed as p/q where p and q are integers and value of q not equal to 0.
For example, -3/4, 5/3, 6/1.
Irrational numbers are not rational numbers but they can be plotted on the number line. It cannot be expressed as a simple ratio.
For example π, √2, -√7.
But √(-7) is an imaginary number.
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What is the end behavior as x → − [infinity] f/x →?
Using the concept of limit, As the x tends to -infinity value, In the expression f/x, The answer is f/x tends to large(infinity) value with negative magnitude.
What do you mean by limit in mathematics?A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals. A limit describes the value that a function approaches as its inputs approach a certain value. All calculus is based on the concept of a limit.
What is the limit rule?According to product law for limits, the limit of a product of functions is equal to the sum of the limits of each individual function. The limit of a quotient of functions is equal to the quotient of the limit of each function, according to the quotient law for limits.
as [tex]\lim_{x \to \infty} \frac{f}{x}[/tex]
=f/ -infinity
=- [infinitely large value]
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How do you show that f and G are inverses of each other?
First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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If triangle LMB is dilated by a scale factor of 0.5, which of the following statements is not true?
A. Triangle LMN is similar to triangle L’M’N’.
B. Triangle L’M’N’is smaller than triangle LMN
C. The sides of triangle LMN are congruent to the sides of triangle L’M’N’.
D. The angles of triangle LMN are congruent to the angles of triangle L’M’N’.
According to the properties of geometry the correct option is C.
What is geometry?
The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.
Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.
If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.
Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.
It is given that LMN is dilated by a scale factor of 0.5.
Since scale factor is lies between 0 to 1, therefore it shows the compression.
Therefore sides of L'M'N' is smaller than LMN.
Since corresponding angles of similar figure are congruent.
So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.
Therefore option C is correct.
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which statement correctly compares the function shown on this graph with the function y=6x+1
The correct statement regarding the comparison of the linear functions is given as follows:
D. The function shown on the graph has a lower slope and a lower starting point.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the output variable y relative to the input variable x, that is, the change in y when x is increased by one.
Function y in this problem in this problem is given as follows:
y = 6x + 1.
Considering the slope-intercept definition, we have that:
The slope is of 6.The starting point is of 1.From the graphed function, we have that:
The slope is of 5, as when x increased by 2, from x = 0 to x = 2, y increased by 10, from -6 to 4.The starting point is of -6, which is the value of y when the function crosses the y-axis, that is, when x = 0.Thus option D is correct.
Missing InformationThe graph is given by the image shown at the end of the answer.
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What is an example of a complex equation?
An example of a complex equation is the Navier–Stokes equations, which are used to describe the motion of fluids and are one of the most important equations in fluid mechanics.
What is complex equation?A complex equation is a mathematical expression that contains multiple variables, operations, and powers. This can include exponents, logarithms, trigonometric functions, and other variables. Complex equations can be used to solve problems or to make predictions, and can be used in a wide range of fields, including economics, engineering, and physics.
These equations consist of a set of partial differential equations that describe the motion of a fluid, such as air or water, and the forces acting on it. The Navier–Stokes equations are used to predict the behavior of liquids and gases in a wide range of applications, from aeronautics, to weather prediction, to oceanography.
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What is the slope of this line y =- 3x 1?
as the value of the correlation coefficient increases from to , or decreases from to , how do the points of the scatter plot fit the regression line? choose the correct answer. the points would be further from the origin. the correlation coefficient determines the relationship, but tells nothing about the points. they would be scattered further from the line. they would be clustered closer to the line.
As the correlation coefficient moves from 0 to 1 or -1 to 0, the points would be closer to the line. Option A
What is the correlation coefficient?The term correlation coefficient is used to show the level of the relationship between the variables. If the correlation coefficient is very close to 1 then it means that there is greater association between the variables. If it is far from one then it means that the variables are not associated at all.
We know that the regression lines show how variables can be associated and they can be used to show us the relationship between variables.
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How do you write an equation of the line containing the given point and perpendicular to the given line?
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
the rational roots theorem - state the possible rational zeros for each function (please show work)
f(x)=3x^2+2x-1
Answer: x=-1 x=1/3
Step-by-step explanation:
f(x)=3x²+2x-1
[tex]3x^2+2x-1=0\\\\3x^2+(3x-x)-1=0\\\\(3x^2+3x)-x-1=0\\\\3x(x+1)-(x+1)=0\\\\(x+1)(3x-1)=0\\\\x+1=0\\\\x=-1\\\\3x-1=0\\\\3x=1[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\x=\frac{1}{3}[/tex]
verify the linear approximation at (0, 0). f(x, y) = y + cos2(x) ≈ 1 + 1 2 y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
In the given question, we have to verify the linear approximation at (0, 0).
f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Let f(x, y) = √(y+cos^{2}x)
f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)
f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]
f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]
f(x, y) ≈ 1+0(x-0)(1/2)(y-0)
f(x, y) ≈ 1+1/2y
Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
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The complete question is:
Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........
A teacher records the following test scores out of 100 for eight of her students:
8, 47, 62, 67, 78, 82, 83, 90
The teacher then realizes that the score of 8 is an error and should instead be 80.
What will this change of score have a greatest effect on?
Mean
Median
Mode
Highest Value
The change of score of the test score from 8 to 80, would have the greatest effect on A. Mean.
Why would mean be the most affected ?Numbers in a data collection that are significantly greater or smaller than the rest are known as outliers. The metrics of central tendency are mean, median, and mode. The only index of central tendency that is consistently impacted by an outlier is the mean.
The value of 8 was an outlier from the rest of the test scores and so it would have had a great effect on mean. If the score was taken back to 80, then the mean would be adjusted correctly and change the greatest.
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the basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. the school plans to make the width of the new court 45 feet. find the perimeters of an NCAA court and the new court in the school
Perimeter of the NCAA court is 288288 ft
Perimeter of the new court is 259.2ft
How to find Perimeter ?Perimeter of NCAA court
=2(length +width)
=2(94ft+50ft)
=2⋅144ft
=288ft
The perimeter of the new court in the school:
=2(length +width)
=2(84.6ft+45ft)
=2⋅129.6ft
=259.2ft
The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. But we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.With the use of the perimeter formula, we can quickly determine the length of a circular or rectangular field given its measurements. Learn from this.To learn more about Perimeter refer to:
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119.43 1 significant figure
The number 119.43 when approximated to 1 significant figure is 100
How to determine the significant figure?From the question, we have the following parameters that can be used in our computation:
Number = 119.43
The number is to be approximated to 1 significant figure
This means that we approximate all number leaving only the first digit
When this is done, we have
Approximation = 100
Hence, the number in 1 significant figure is 100
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The table shows the total number of text messages that Ashley sent over 4 days. Write an equation to find the total number of messages sent in any number of days. Use the equation to find how many text messages Ashley would send in 30 days.
Answer:
1d=25m
30d=?
cross mutiply
30×25=750messages
Answer:
The equation is m = 25d
Ashley would send 750 text messages after 30 days.
Step-by-step explanation:
The equation is y = mx + b
We see that each day the number of text increase by 25, so our equation is
m = 25d
Now we ask how many text messages Ashley would send in 30 days. We need to put 30 in for d and solve it.
m = 25(30)
m = 750 text messages
So, Ashley would send 750 text messages in 30 days.
Simplify the expression xy+x^2+2xy+y^2-3x^2
982,399,895,054
Select the place where the digit 3 sits in this number.
Answer:
Step-by-step explanation:
3000000000000000000000000000000000000
What is the discriminant and nature of roots of 2x² 3x 5 0?
The quadratic equation [tex]2x^{2}+3x-5=0[/tex] has a discriminant of 49.
In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its classification or solution. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots include a conjugate pair of complex roots.
For an equation, [tex]ax^{2}+bx+c=0[/tex]
Discriminant, D = [tex]b^{2}-4ac[/tex]
Given in question,
[tex]2x^{2}+3x-5=0[/tex]
a = 2
b = 3
c = -5
D = [tex]3^{2}[/tex] - 4(2)(-5)
= 9 + 40
= 49
Hence, the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] is 49.
Correct Question :
What is the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] ?
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Question
Graph 13x−16y=−23 using intercepts.
Solve the following system of equations and show all work. y = −x2 +4y = 2x + 1
The solution to the system of equations is x = 3/2 and y = 7/4.
The given system of equations can be written as:
y = -x^2 + 4
y = 2x + 1
To solve this system of equations, we can use the substitution method. First, we'll substitute the expression for y in the second equation into the first equation. We can then solve the resulting equation for x.
In the first equation, [tex]y = -x^2 + 4[/tex] . Substituting this expression into the second equation, we get:
[tex]-x^2 + 4 = 2x + 1[/tex]
We can rearrange the terms on the left side of the equation to solve for x. To do this, we'll subtract 4 from both sides, then add x^2 to both sides:
-4 = 2x + 1 - 4
-4 + 4 = 2x + 1 - 4 + 4
0 = 2x - 3
Now, we'll divide both sides of the equation by 2 to solve for x:
0/2 = (2x - 3)/2
0 = x - 3/2
We can rearrange the terms on the right side of the equation to solve for x. To do this, we'll add 3/2 to both sides:
0 + 3/2 = x - 3/2 + 3/2
3/2 = x
Now that we have the value of x, we can substitute it into either equation to solve for y:
[tex]y = -x^2 + 4y = -(3/2)^2 + 4y = -(9/4) + 4[/tex]
y = 7/4
Therefore, the solution to the system of equations is x = 3/2 and y = 7/4.
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What is the value of root 2 into 1?
0.707 is obtained by multiplying one by root 2 . Commonly used to represent the square root is the symbol '√'. Using this symbol, the number "x" can be represented as the square root of "x" by writing '√x'.
what is square root ?A mathematical term for a factor that, when multiplied by itself, equals the original value of the original integer is the square root. Early in the second millennium BC, the Babylonians devised effective methods for approximating square roots.
here
=√2 / 2
= 1 / √2
=√2 / √2=1
=1√2 / √2√2
=√2 / 2
= 0.707
so , 0.707 is obtained by multiplying one by root 2.
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y = 4/5x + 8
2x+y = -6
Plot two lines by clicking the graph.
Answer:
Just use Desmos
Step-by-step explanation:
Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14
9
2
km14, start fraction, 2, divided by, 9, end fraction, start text, space, k, m, end text taxi ride. The cost per kilometer is constant. As a simplified proper fraction
The cost per kilometer for Emanuel's taxi ride is given as follows:
$9/4.
How to obtain the cost per kilometer?To obtain the cost per kilometer of the tax ride, we apply the proportion, dividing the total cost by the distance of the taxi ride.
From the text given in this problem, the parameters are given as follows:
Total cost: $32.Total distance: 14 and 2/9 kilometers = 14 + 2/9 kilometers = 14.22 kilometers. (conversion of mixed number to decimal).Then the cost per kilometer for Emanuel's taxi ride is found applying the proportion as follows:
Cost per kilometer = 32/14.22 = 2.25.
We have that the fraction equivalent of .25 is given as follows:
1/4.
Thus the proper fraction that represents the cost is given as follows:
2 + 1/4 = 8/4 + 1/4 = $9/4.
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How do the coefficients in a balanced equation compare quantities of two substances?.
The coefficients in a balanced equation compare quantities of two substances by the ratio of the substances' coefficients equals the ratio of their number of moles.
A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.
In many chemical situations, mole ratios are employed as conversion factors between products and reactants.
In a balanced chemical equation, the coefficients in front of the formulae can be used to determine the mole ratio.
Complete question:
How do the coefficients in a balanced equation compare quantities of two substances?
A. The ratio of the coefficients equals the ratio of the masses of the
substances
B. The sum of the coefficients of the reactants equals the sum of the
products
C. The ratio of the substances' coefficients equals the ratio of their
number of moles.
D. The coefficient of the reactant tells how many product molecules
will form.
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A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.
In many chemical situations, mole ratios are employed as conversion factors between products and reactants.
Complete question:
How do the coefficients in a balanced equation compare quantities of two substances?
A. The ratio of the coefficients equals the ratio of the masses of the
substances
B. The sum of the coefficients of the reactants equals the sum of the
products
C. The ratio of the substances' coefficients equals the ratio of their
number of moles.
D. The coefficient of the reactant tells how many product molecules
will form.
Х
15
9
18
9
y
17
9
4
Is this relation a function?
yes
no
To be a relation of a function for every value of x there must be a single value of y thus the given relation is not a function.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given table,
At x = 9
y = 9 and y = 3
Since at a single value of x there exist two values of y thus it will not be a function.
Hence "The provided relation is not a function since there must only be one value of y for a relationship to be considered a function.".
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5.22860492 rounded to 3 significant figures
Answer:
5.22 is the answer required
Solve the following equations:
Solving multi-step equations
1) 3x+7+ 6x = 34
2) b-9+6b=30
How do you determine if a graph has a positive or negative leading coefficient?
To determine if a graph has a positive or negative leading coefficient, look at the sign of the coefficient of the first term of the equation for the graph. If the coefficient is positive, the graph has a positive leading coefficient. If the coefficient is negative, the graph has a negative leading coefficient.
To determine the sign of the leading coefficient of a graph, first look at the equation for the graph. The leading coefficient of a graph is the coefficient of the first term in the equation, so find the coefficient of the first term. If the coefficient of the first term is positive, then the leading coefficient is positive. If the coefficient of the first term is negative, then the leading coefficient is negative. For example, if the equation is y = 4x2 + 3x + 5, the coefficient of the first term is 4, and so the leading coefficient is positive. Conversely, if the equation is y = -2x2 + 3x + 5, the coefficient of the first term is -2, and so the leading coefficient is negative.
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what is the slope of the line that contains the points
Answer: 0
Step-by-step explanation:
The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.
How many triangles can be drawn given 2 sides and a non-included angle?
Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.
What is meant by Angle ?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays known as the vertex is referred to as an angle's sides. Angles are often measured using one of two different units. The degree is the measurement unit that is most widely used. A straight angle is 90 degrees when a circle is divided into 360 equal degrees.To learn more about Angle refer to:
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What is the value of 0 1?
The value of 0 1 is 1.
This is because any number to the power of 0 is equal to 1. This is part of the fundamental rules of exponents in mathematics. For example, if we take 2 to the power of 0, that would be equal to 2^0=1.
Similarly, 5^0=1, and so on. This is because any number to the power of 0 is equal to 1, regardless of the number. This is because any number multiplied by 1 is equal to itself. This holds true for 0 as well, and so 0^1=1. This is why the value of 0 1 is 1.
This is a basic mathematical equation in which the answer is 1. This equation can be used to illustrate the concept of addition, which is the process of combining two numbers to get a total.
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