The most appropriate viewing window for determining the domain and range of a function when graphing it on a graphing calculator would depend on the specific function and what information you are trying to gain from the graph.
DETERMINING THE DOMAIN AND RANGE OF THE FUNCTIONWhen graphing a function, it is important to set the viewing window correctly so that the full behavior of the function is visible. The domain of a function is the set of all input values for which the function is defined. The range of a function is the set of all output values that the function can produce. To determine the domain and range of a function from its graph, you need to be able to see all of the points where the function is defined, as well as any asymptotes or singularities.
To set the appropriate viewing window, you should start with a wide window that includes the x- and y-values where the function is defined. For example, if the function is defined for all real numbers, you would want to set the x-min and x-max to a large negative and positive number respectively, and y-min and y-max to a large negative and positive number respectively. This will ensure that all of the function's behavior is visible on the graph.
Once you have a general idea of the function's behavior, you can adjust the viewing window as needed.
Also, it is a good idea to check the graph for symmetry or periodicity, which can help to narrow down the domain or range. For example, if the graph is symmetric about the y-axis, you know that the domain includes all real numbers. If the graph is periodic, you know that the domain includes all real numbers and the range is limited.
By adjusting the viewing window and looking for symmetry or periodicity, you should be able to determine the domain and range of the function from its graph.
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Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
The third side of the triangle will be less than 35.
What is a triangle?A polygon with three angles, sides and angles is called a triangle.
Given that, Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
We know that, triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, length of the third side < 15+20 < 35
Hence, the third side of the triangle will be less than 35.
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Write f(x)=1/2x^2+1/2x-10 in intercept form. Then find the x-intercepts, the vertex, and the axis of symmetry of the graph of f.
f(x)=1/2x^2+1/2x-10 in intercept form is (1/2)(x+4)(x-3)
The x-intercepts are x=-5 and x=4.
The vertex of symmetry is (-1/2, -81/8).
The axis of symmetry is: x = -1/2
What is intercepts?A vertical intercept is a point where the graph of a function or relation meets the y-axis of the coordinate system in analytical geometry,
f(x) = 1/2x^2+1/2x-10
= (1/2)(x² + x - 20)
= (1/2) (x² + 5x - 4x - 20)
= (1/2) { x(x+5) -4(x+5)
= (1/2) (x+5)(x-4)
Hence, Intercept form: f(x) =(1/2) (x+5)(x-4)
The x-intercepts will be where the factors = 0
x + 5 = 0 ⇒x = -5
x - 4 = 0 ⇒ x = 4
Therefore, the x-intercepts are x=-5 and x=4
To find the axis of symmetry, take the average of intercepts (to find the center of parabola)
(-5 + 4)/2 = -1/2
Axis of symmetry ⇒ x = -1/2
To find the vertex, put the axis of symmetry into the equation
f(x) = (1/2)(x + 5)(x - 4) = (1/2)(-1/2 + 5)(-1/2 - 4) = (1/2)(9/2)(-9/2) = -81/8
vertex is (-1/2, -81/8)
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The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
f(x) = (1/2)x² + (1/2)x - 10
2f(x) = x² + x - 20
2f(x) = x² + x + 1/4 - 1/4 - 20
2f(x) = (x + 1/2)² - 81/4
f(x) = 1/2 (x + 0.50)² - 10.125
The x-intercepts are given as,
f(x) = 0
1/2 (x + 0.50)² - 10.125 = 0
(x + 0.50)² = 20.25
x + 0.50 = ± 4.50
x = - 0.50 ± 4.50
x = - 0.50 - 4.50, - 0.50 + 4.50
x = - 5, 4
The equation of the axis of symmetry is given as,
x + 1/2 = 0
x = - 1/2
The graph is attached below.
The x-intercepts, vertex, and axis of symmetry will be - 5 & 4, (-0.50, -10.125), and x = - 1/2, respectively.
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Can someone help me please? Picture attached
Answer:
Step-by-step explanation:
A^2 + B^2 = C^2
12^2 + B^2 = 18^2
144 + B^2 = 324
Subtract 144 from both sides
B^2 = 324 - 144
B^2 = 180
[tex]\sqrt{180}[/tex] = 13.416
B^2 = 13.4
How do you solve a math problem step by step?
Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.
There are few basic steps to be followed while solving any mathematics problem:
1. Read and understand the problem.
2. Identify what is given and what is needed to solve the problem.
3. Choose an appropriate strategy to solve the problem.
4. Carry out the strategy.
5. Check your answer to make sure it is correct.
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How do parallel algorithms differ from sequential?
The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel method over a sequential one.
Differences between Sequential and Parallel ComputingSequential Computing: One instruction is delivered at a specific time, and the subsequent instruction must wait for the first instruction to complete before it can be executed. This is known as sequential computing. Because all the instructions are carried out in order, it is often referred to as a conventional computing technique. It has a single CPU that performs poorly and has a heavy workload. The biggest drawback of employing this computing is that it requires more time because just one instruction is being processed at a time.
Parallel Computing: A computing method known as parallel computing involves running numerous calculations or processes simultaneously in parallel. Parallel computing is a kind of computing in which multiple processes can run at once.
Due to the simultaneous execution of the operations, time is saved. It resolves more complex issues. There are many processors with high performance and little work being put on each of them.
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What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to
Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.
What do "multiply" and "factor" mean?A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.
What connection exists between the factor theorem and the division of polynomials?When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.
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What are equivalents in a reaction?
In a reaction the amount f a substance which react with another substance is known as it's equivalent.
The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."
It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.
The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.
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HELP ASAP!!!!
A person is standing 19 feet from the base of a tree and there is a bird's nest in the tree 10 feet above the groundWhat is the angle off elevation from the person to the bird's nest? Round to the nearest tenth of a degree
Answer:
do your own work don't ask any question
A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
Answer:
262.5 $
Step-by-step explanation:
A karate studio offers a 6 week session for
$175. How much would you expect to pay for
a 9 week session?
find the cost of 1 session175 : 6 = 29.16
multiply by the number of weeks29.16 x 9 = 262.5
or
175 : 6 = x : 9
x = 175 x 9 : 6
x = 262.5
A rectangular school banner has a length of 21 inches and a perimeter of 66 inches. A sign is made that is similar to the school banner and has a length of 7 inches. What is the perimeter of the sign?
The perimeter of the sign is 22 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular school banner has a length of 21 inches and a perimeter of 66 inches.
Let the perimeter of the sign for the length of 7 inches of the banner = x
So, By definition of proportion, we get;
⇒ 21 / 66 = 7 / x
Solve for x;
⇒ x = 7 × 66 / 21
⇒ x = 22
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A triangle has sides with lengths that are
consecutive even integers. The perimeter of the
triangle is 72 centimeters. Sketch the triangle
and label the lengths of the sides, using the
variable. Find the length of the largest side.
Show work
The largest side of the length is 26cm.
Now, According to the question:
Three consecutive even numbers can be expressed in terms of n. If n is an even number then,
(n -2), (n), (n + 2)
are three consecutive even numbers.
Therefore,
(n -2)+ (n)+ (n + 2) = 72cm.
We can simplify so...
3n + 2 - 2 = 72 cm.
3n + 0 = 72 cm.
3n = 72cm.
Divide both sides by 3 to solve for n
n = 24 cm.
24 is an even integer. Input 24 into the original equation.
(n -2)+ (n)+ (n + 2) = 72cm.
(24 - 2) + 24 + (24 + 2) = 72cm
22 + 24 + 26 = 72
72 = 72
Hence, The largest side of the length is 26cm.
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Identify an irrational number between 7 and 8
If the area of Square 3 is 80cm and the area of square 2 is 100cm, what is the area of square1
The area of square 1 is 180 sq cm
What is the area of square?The area of a square is calculated with the help of the formula: Area = s × s, where, 's' is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units
Square 1 formed on hypotenuse of the triangle, squares 2 and 3 are formed on the perpendicular legs of the triangle. Thus, by Pythagoras Theorem, A(square 1) will be equal to the sum of the areas of (square 2) and (square 3).
Area of square 1 = Area of square 2 + Area of square 3
Area of square 1 = 100 + 80
Area of square 1 = 180cm^2
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Mr. Hurd buys a trampoline for his kids. The cost of the trampoline is $699.99. He gets the items for $429.99. What is the percent of discount? Round to the nearest percent.
Answer:
Mr. Hurd received a discount of 57% on the trampoline. The cost of the trampoline was $699.99 and he got it for $429.99, resulting in a discount of 57% when rounded to the nearest percent.
Step-by-step explanation:
Solve the following system of equations graphically on the set of axes below.
y = x + 8
y = -1/2x+5
Plot two lines by clicking the graph. Click a line to delete it.
By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).
How to solve the system of equations?Here we have the following system of equations:
y = x + 8
y = -(1/2)x+5
And we want to solve it graphically.
To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.
The graph of the system of equations can be seen in the image below:
There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.
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Is the area of an equilateral triangle is 9 root 3 cm square then the semi perimeter of the triangle is?
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
area of equilateral triangle = [tex]9\sqrt{3}cm^{2}[/tex]
formula of area of equilateral triangle = [tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]
a = side of triangle
[tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex] = [tex]9\sqrt{3}cm^{2}[/tex]
[tex]a^{2} = \frac{4* 9\sqrt{3} }{\sqrt{3} }[/tex]
[tex]a^{2} = 36\\ a = 6 cm[/tex]
since equilateral triangle all sides are equal
perimeter of triangle = 6 + 6 + 6
= 18cm
the semi perimeter of the triangle = 18 /2 = 9 cm
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
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A straight line is shown on the coordinate grid below. a) What is the y-intercept of this line? b) What is the gradient of this line? Give each of your answers as an integer or as a fraction in its simplest form. Y 8- 7- 6- 5- 4- 3- 2- 1- ܝ ܚ ܚ ܢ ܗ ܘ ܙܢ ܣ -8-7-6-5 -4 -32 -1.0 -2+ -3. -4- -8- 12 4 X
Answer:
a. 4
b. -2
Step-by-step explanation:
coordinate: (2,0), (0,4)
gradient = 4 - 0 / 0 - 2
= -2
What does r equal?
Answer: r = ________
The following equation has an error in one of the operations.
12(2x+6)+4(x+5)=5x−17
Which answer would correct the error?
A. Change 5x−17 to 5x+17.
B. Change 12(2x+6) to 12(2x−6).
C. Change (x+5) to (x−5).
D. Change +4(x+5) to −4(x+5).
The Correct change to make the Equation correct is Change (x+5) to (x−5).
The Correct option is (C).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
12(2x+6)+4(x+5)=5x−17
28x + 72= 5x-17
23x = 109
x= 4.73
First, change (2x+6) to 12(2x−6).
12 (2x - 6) + 4(x+5) = 5x- 17
24x - 72 +4x +20 = 5x- 17
28x -52 = 5x- 17
23x = 35
x= 1.52
Now, Change (x+5) to (x−5).
12 (2x + 6) + 4(x-5) = 5x- 17
24x + 72 +4x -20 = 5x- 17
28x + 52 = 5x- 17
23x = 69
x=3
Hence, Change (x+ 5) to (x-5).
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On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1. 25 for children and $2. 25 for adults. Receipts for admission totaled $865. 25. How many children and how many adults swam at the public pool that day?
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
The number of children =X=217
The number of adults=264
Let say the number of children are denoted by X
Then the number of adults are (481-X)
Price for children =1.25X
Price for adults=2.25(481-X)
Price for children +Price for adults=865.25
1.25X+2.25(481-X)=865.25
Solving for X:
1.25X+1082.25-2.25X=865.25
-X=865.25-1082.25
-X=-217
X=217
The number of children =X=217
The number of adults=(481-X)
The number of adults=(481-217)
The number of adults=264
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
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Similar figures review
The width for the second rectangle which is HIJK will be A. 24 inches.
How to illustrate the relationship?From the diagram, it should be noted that rectangle ABCD is similar to rectangle HIJK. Therefore it should be noted that the relationship between the width and length is expressed as:
= Width / Length
= 12/16
= 3/4
Therefore, the width for the second rectangle will be:
= 3/4 × 3.2
= 2.4
In conclusion, the correct option is A.
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How much of a radioactive kind of barium will be left after 39 days if you start with 52,256 grams and the half-life is 13 days?
Answer:
Step-by-step explanation:
Answer:
6,532
Step-by-step explanation:
ixl
i dont understand it
Answer:
x=-3
y=10
Step-by-step explanation:
Josh exercises no less than 40 minutes per day.
Use t to represent Josh's amount of exercise (in minutes per day).
Answer
x ≥ 40
Step-by-step explanation:
Since Josh only exercises more or equal to 40 min, this is how you would represent this problem.
What is the formula for vector direction?
The formula for vector direction is: Direction = arctan (y/x) , Where x is the x component of the vector and y is the y component of the vector.
1. Find the x and y components of the vector
2. Divide the y component by the x component
3. Calculate the arctan (inverse tangent) of the result
4. The result is the direction of the vector in radians (or degrees if you prefer).
If you want to convert the result from radians to degrees, you can use the following formula:
(in degrees) = arctan (y/x) * (180/π)
Where π (pi) is approximately equal to 3.14.
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The area of a sector of a circle is
18 pie cm². The radius of the circle is
6 cm. The angle in the sector is
Answer:
The angle in the sector is 180°.
Because the area of circle is 36 pie cm². So the angle is the half of 360°.
[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]
△ABC, BD &CE are the altitude of the ide AC & AB and BD=CE. Prove that △BCD≅△CBE
We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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PLEASE HELP ME I REALLY NEED IT!!!!!!!!
Answer: for A it is: 3 and 4 represent the number values for X and Y.
Step-by-step explanation:
Sorry, but you B and C you did not give enough information
g Suppose that the retail price of a product has a normal distribution with a mean of $37 and a standard deviation of $20. Approximately, what is the probability that the price grows beyond double the mean
Retail price of the product will be double its mean will have a prbability of 0.0401.
What is Normal Distribution ?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The value of the product considering = $37*2 = $74(x)
Mean = $37
Standard Deviation (SD)= $20
here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]
P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401
Retail price of the product will be double its mean will have a prbability of 0.0401.
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Gaya buys 2 oranges and 1 cauliflower she pays £2.00
Esteben buys 4 oranges and 1 cauliflower he pays £2.90
Work out the price of one orange
Answer:
Step-by-step explanation:6