f(x)
Which type of function describes f(x)?
•
Rational
Polynomial
O Logarithmic
• Exponential
Answers
Answer:
Exponential function
[tex]y=1.25(2)^x[/tex]
Step-by-step explanation:
Definitions
Asymptote: a line that the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
Polynomial Function[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]
An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.
A continuous function with no holes or asymptotes.
Rational Function[tex]f(x)=\dfrac{h(x)}{g(x)}[/tex]
An equation containing at least one fraction whose numerator and denominator are polynomials.
A rational function has holes and/or asymptotes.
A rational function has holes where any input value causes both the numerator and denominator of the function to be equal to zero.A rational function has vertical asymptotes where the denominator approaches zero.If the degree of the numerator is smaller than the degree of the denominator, there will be a horizontal asymptote at y = 0.If the degree of the numerator is the same as the degree of the denominator, there will be a horizontal asymptote at y = ratio of leading coefficients.If the degree of the numerator is exactly one more than the degree of the denominator, slant asymptotes will occur. Logarithmic Function[tex]f(x) =\log_ax[/tex]
A continuous function with a vertical asymptote.
A logarithmic function has a gradual growth or decay.
Exponential Function[tex]f(x)=ab^x[/tex]
The variable is the exponent.
A continuous function with a horizontal asymptote.
An exponential function has a fast growth or decay.
Answer: exponential
Step-by-step explanation:
Related Questions
Gustavo is in a contest where he will win one of four possible prizes. he creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. he spins the spinner several times to demonstrate the likelihood of winning a certain prize. what is true about gustavo’s method of data collection and his data on the possible prizes?
Answers
Answer:
Gustavo used a simulation where the data is quantitative’
If a sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.Find the rate of interestsl
Answers
The rate of interest applied on the amount is 15%.
According to the statement
we have given that the sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.
And we have to find the rate of interest on this money.
So, For this purpose,
The given equation is:
Money in 3 years = 2175
Money in 5 years = 2625
Amount increased in 2 years = 2625-2175
Amount increased in 2 years = 450
And amount increased per year = 450/2
Amount increased per year = 225.
SI in 3 years=450/2 *3=Rs. 675
Principal amount= 2175-675=1500
so again,
R=(I*100)/(P*T)
R=15%
So, The rate of interest applied on the amount is 15%.
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Hazing has been reported all across america. What percentage of students say they have witnessed hazing and did not report it?.
Answers
percentage of students say they have witnessed hazing and did not report it are = 95%
What is Hazing?No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.
involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.
What is an example of hazing?Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.
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john is constructing a satellite dish . The receiver is going to be located 15 inches above the vertex of the dish. The dish is going to be 84 inches wide. How deep will the dish be
Answers
The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.
How can the equations of a parabola be used to find the depth of the dish?The location of the receiver = 15 inches above the vertex
Width of the dish = 84 inches
The receiver of a satellite dish is normally located at the focus (focal point).
Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;
Coordinates of the focus = (0, a)
Where;
a = The distance of the focus above the vertex
Therefore;
a = 15 inches
The dish is horizontally spaced equally about the vertex.
The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.
At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;
X = 84 ÷ 2 = 42
Which gives;
42² = 4 × 15 × Y
Y = 42² ÷ (4 × 15) = 29.4
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The figure shows a square, a regular pentagon and a regular hexagon put together. What is the measure of ∠BAC
Answers
Answer:
42
Step-by-step explanation:
One angle of a regular pentagon = 108°
One angle of a regular hexagon = 120°.
One angle of a square = 90°
∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°
Simplify[tex](\frac{16}{81}x^{16}\right))^{\frac{1}{2}}[/tex]
Answers
Answer:
[tex]\sf \dfrac{4}{9}x^8[/tex]
Step-by-step explanation:
Law of exponents:[tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]
16 = 4 *4 = 4²
81 = 9 *9 = 9²
[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]
[tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]
(50 POINTS PLEASE HELP!!!)
!!!THE QUESTION THAT I NEED TO BE ANSWERED IS THE PICTURE ATTACHED!!! BELOW IS JUST THE REQUIREMENTS AND EXAMPLE!!!
He has hired you as their new production manager. Your job is to look at four different figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the four options shown below. The candy is animal gummies. The package must hold between 80 and 100 cubic inches (roughly 5-7 cups of space). The cost of the plastic for the packaging is $0.004 per square inch. When finding cost you would multiply the Total Surface Area by $0.004.
For example:
Total Surface Area = 86 sq. in
Cost per sq in = $0.004
86 * .004 = .344 when rounded to nearest penny = $0.34
Your project should include the volume, total surface area, and materials cost for each figure given below, including the formulas you used and each step of your work. Be sure to find all measures for each figure, even if the figure does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.
Answers
The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;
Surface area of the packaging = 168 in.²Package volume = 108 in.³Cost of packaging = $0.672Which method can be used to provide the packaging estimates for the company?The dimensions of the box in the given figure are;
Length, L = 9 in.
Width, W = 2 in.
Height, H = 6 in.
The surface area, A, of a box is found using the following formula;
A = 2•L•W + 2•L•H + 2•H•W
Therefore;
A = 2×9×2 + 2×9×6 + 2×2×6 = 168
The surface area of the figure, A = 168 in.²The volume of a box, V, is calculated as follows;
V = L•W•HFor the given figure, therefore;
V = 9 × 2 × 6 = 108
The volume of the given figure, V = 108 in.³Cost of packaging per square inch, c = $0.004
Cost to package the figure, C, is therefore;
C = c × AWhich gives;
C = $0.004/in.² × 168 in.² = $0.672
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i do not know how to get what they are asking me too
Answers
1.115 multiplied by 100
111.5% - 100% = 11.5% rate of increase
Find the surface area of the composite figure.
4 cm
13 cm
3 cm
4 cm
SA =
12 cm
[?] cm²
5 cm
3 cm
Answers
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
What is the surface area of a truncated prism?
The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:
A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)
A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²
A = 276 cm²
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
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Puedes colorear el 20% del triangulo? Aqui tienes una pista
Answers
The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively. find the common difference
Answers
The first term of the arithmetic progression exists at 10 and the common difference is 2.
How to estimate the common difference of an arithmetic progression?
let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.
We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula
The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.
9th term = 50
a + 8d = 50 ...............(1)
12th term = 65
a + 11d = 65 ...............(2)
subtract them, (2) - (1), we get
3d = 15
d = 5
If a + 8d = 50 then substitute the value of d = 5, we get
a + 8 [tex]*[/tex] 5 = 50
a + 40 = 50
a = 50 - 40
a = 10.
Therefore, the first term is 10 and the common difference is 2.
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Which line does a better job capturing the trend of the data? Explain.
10
•
Graph A
10
10
00
6
-
2
O
●
N
●
4
20
●
Graph B
9
Answers
Answer:
B
Step-by-step explanation:
Line A mostly follows the trend of the higher points, entirely neglecting the existence of the lower points. Line b acknowledges the lower points and adjusts the line accordingly to be lower.
please help me with questions 1 and 2 (with explanations and calculation) thank you so much
Answers
Ans of 1b= 0.5
Ans of 2 = 300ml
Hey so I’m stuck on this. What is the solution to the equation 2= -8 -x?
Answers
Answer:
X = -10
Step-by-step explanation:
2 = -8 -X
2+X = -8
X = -10
Answer:
x = - 10
Step-by-step explanation:
Comment
The trick to any equation like this one is to get the numbers on one side and the term with an unknown on the other side. That way, your last step is to divide by the number in front of the letter into a number on the other side.
Solution
2 = - 8 - x Add 8 to both sides
2 + 8 = -8 + 8 - x Combine
10 = - x The number in front of x is - 1. Divide.
10/-1 = -x/-1
-10 =x
The letter usually has to be expressed as a number greater than 0. In other words x is positive for this question
what all can you tell me about this shape?
Answers
Answer: It is an equilateral square
Step-by-step explanation: it has 4 tick marks
In 15 minutes Frankita created 15 drawings. In 30 minutes she created 17 drawings. In 45 minutes she created 20 drawings. In 60 minutes she created 24 drawings. If Frankita continues making drawings in the same pattern, how many total drawings will Frankita have created at the end of 90 minutes?
Answers
In 90 minutes, she would have created 36 drawings.
How many total drawings will Frankita have created at the end of 90 minutes?The first step is to establish a pattern between time and the number of drawing that Frankita creates.
When the question is studied, it can be deduced that every 15 minutes the rate of increase in drawing is (previous drawing + (1 + rate of increase of previous drawing.
Drawing created in 30 minutes = 15 + 2 = 17
Drawing created in 45 minutes = 17 + ( 1 + 2) = 20
Drawing created in 60 minutes = 20 + (3 + 1 ) = 24
Drawing created in 75 minutes = 24 + (4 + 1) = 30
Drawing created in 90 minutes = 30 + (5 + 1) = 36
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The sky wheel has 42 glass enclosed gondolas. What is the measure of each central angle between gondola cars, to the nearest hundredth degree?
Answers
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].
From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.
Therefore,
the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]
where n represents the number of gondolas (42).
Thus,
the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]
= 8.5714
The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].
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Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) f(x) = x(18x 4)
Answers
Answer:
Below in bold.
Step-by-step explanation:
f(x) = x(18x + 4)
f(x) = 18x^2 + 4x
Antiderivative = 18 * (x^2+1)/(2 + 1) -+4x(1+1) / (1+1) + C
= 18x^3 / 3 + 4x^2 / 2 + C
= 6x^3 + 2x^2 + C.
Checking by differentiating:
f'(x) = 6*3 x^(3-1) + 2*2x^(2-1)
= 18x^2 + 4x
= x(18 -+4)
What are the restricted values for x2−3x−2−4y⋅2x−2−xy2+2y2?
Answers
The restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
How to determine the restricted values for the function?The complete question is added as an attachment
The equation is given as:
(x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2)
Set the products of the denominators to 0
-4y * (-xy^2 + 2y^2) = 0
Split the equation
-4y = 0 or (-xy^2 + 2y^2) = 0
Remove the bracket
-4y = 0 or -xy^2 + 2y^2 = 0
Divide both sides by -4 in -4y = 0
y = 0
Factor out y^2 in -xy^2 + 2y^2 = 0
y^2(-x + 2) = 0
This means that y^2 = 0 or -x + 2= 0
This gives y = 0 or -x + 2 = 0
Solve for x in -x + 2 = 0
x = 2
Hence, the restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
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Hey I'm sunny, and i request someone's help (please)
1. Value of b (b - 4.21 = 87.654)
2. Divide: 1.86 and 8.4
3: Compare: 1.92
that's it
Bye! - SunnyBunny <3
Answers
The computation shows that the value of b will be 91.864.
How to illustrate the information?From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:
b - 4.21 = 87.654
b = 87.654 + 4.21
b = 91.864
Also. dividing 1.86 and 8.4 will be:
= 1.86/8.4
= 0.2213
Therefore, the values are 91.864 and 0.2213.
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please help me, i will give brainliest!! help me please
Answers
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
Ratio = Number of event 1 : Number of event 2 (in same unit, if necessary)
10
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
11
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
1 minute = 60 seconds1 week = 7 days1 hour = 60 minutes12
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
13
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
14
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
Which intervals show f(x) decreasing? Check all that apply.
Answers
The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].
Which intervals naming the answer choices show the function f(x) decreasing?It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.
On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.
Also, between the interval; [–2, –1.5], the function f(x) is decreasing.
Also, between the interval; [1.5, 2], the function f(x) is decreasing.
Also, between the interval; [2, 2.5], the function f(x) is decreasing.
Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]
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give the answer please
Answers
The inverse of a function is given as √x - 1
Inverse of a functionTo get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.
Given the following function
f(x) = (x+1)^2
Let y= f(x) to have:
y = (x+1)^2
Replace y with x to have:
x = (y+1)^2
Make y the subject of the formula
√x =y + 1
Subtract 1 from both sides
√x - 1 = y
Swap
y = √x - 1
Hence the inverse of a function is given as √x - 1
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find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answers
Combining of the two cylinders gives a composite figure that has the surface area of a solid cylinder of radius 7 mm and height 6 mm, such that the surface area of the figure is approximately 571.5 mm².
Which method can be used to find the surface area of the figure?Radius of the inner cylinder, r = 3 mm
Radius of the outer cylinder, R = 7 mm
Height of the cylinders, h = 6 mm
Given that the inner cylinder exactly fits into the outer cylinder, we have;
The surface area of the composite figure is the surface area of the hollow outer cylinder + The area of the top and bottom of the inner cylinder.
Which gives;
The surface area of the composite figure, A, is the surface area of a solid cylinder, using the dimensions of the hollow outer cylinder.
A = 2•π•R² + 2•π•R•hWhich gives;
A = 2 × π × 7² + 2 × π × 7 × 6Where, π = 3.14, we have;
A = 2 × 3.14 × 7² + 2 × 3.14 × 7 × 6 ≈ 571.5
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Janice walks 2 kilometers every morning. how many meters does janice walk each day? a) 0.20 meters b) 20 meters c) 200 meters d) 2,000 meters
Answers
Answer: 2000 meters
Step-by-step explanation: A kilometer means 1,000 meters a kilo means 1000. So, 2 x1000 = 2000 meters.
The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping the bus fare as part of a promotion to increase the ridership on that route. Lately, the busses have only been at half capapcity. The bus company's research shows that for every $5 decrease they will gain 2 more riders.
a) define variables and set up an equation to represent this scenario
b) What is the maximum revenue the bus company can earn and what will be the cost of a ticket when the revenue is at a maximum
Answers
If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6
Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.
We are required to find the maximum revenue that the bus company can earn.
Suppose x represents the number of seats, y represents the total amount.
Price=$156
Seats=56
When the bus is of half capacity the bus seats will be 28.
As price decreases th rider gains 2 more.
Revenue equation.
y=(156.5x)(28+2x)-------------1
Expanding the equation.
y=4368-140x+312-10[tex]x^{2}[/tex]
Differentiating with respect to x.
dy/dx=0-140+312-20x
=172-20x
Put dy/dx=0
172-20x=0
x=8.6
Substitute the value of variable x in the equation 1.
y=(156-5x)(28+2x)
=$5107.6
Hence the maximum revenue that the bus company can earn is $5107.6.
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in the diagram below all angles are given in degrees(°)
find X with 50°,3x,X,X+110
Answers
The value of x in the angles of Quadrilateral is 52 degree.
According to the statement
we have given a four angles and we have to find the value of x in these give angles.
From given 4 angles it is clear that the these angles are of a quadrilateral.
And we know that the
A quadrilateral is a four-sided polygon, having four edges and four corners.
And the sum of all angles of a quadrilateral is 360 degree.
so,
50° + 3X + X + (X+110) = 360 degree
50° + 4X + (X+110) = 360 degree
50° + 5X + 110 = 360 degree
160° + 5X = 360
5X = 360-100
5X = 260
X = 52 degree.
So, The value of x in the angles of Quadrilateral is 52 degree.
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Which equations for the line of best fit do not accurately represent the data in the scatter plot? Select all that apply.
Answers
The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).
What linear equation best fits the scatter plot?
The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.
In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)
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This question is down below.
Answers
Answer:
Step-by-step explanation:
15 hope it help
The odds in favor of a horse winning a race are 9:5. find the probability that the horse will win the race.
Answers
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.