Use the graph of the function to find the domain and range of f. (Enter your answer using interval notation.)
Answers
The domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.
What is vertex form of a quadratic function of graph?The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
From the graph, vertex is (h, k)=(0, 4) and (x, y)=(2, 0)
Here, y= a(x - h)² + k
0=a(2-0)+4
-4=2a
a=2
Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get
y=2(x-0)²+4
y=2x²+4
So, f(x)=2x²+4
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞),{x|x∈R}
Range: [4,∞),{y|y≥4}
Now,
(a) f(-3)= 2(-3)²+4=18
(b) f(2)= 2(2)²+4=12
(c) f(0)= 2(0)²+4=4
(d) f(3)= 2(3)²+4=18
Therefore, the domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.
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Related Questions
Please help quickly!
Use the figure below to answer questions 18-21
Answers
Answer:
Step-by-step explanation:
18. m∠1 = 104°
19. m∠2 = 79°
20. m∠3 = 65°
21. m∠5 = 73°
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EOC Review #2
.
If another line is perpendicular to the line
shown on the graph, what must be its slope?
A.
B.
NI UN NIIN
C.
D.
ОА
OB
OD
Answers
A horizontal curve is being designed around a pond with a tangent length of 1200 ft and a central angle of 29.86 degrees. If the PI is at station 105 00, determine the station of PT
Answers
The station of PT is 12305.58 ft
The station of PT can be determined using the formula:
PT = PI + R * (central angle in radians)
To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)
Next, we need to determine the radius (R) of the curve. We can use the formula:
R = L / (central angle in radians)
Where L is the tangent length.
Finally, we can substitute the values into the formula for PT:
PT = 105 00 + (1200 / (29.86 * (π/180)))
PT = 105 00 + (1200 / (0.5236))
PT = 105 00 + 2295.58
PT = 12305.58
It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.
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Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buts two new pair of pants.
Answers
There are 9 possible outcomes to buy two new pair of pants.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Given:
we have the following Styles
Boot cut (B), Skinny (S), and Relaxed fit (R).
So, if her buys two paints then the possible combination he can take as
Boot cut x Boot cut
Skinny x Skinny
Relaxed fit x Relaxed fit
Boot cut x Skinny
Boot cut x Relaxed fit
Skinny x Relaxed fit
Skinny x Boot cut
Relaxed fit x Boot cut
Relaxed fit x Skinny
Hence, there are 9 possible ways.
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' I did he heard diamster of 76 ice. Whidh meekureman it dosef to the draunference of the
Answers
Since the diameter of this circle is 76 inches, a measurement which the circumference of this circle has include the following: C. 238.64 inches.
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Substituting the given parameters into the circumference of a circle formula, we have;
Circumference of circle, C = πD
Circumference of circle, C = 3.14 × 76
Circumference of circle, C = 238.64 inches.
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Complete Question:
The diameter of a circle is 76 inches. Which measurement does the circumference of this circle have?
A. 123.45 inches.
B. 438.65 inches.
C. 238.64 inches.
D. 338.64 inches.
1) state whether the dilation with the given scale factor would be a reduction or an enlargement
k=4
k=1/2
k= .75
k=5/2
Answers
Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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Your mortgage payment is $954. 32/month. Using proportions, what is the minimum yearly amount you must have in realized income to keep your housing expenses in the acceptable range? $Fill in the blank text field 1
Answers
The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What is meant by mortgage payment?Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount in the principal part. Borrowing money has a cost, which is interest. Both the interest rate and the loan balance affect how much interest you pay.
You repay your mortgage loan through monthly payments. This will often be a monthly payment that aids in your gradual mortgage repayment. There will also be taxes, insurance premiums, and loan interest due.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]$& \frac{\text { Mortgage }}{\text { Acceptable Rate\% }} * 12 \\[/tex]
substitute the values in the above equation, we get
[tex]$& =\frac{954.32}{0.27} * 12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What do you mean by mortgage payment?Generally speaking, mortgage payments are made up of principal, interest, taxes, and insurance. The sum in the principle component is deducted from your outstanding loan balance. Interest is a cost associated with borrowing money. The amount of interest you pay depends on both the interest rate and the loan balance.
Monthly payments are made to pay down your home loan. This will frequently be a monthly payment to help you slowly pay down your mortgage. Taxes, insurance premiums, and loan interest will all need to be paid.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]\frac{Mortage}{Acceptable rate } *12[/tex]
substitute the values in the above equation, we get
[tex]\frac{954.32}{0.27} *12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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Write the simplified expression: 2(-2n + 2)
Answers
Answer:
-4n+4
Step-by-step explanation:
hope this helps :)
Answer:
2(-2n+2)
-4n+4
() means multiply, negative times positive is negative and it keeps the variable
Let the random variable h represent the height of a woman in the population. P(h<60) represents the probability of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model or the normal model. 1. Give an example of a probability h that can be found using the discrete model but not the normal model
Answers
The probability of h that can be found using the discrete model but not the normal model is 0.03.
A discrete probability distribution or DPD (also known as a discrete probability model) records all possible values of a discrete random variable and gives their probabilities.
The normal probability model involves when the distribution of the continuous outcome conforms reasonably well to a normal or Gaussian distribution, which resembles a bell-shaped curve.
H represents the height of women
Determine P ( H < 60 ) using either a discrete or normal model
using discrete model
P ( H < 60 ) = ∑ relative frequencies of the women with height < 60 inches
P ( H < 60 ) = 0.01 + 0.02 = 0.03
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Sue has 18 sweets
Tony also has 18 sweets
Sue gives Tony × sweets
Sue then eats 5 of her sweets
Tony then eats half of his sweets
Write expressions for the amount of sweets Tony and Sue now have
Answers
The expressions for the number of sweets that Tony and Sue now have are:
Given:
Sue has 18 sweets
Sue = 18
Tony also has 18 sweets, that is:
Toney = 18
Sue gives Tony × sweets; that is
Sue = 18 - x; and
Tony = 18 + x
Sue then eats 5 of her sweets, Tony then eats half of his ⇒ Sweets:
that is ⇒
Sue = 18 - x - 5
Tony = (18 + x) / 2
Thus, simplifying the above, we have:
Sue = 13 - x
Tony = (18 + x) / 2
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Express 60 as the product of its prime numbers
Answers
Answer:
60 = [tex]2^2[/tex] * 3 * 5
Step-by-step explanation:
The process of prime factorization is when one breaks up a number such that it can be represented as the product of many prime numbers. One does this by dividing the prime number by its smallest prime factor. Then one will divide the composite factor by its smallest prime factor, and so on. All of the resulting prime numbers are prime factors of the original number.
60 = 2 * 30
30 = 2* 15
15 = 3 * 5
60 = [tex]2^2[/tex] * 3 * 5
How much money will you have if you were to earn 10$ every week for 2 years?
Answers
Answer: $1,040
Step-by-step explanation:
52 weeks in a year
52x 10= 520
520x 2(for the years)= 1,040
Answer:
1,040$
Step-by-step explanation:
52 weeks in each year
52 x 2 is 104.
104 x 10 is 1,040.
Write and Solve an equation to determine the missing dimension of the prism with a volume of 160cm. Height is missing the numbers given are 10cm and 2cm
Answers
Explain why (-5)2 -52 is true.
Answers
Step-by-step explanation:
(-5)2-52-10-52-62hope it helps.
Answer:
(-5)2 -52-10-52-62hope it is helpful to you
What is the Oder of rotation? What is the angle of rotation? Express in degrees and as a fraction of a turn?
Answers
Answer:
Order of rotation is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure.
Step-by-step explanation:
We have the counter and the clockwise rotation where counter you move back in in 90 degrees and clockwise you move forward
Which ratio forms a probation with 18/30
=20/35
=50/90
=36/46
=60/100
Answers
Answer:
Which ratio forms a probation with 18/30
=20/35
=50/90
=36/46
=60/100
Step-by-step explanation:
name the solid ?m
# of faces ?
# of edges?
# of vertices?
what’s the height ?
Answers
Answer:
rectangle
6 faces
12 edges
8 vertices
10ft height
hope this helps
Brie bought a rug for her bedroom. The area of the rug measures 25 square feet. Her bedroom is ten feet wide and twelve feet long. Using the given measurements, what is the amount of her bedroom NOT covered by the rug
Answers
The area of bedroom rug is 15 square feet. the longer side measures 5 feet. his living room rug is twice as long and twice as wide as the bedroom rug.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares. The area of a figure is counted as the number of unit squares required to cover the overall surface area of that particular 2-D shape. Square cms, square feet, square inches, square meters, etc., are some of the common units of area measurement.To find out the area of the square figures drawn below, draw unit squares of 1-centimeter sides. Thus, the shape will be measured in cm², also known as square centimeters.To learn more about square centimeters refer to:
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Find the sum of the arithmetic series 22,33,44,55,…,605
Answers
Answer:
66
Step-by-step explanation:
a^5
Answer:
16 929
Step-by-step explanation:
a1 = 22 d = 11 a 54 = 605
Sum = 54 ( 22 + 605) /2 = 16 929
There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?
Answers
Answer:
.
green 0.416 red0.25 blue0.3
Step-by-step explanation:
Answer:
47/66 or 0.71 or 71%Step-by-step explanation:
4 blue, 3 red and 5 green marblesTotal marbles = 12Possible options for 2 different colors are:
BR, BG, RB, RG, GB, GRProbability of each:
P(BR) = 4/12*3/11 = 1/11P(BG) = 4/12*5/11 = 5/33P(RB) = 3/12*4/11 = 1/11P(RG) = 3/12*5/11 = 5/44P(GB) = 5/12*4/11 = 5/33P(GR) = 5/12*3/11 = 5/44Now, the probability of 2 different colors:
P(2 different colors) = 1/11*2 + 5/33*2 + 5/44*2 = 2/11 + 10/33 + 5/22 = (2*6+ 10*2 + 5*3)/66 = 47/66 = 0.71 = 71%What is the area of a regular hexagon with sides that measure 10 feet and an
apothem that measures 8.66 feet?
Answers
Answer:
259.8 square feet
Step-by-step explanation:
What is the area of a regular hexagon with sides that measure 10 feet and an
apothem that measures 8.66 feet?
The formula to solve the above question is given as:
Area = (3√3 s²)/ 2 where
s is the length of a side of the regular hexagon
Area of this Hexagon is calculated as:
= (3√3 × 10²)/2
= 3√3 × 100/2
= 259.80762114 square feet
Approximately = 259.8 square feet
The area of the regular hexagon = 259.8 square feet
Reduce the fraction and find the domain
Answers
The simplification of all the given algebra fractions are;
1) a/c
2) (a - b)/(a - 1)
3) (x + 1)/(x - 4)
How to solve algebraic fractions?An algebraic fraction is defined as a fraction whose numerator and denominator are algebraic expressions.
1) (abc + ab²)/(b²c + bc²)
Factorizing numerator and denominator gives;
ab(c + b)/bc(b + c)
b(b + c) will cancel out to get; a/c
2) (a² - b²)/(a² - a + ab - b)
Factorizing numerator and denominator gives;
[(a + b)(a - b)]/[a(a - 1) + b(a - 1)]
= [(a + b)(a - b)]/(a + b)(a - 1)
(a + b) will cancel out to get;
(a - b)/(a - 1)
3) (x² - 2x - 3)/(x² - 7x + 12)
Expanding the numerator and denominator gives;
(x² - 3x + x - 3)/(x² - 4x - 3x + 12)
= ((x + 1)(x - 3))/((x - 3)(x - 4)
(x - 3) will cancel out to get;
(x + 1)/(x - 4)
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What is the distance between the points (5, 1) and (-3,-5)?
Answers
Answer:
10
Step-by-step explanation:
distance formula = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}
(x_1, y_1) = (5, 1)
(x_2, y_2) = (-3, -5)
\sqrt{ [(-3) - (5)]^2 + [(-5) - (1)]^2 }
\sqrt{ [-8]^2 + [-6]^2 }
\sqrt{ 64 + 36 }
\sqrt{ 100 }
= 10
Answer:
[tex] Distance = 10 \ u [/tex]
Step-by-step explanation:
Given :-
Two points (5,1) and (-3,-5) .And we need to find the distance between the two points . We can use distance formula here to find the distance between the two points . The distance formula for two points ,
[tex]( x_1,y_1)[/tex][tex](x_2,y_2)[/tex]Distance Formula :-
[tex]\implies Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Plug in the respective values ,[tex]\implies Distance =\sqrt{\{5-(-3)\}^2+\{1-(-5)\}^2 } \\\\\implies Distance =\sqrt{ (5+3)^2+(1+5)^2}\\\\\implies Distance =\sqrt{ 8^2+6^2}\\\\\implies Distance =\sqrt{64+36}\\\\\implies Distance =\sqrt{100}\\\\\implies Distance = 10\ units [/tex]
Hence the distance between the two points is 10 units .
PLEASE HELP ILL GOVE BRAINLIEST!!!
a box will be used to ship number cubes. the dimensions of the box are h=6 in, width=10 in, length= 4 in. the number cubes have sides that each measure 1/2 in. how many number cubes can fit in the box?
Answers
Answer:
120
Step-by-step explanation:
Find the volume of the box by finding the area of the base then multiplying it by the height then divide by 1/2
Help please!!!!!!!!!!!!
Answers
Answer:
a=13.2
b=21
c=36
d=9
Step-by-step explanation:
a good way to do these is to find the simplest fraction, and multiply the number over 1 (a- 1/5*11/1 =11/5=2.2) then add the number to the total you have (a- 2.2+11=13.2) I have not done these questions in a while, so they may be off by a bit, or the formula may have a mistake, hope this helps anyway. :)
Answer:
Step-by-step explanation:
A x 20%=11
so a=11/.20
a=55
b x 75%=12
b=12/.75
B=16
c X 80%=20
c=20/.80
c=25
d x 200%=18
d=18/2
d=9
A farmer fills a rectangular water trough to a depth of 1 foot.
The trough is 4 feet long and 2 feet wide. How much water
is in the trough?
Answers
Answer:
Step-by-step explanation:
Is 8ft
Answer:
It is 8ft
Step-by-step explanation:
easy work
What is the negation of P → PV Q?
Answers
The statement "it is not the case that p and q are both true" is made in the negation of p ^ q.
As a result, when p q is true, that is, when one or both of p and q are true, (p q) is true precisely. The sentence is only untrue when both p and q are true. The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "~P" is the statement's negation.
The words "~" or "¬" are used to denote a statement's denial.
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The intensity level of sound, L measured in decibels (dB), is a function of the sound
intensity, S watts per square metre (W m-2). The intensity level is given by the following
formula.
(a) An orchestra has a sound intensity of 6. 4 × 10-3 Wm-2. Calculate the intensity level, L of
the orchestra.
(b) A rock concert has an intensity level of 112 dB. Find the sound intensity, S
Answers
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound, L, is 98.062 dB.
(b) If a rock concert has an intensity level of 112 dB, then the sound intensity, S, is [tex]10^{-0.8}\ Wm^{-2[/tex].
Sound intensity, also known as acoustic intensity, is defined as the dominion ferried by sound waves per unit area in a direction perpendicular to that area.
Given that the intensity level of sound, L, measured in decibels (dB), is a function of the sound intensity, S, watts per square meter ([tex]Wm^{-2[/tex]) as
[tex]L = 10log_{10}(S\times10^1^2), S\geq 0[/tex]
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound,
[tex]L = 10log_{10}(6.4\times10^{-3}\times10^1^2)[/tex]
[tex]= 10log_{10}(6.4\times10^9)\\= 10(log_{10}6.4\ +\ log_{10}10^9 )\\= 10(0.8062\ +\ 9)\\=10 \times 9.8062\\= 98.062\ dB[/tex]
(b) If a rock concert has an intensity level of 112 dB, then
[tex]112 = 10log_{10}(S\times10^1^2)\\log_{10}(S\times10^1^2) = \frac{112}{10}\\log_{10}(S\times10^1^2)= 11.2\\S\times10^1^2 = 10^{11.2}\\S = \dfrac{10^{11.2}}{10^1^2} \\S = 10^{-0.8}\ Wm^{-2[/tex]
The sound intensity is [tex]10^{-0.8} Wm^{-2[/tex].
Hence, (a) L = 98.062 dB and (b) S [tex]= 10^{-0.8}\ Wm^{-2[/tex].
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How do you select sample size using simple random sampling?
Answers
Using the method of simple random sampling, The answer is we select sample before collecting data.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
In simple random sampling, the sample size is determined before collecting data. There are several ways to determine the sample size, but one common method is to use a sample size calculation formula, such as: n = (z^2 * p * (1-p)) / e^2
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Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)
Answers
The value would be [tex]34^{-1} \pmod{47}=30[/tex]
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.
In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.
We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]
We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.
Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:
[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]
Now we can substitute the right side of the equation:
[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]
And now we can substitute the left side of the equation:
[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]
And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.
Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]
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The value would be 13.
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
We can use the property of modular inverse that
[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]
So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]
[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]
Hence, The value would be 13.
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