Using the provided function and finding the values of input for which it will provide valid output values we can find the domain.
What is the difference between domain an range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Can a function's domain and range be the same?Yes. For instance, the set of all real numbers is the domain and range of the cube root function.
Choose the input values.
Exclude any real numbers that produce a negative value in the radicand because there is an even root. Solve for x by setting the radicand to be greater than or equal to zero.
The domain of the function is the solution(s). If at all possible, format your response as an interval.
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help me please asaaaaaapppp
The continuity of the piece-wise functions is defined as follows:
1. Not continuous.
2. Not continuous.
3. Not continuous.
How to define the continuity of the functions?A piece-wise function is a function that has multiple definitions, depending on the input.
Then the function is classified as continuous if the lateral limits at the points that the function change the definition are equal, and also equal to the numeric values of the function.
None of the functions in this problem are continuous, as:
For function 1, lim x -> 0^- = 0, lim x -> 0^+ = 2, hence different lateral limits. At x = 3, the lateral limits are also different.For function 2, lim x -> -6^- = 0, lim x -> -6^+ = 4. At x = 2, the lateral limits are also different.For function 3,lim x -> 0^- = 3, lim x -> 0^+ = -3.More can be learned about the continuity of a function at https://brainly.com/question/24637240
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pls help me
The line 2y + x = 1 is perpendicular to a line L. Line L passes through point (2, -1). Determine the equation of L in the form y = mx + c, where m and c are constants.
The equation of the perpendicular line is y = 2x - 5
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
2y + x = 1
Make y the subject
y = -1/2x + 1/2
Also, from the question;
We have the following points
Point = (2, -1) i.e. (x, y) = (2, -1)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -1/2
This means that the slope is -1/2
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 2
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 2
(x₁, y₁) = (2, -1)
So, we have
y = 2(x - 2) - 1
Evaluate
y = 2x - 5
Hence, the line has an equation of y = 2x - 5
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Which of the relations given by the following sets of ordered pairs is not a function?
{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)} ordered pairs is not a function. A mapping between two sets, which is a relation and can potentially be a function, can be represented by a set of ordered pairs.
Which relation is not a function?A relationship is not a function if each input does not have a distinct output. For a relation to be a function, each input must have a distinct output, and the order of the set's items must be paired in a unique way or the elements of sets must be mapped in a unique way.A function is a special type of relation in which each element in the domain is paired with exactly one element in the range. For example, the relation {(1, 2), (3, 4), (5, 6)} is a function because each element in the domain (i.e., {1, 3, 5}) is paired with exactly one element in the range (i.e., {2, 4, 6}). On the other hand, the relation {(1, 2), (3, 4), (1, 6)} is not a function because the element 1 is paired with two elements in the range (2 and 6).All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)Complete question :
Which of the relations given by the following sets of ordered pairs is not a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.
How to find the number of two and three points made?The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.
Therefore, the number of two-points and three-points the cruiser scored is as follows:
let
x = number of two-points
y = number of three-points
Hence, using equation
x + y = 43
2x + 3y = 105
Multiply equation(i) by 2
2x + 2y = 86
2x + 3y = 105
subtract equation(i) from equation(ii)
y = 19
Let's find x as follows:
x = 43 - 19
x = 24
Therefore,
number of two points = 24
number of three points = 19
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Where in an equation for photosynthesis does glucose belong?on the left, because it is a producton the left, because it is a reactanton the right, because it is a producton the right, because it is a reactant.
Answer:
carbon dioxide + water sunlight glucose + oxygen
Step-by-step explanation:
glucose on the right because it is a by product of photosynthesis.
urgent..................
Answer:
√6
Step-by-step explanation:
the altitude is √a*b
and and b being the base so find their distance then multipky them under the root
subtracdt the x values to find the distance
4-1=3
6-4=2
the root of 2*3 is the root of 6
done
Answer:
x = 4
Step-by-step explanation:
You want the equation of AD perpendicular to BC, where the point coordinates are A(4, 6), B(1, 2), C(6, 2).
Horizontal lineWe notice the y-coordinates of point B and C are the same, indicating the line is horizontal. Its equation is y = 2.
Perpendicular lineThe line perpendicular to the horizontal line y = 2 will be a vertical line. Its equation will be of the form ...
x = c
where c is some constant.
We want this line to go through the point (4, 6), which has an x-coordinate of 4. That means the constant in the equation must be 4:
x = 4 . . . . . . equation of AD
The table represents a quadratic function. Write an equation of the function in
standard form.
The standard form of the equation of the line for the function is; y =6x + 18
What is the equation?We know that it is possible to obtain the equation of the line by obtaining the slope of the data points. The slope of the data points can be obtained by the use of the points that have been shown in the table.
Taking any two points on the table we have;
[tex]y_{1}[/tex] = 0
[tex]y_{2}[/tex] = -12
[tex]x_{1}[/tex] = -3
[tex]x_{2}[/tex] = -1
Using;
y - [tex]y_{1}[/tex] = [tex]y_{2}[/tex] - [tex]y_{1}[/tex] /[tex]x_{2}[/tex] - [tex]x_{1}[/tex] (x - [tex]x_{1}[/tex] )
We have;
y - 0 = (-12) - 0/(-1) - (-3) ( x - (-3))
y = 12/2 (x + 3)
y =6x + 18
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An Olympic-sized pool, which holds 660,000 gallons of water,
is only 63% full. The pool maintenance company adds more
water, filling the pool to 90% full. How many gallons of water
did they add?
P
7.AR 3.1
a
244 200
178 200
B) 594 000
415.800
134
Answer:
178,200
Step-by-step explanation:
You want to know the number of gallons added to a 660,000 gallon pool to raise it from 63% full to 90% full.
IncreaseThe increase from 63% to 90% is an increase of ...
0.90 -0.63 = 0.27
of the capacity of the pool. That fraction of the capacity is ...
0.27 × 660,000 gallons = 178,200 gallons
The maintenance company added 178,200 gallons.
What is the equation in slope intercept form of the line that is parallel to the given line?
The equation in slope intercept form of line , parallel to the line 6x - y = 1 and passing through point (-2,2) is y = 6x + 14 .
When the two line are parallel , then their slopes are same .
the required line is parallel to the given line 6x - y = 1 ,
rewriting it , we get ;
y = 6x - 1 ;
on comparing it with the slope intercept form of line , "y = mx + c" ,
we get ,
slope(m) ⇒ 6 .
So , the equation of the required line becomes ⇒ y = 6x + c ;
Since this line passes through the point (-2,2) ,
we get ,
2 = 6(-2) + c ;
2 = -12 + c ;
c = 12 + 2 ;
c = 14 .
the equation becomes ⇒ y = 6x + 14 .
Therefore , the equation of the line is y = 6x + 14 .
The given question is incomplete , the complete question is
What is the equation in slope intercept form of the line that is parallel to the given line 6x - y = 1 and passes through point (-2,2) ?
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What is 5x 2y 3 in slope intercept form?
The line's equation is written as y = (-5/2)x + (3/2) in slope-intercept form.
According to the slope-intercept form, in the equation for a straight line, y=mx+b, the slope is the quantity represented by m that is multiplied on the x, and b is the y-intercept, i.e., the point where the line crosses the vertical y-axis.
To put the equation 5x + 2y = 3 in slope-intercept form, you need to rearrange the equation to have the form y = mx + b, where m is the slope and b is the y-intercept.
To do this, you can start by isolating the y term on one side of the equation:
5x + 2y = 3
2y = -5x + 3
y = (-5/2)x + (3/2)
In this configuration, the line's slope is -5/2, and its y-intercept is 3/2. Therefore, the equation of the line in slope-intercept form is y = (-5/2)x + (3/2).
The complete question is:-
What is 5x + 2y = 3 in slope intercept form?
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Determine the largest integer value of x in the solution of the following inequality.
2x+6<-4
Answer: -6
Step-by-step explanation: To determine the largest integer value of x in the solution of the inequality 2x+6<-4, we first need to isolate x on one side of the inequality. We can do this by subtracting 6 from both sides of the inequality, which gives us 2x<-10. Next, we can divide both sides of the inequality by 2, which gives us x<-5. Since the inequality has a strict inequality symbol, we can conclude that the largest integer value of x that satisfies the inequality is -6.
what is 18+15 writen as an expression
In triangle ABC,
AC=8 cm,
BC-15 cm,
Angle ACB = 70°.
(a) Calculate the length of AB. Give your answer correct to 3 significant figures.
Calculate the size of angle BAC.
(b) Give your answer correct to 1 decimal place.
a) The length of AB is given as follows: 14.387.
b) The measure of angle BAC is given as follows: 78.4º.
How to obtain the length of AB?The length of AB, from the sketch of the triangle given by the image at the end of the answer, is obtained using the law of cosines, as follows:
x² = a² + b² - 2abcos(C).
The parameters from the triangle are given as follows:
a = 8, b = 15, C = 70º.
Hence the length of AB is given as follows:
x² = 8² + 15² - 2 x 8 x 15 x cos(70º)
x² = 207
x = square root of 207
x = 14.387.
How to obtain te measure of angle BAC?
The measure of angle BAC is obtained using the law of sines, as follows:
sin(x)/15 = sin(70º)/14.387
sin(x) = 15 x sin(70º)/14.387
sin(x) = 0.9797.
x = arcsin(0.9797)
x = 78.4º.
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How do you know if it's AAS or ASA?
The triangles are congruent if two sets of comparable angles and the side separating them are known to be congruent. Angle-side-angle is the name of this shortened phrase (ASA). Angle-angle-side (AAS), which takes use of the fact that two sets of angles and the excluded side are known to be congruent, is another shortcut.
ASA is another name for angle side angle. According to the criterion, any two angles and the side that is contained between them in one triangle are equivalent to the corresponding angles and the included side of the other triangle if the two triangles are congruent.
According to the Angle Angle Side (AAS) Postulate, two triangles are congruent if two consecutive angles and a non-included side of one triangle are congruent with the equivalent two consecutive angles and a non-included side of another triangle.
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What are the solutions of x2 3x 4 0?
The solution of [tex]x^{2} - 3x-4=0[/tex] is x=(4,−1).
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator. In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions.
Have given ,
[tex]x^{2} - 3x-4=0\\x^{2} -4x +x-4=0\\x(x-4)+1(x-4)=0\\(x-4)(x+1) = 0\\[/tex]
x - 4 = 0
x = 4
and x + 1 = 0
x = -1
The solution of [tex]x^{2} - 3x-4=0[/tex] is x = (4,−1).
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What is nature of roots formula?
The Formula for the nature of roots is D = b² - 4ac .
The Nature Of Roots of the quadratic equation "ax² + bx + c" formula can be determined by the discriminant formula ,
the discriminant formula is D = b² - 4ac ; where a is the coefficient of x² and b is the coefficient of x .
If the value of Discriminant is greater than 0 , then the roots are Real and distinct .
If the value of Discriminant is 0 , then the roots are Real and Equal .
If the value of Discriminant is less than 0 , then the roots are Imaginary and conjugate .
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What is an example of f x G X?
The example of composition function f(g(x)) is given by f(x) = 2x + 1 and g(x) = 3x then f(g(x)) = 6x + 1.
As given in the question,
Composition function is written as :
(fog)(x) = f(g(x))
Here substitute the value x in the function f(x) as function g(x) :
Example of the composition function is:
f(x) = 2x + 1
g(x) = 3x
(fog)(x)
= f(g(x))
=f(3x)
= 2(3x) + 1
= 6x + 1
Therefore, the example of the composition function f(g(x)) is given by :
f(x) = 2x + 1 and g(x) = 3x then f(g(x)) = 6x + 1.
The above question is incomplete, the complete question is:
What is an example of the function f (g(x))?
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Factor 30q+ 5r. Write your answer as a product with a whole number greater than 1.
Answer:
5(6q+r)
Step-by-step explanation:
We first find the GCF of 30q +5r
The GCF is 5
So, our answer is 5(6q+r)
We can't factor more after this
Now Let's test to see it is correct or not
5(6q+r)
= 30q + 5r
So, my answer is correct
Answer:
[tex]=5(6q+r)[/tex]
Step-by-step explanation:
[tex]Factor 30q+5r\\30q+5r\\=5(6q+r)[/tex]
Hope it helps
PLEASE HELP!!
Which statement best explains whether △JKL is congruent to △MNP?
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
The statement that best explains whether △JKL is congruent to △MNPis:
"△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin." (Option B).
What is a reflection in Maths?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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How to get Universal Credit Loophole $1,500?
You can get Universal Credit Loophole for $1,500 through Advance Payment.
While you wait for the first distribution of Universal Credit, advance payments up to the full amount of the first anticipated payment are available if you need money to pay bills and other household needs. In your online account or by contacting your Job-Centre Plus job coach, you can submit an application for an advance payment.
You will require:
Describe why you require an advance.the identity of the person (you do this when you apply online or on the phone with a work coach)supply the advance's bank account information (talk to your work coach if you cannot open an account)The money must be repaid within a year by taking deductions from your Universal Credit installments.
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What is the area of a triangle with a base of 7 1/2 feet and a height of 8 feet
Answer:
[tex]30ft^{2}[/tex]
Step-by-step explanation:
which is higher? determine if i or ii is higher or if they are equal. explain your reasoning. for a regression line, the uncertainty associated with the slope estimate, b1, is higher when
When I. there is a lot of scatter around the regression line, b1 is higher.
Define regression.A statistical measure that identifies the link or co-relationship between two variables. explains the relationship between an independent variable and a dependent variable. The scatter of data points around the regression line plays a key role in estimating the slope's uncertainty in regression analysis. The data points are more dispersed and the estimation of the slope is less accurate when there is a lot of scatter. Because the estimation of the slope is based on the data points, it is less accurate when there is greater scatter in the data points.
Given
When I. there is a lot of scatter around the regression line, b1 is higher.
I am higher. The uncertainty surrounding the slope estimate, b1, increases with the amount of scatter around the regression line. The calculated slope is less dependable when there is a lot of scatter than when there is very little scatter.
When there is a large amount of scatter around the regression line, the uncertainty associated with the slope estimate, b1, is higher. This is due to the fact that the estimate of the slope depends on the data points, and when there is a lot of scatter, the data points are more dispersed, making the estimate of the slope less accurate.
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What is the asymptote calculator?
An asymptote calculator is a tool that can be used to find the asymptotes of a given function.
What is an asymptote calculator?Generally, An asymptote is a straight line that a curve approaches, but never touches, as it extends indefinitely in one direction or another. There are three types of asymptotes: horizontal, vertical, and oblique.
To use an asymptote calculator, you would typically enter the equation of the function for which you want to find the asymptotes. The calculator will then analyze the equation and determine the type and location of the asymptotes, if any. Some asymptote calculators may also provide a visual representation of the function and its asymptotes, using a graph.
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Find the slope of the line that passes through the points. (2,-2) (- 3, -3)
Answer:
Step-by-step explanation:
Slope (m) = ΔY/ΔX = 1/4 =0.25
Answer:
Step-by-step explanation:
what is the slope between (-9,3) and (-1,1)
Answer:
m = -1/4
Step-by-step explanation:
The slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 2 and the x increase by 8, so the slope is
-2/8 = -1/4
Answer:
Slope = -1/4
Step-by-step explanation:
Now we have to,
→ find the needed slope.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (1 - 3)/(-1 -(-9))
→ m = -2/(-1 + 9)
→ m = -2/8
→ [ m = -1/4 ]
Hence, the slope is -1/4.
When solving an equation, Anne's first step is shown below. Which property justifies Anne's first step?
\text{Original Equation:}
Original Equation:
3x-1 =
3x−1=
\,\, 3
3
\text{First Step:}
First Step:
3x =
3x=
\,\, 4
4
distributive property of multiplication over addition
addition property of equality
division property of equality
multiplication property of equality
The first step that justifies Anne's first step while solving the expression is the commutative law of addition.
The property that best justifies Anne’s first step is the addition property of equality. This allows you to add four on the left side of the equal sign to cancel it out. In order to be fulfill the property, what you do to one side you must do to the other so you add that same amount (4) to the right side of the equal sign.
3x-4 = 5
(3x-4) +4 = 5 + 4
3x = 9
Final Answer: Addition Property of Equality
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What is the area of 4 in a circle?
On solving the provided question, we can say that, 16 square units make up the area of a circle with a radius of 4 units.
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. Through the center of the circle, a straight line defines the diameter. Half of the diameter is the radius. End in the circle's center after beginning at one of its points.
what is area of circle?Pi times the radius squared equals the area of a circle (A = π r²). Learn how to apply this equation to determine a circle's area given its diameter.
16 square units make up the area of a circle with a radius of 4 units.
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Which equation is the inverse of y 16x2 1?
This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y
x = (y - 1) / 16
In order to find the inverse of a given equation, we need to switch the x and y values and solve for the new x. To do this, we start by subtracting 1 from both sides of the equation to isolate the y variable. Then, we divide both sides of the equation by 16 to find the inverse equation, x = (y - 1) / 16. This equation expresses x as a function of y, meaning y is the input and x is the output. This inverse equation can be used to solve for x when given a value of y
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How does estimating the number 3,456 to the nearest thousand affect accuracy?
The point (5,5) is on a line with slope 1/3. How much is is the bonus/penalty in this equation?
The equation is y = 1/3 x + 10/3. The y-intercept is 10/3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the point (5,5) is on a line with slope 1/3. The y-intercept will be calculated as,
y = mx + c
5 = (5/3)) + c
c = ( 15 - 5 ) / 3
c = 10 / 3'
y = 1/3x + 10/3
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