Topic Test Topic Test Active Does this graph represent a function? What is the domain and range of the graph? a. Yes, domain: all real numbers, range: y=0 b. Yes, domain: all real numbers; range: y>=0 c. No: domain: all whole numbers; range: y<=0 d. Yes domain: all real numbers; range: y>0
Answers
The correct answer is b. Yes, the graph represents a function. The domain of the graph is all real numbers, and the range is y greater than or equal to 0.
To determine if a graph represents a function, we need to make sure that for every input value (x-coordinate), there is only one corresponding output value (y-coordinate). In this graph, for every x-value, there is only one y-value or a horizontal line passing through the graph. Therefore, it satisfies the definition of a function.
The domain refers to all possible input values of the function. In this case, the graph extends infinitely in both directions along the x-axis, indicating that the domain includes all real numbers.
The range, on the other hand, represents all possible output values of the function. Looking at the graph, we can see that the y-values start from 0 and go upward indefinitely, but they never go below 0. Therefore, the range is y greater than or equal to 0.
In summary, the graph represents a function because it passes the vertical line test, ensuring that each x-value has a unique y-value. The domain of the graph is all real numbers, and the range is y greater than or equal to 0, indicating that the graph never goes below the x-axis.
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Related Questions
what is the population being studied warts
Answers
The average population being studied is people with warts. Specifically, this population includes individuals of all ages who have been diagnosed with any type of wart caused by a virus, such as common warts, plantar warts, and flat warts.
The population being studied is people with warts. Warts are caused by a virus and can occur anywhere on the body. Common warts, plantar warts, and flat warts are the most common types. Common warts are usually found on the hands and fingers, and are usually round and raised. Plantar warts are found on the soles of the feet and can be painful. Flat warts are usually found on the face, arms, and legs, and are generally flat and smooth. People of all ages can be affected by warts, and they are highly contagious and can be spread through contact with an infected person or surface. Treatment options include over-the-counter medicines and prescription medications, as well as cryotherapy and laser treatments. This population is being studied to better understand the causes, risk factors, and treatments for warts.
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The complete question is
what is the population being studied warts and the prevalence of warts in the population being studied?
Solve Eq. 7.5 and Eq. 7.6 ( 2 equations with 2 unknowns) for v1 in terms of: m,M,g,h. (20 pts) mv1=(m+M)V2(Eq.7.5)21(m+M)V22=(m+M)gh(Eq.7.6) 6. You shoot a ball, m=50.0 g, into a catcher, M=200.0 g, the center of mass rises 15.0 cm. Calculate vi. Refer to your answer for Question 5.
Answers
The initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.
To solve Eq. 7.5 and Eq. 7.6 for v1 in terms of m, M, g, and h, we will substitute the given values of m, M, and h into the equations.
Eq. 7.5: mv1 = (m+M)V2
Eq. 7.6: (m+M)V22 = (m+M)gh
Given:
m = 50.0 g (mass of the ball)
M = 200.0 g (mass of the catcher)
h = 15.0 cm (rise in the center of mass)
First, let's solve Eq. 7.6 for V2 by dividing both sides by (m+M):
V22 = gh
Next, substitute the expression for V2 into Eq. 7.5:
mv1 = (m+M)(gh)
Now, solve for v1 by dividing both sides by m:
v1 = (m+M)(gh) / m
Substituting the given values:
v1 = (50.0 g + 200.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)
Calculating the expression:
v1 = (250.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)
v1 = 367.5 m/s
Therefore, the initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.
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16x - 4y = 3 y = 4x + 7
Answers
y in equation 1
\(\begin{gathered} 16x-4\mleft(4x+7\mright)=3 \\ 16x-16x-28=3 \\ -28=3 \end{gathered}\)-28=3 is false, therefore the system of equations has no solution
15 points please help!
What is the volume of a spherical balloon after 11 seconds if the radius of the balloon is increasing at 1.3cm/sec? Round to the nearest tenth of a centimeter
Answers
Answer:
14?
Step-by-step explanation:
Define the term functions limits and continuity as used in
business calculus and use an example
Answers
In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.
The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.
"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.
For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.
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This is pre calculas summation please help lol
Answers
Answer: 1 - 2 + 4 - 8 + 16
Step-by-step explanation:
Answer:
-1-2-4-8-16
Step-by-step explanation:
(-2⁰)+(-2¹)+(-2²)+(-2³)+(-2⁴)
-1-2-4-8-16
-31
Select the correct antiderivative.
dy/dx - 1/x^2+1
a. in √x^2+1+C
b. 2x/(x^2+1)^2+C
c. arctan x+C
d. In(x^2+1)+C
Answers
The correct antiderivative for dy/dx - 1/x^2+1 is option D, In(x^2+1)+C.
The term "anti" in antiderivative refers to the opposite operation of differentiation, which means finding the function whose derivative is given.
The given function's derivative is dy/dx - 1/x^2+1, and option D represents the antiderivative of this function.
Option A is incorrect because it does not have the -1/x^2+1 term, option B is incorrect because it has a 2x term instead of -1/x^2+1, and option C is incorrect because its derivative is 1/(x^2+1) instead of dy/dx - 1/x^2+1.
Hence the antiderivative for dy/dx - 1/x^2+1 is In(x^2+1)+C.
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Solve for m.
5m - 2p = 4
m=
Answers
Answer:
m=1
Step-by-step explanation:
5m-2p=4
-4 -4
1m-2p=0
divide 1m over 2p
ANSWER 0.5
What type of dilation is formed when the scale factor K is greater than one
Answers
Answer:
Enlargement
Step-by-step explanation:
When k > 1, the dilation is an enlargement. When k > 0 and k < 1, the dilation is a reduction. In a dilation, the original figure and its image are similar. The ratio of the side lengths of the image to the corresponding side lengths of the original figure is the scale factor of the dilation.
3. A cubic polynomial with rational coefficients has the roots 6+ Fo and. Find one additionalroot.
0-6-v6
06-16
0-6+ /6
06- 6
Answers
Answer:06-16
Step-by-step explanation:
Find the value of x.
B
6
8
А
х
D
x = [?]
Answers
Answer:
What's the question is that a good thing
Answer: 3
Step-by-step explanation:
Q \( \rightarrow \) Find the Fourier transform of the signal below \[ X(t)=e^{(-1+2 j) t} u(t) \]
Answers
The Fourier transform of the signal equation X(t) = \(e^{(-1+2 j) t} u(t)\) is X(jw) = \(\frac{1}{1-2 j+jw}\).
Given that,
We have to find the Fourier transform of the signal equation X(t) =\(e^{(-1+2 j) t} u(t)\)
We know that,
Take the signal equation,
X(t) =\(e^{(-1+2 j) t} u(t)\)
Now, Fourier transform of X(t) formula is X(jw) which is the function represent the Fourier transform
X(jw) = \(\int\limits^\infty_{-\infty}{X(t)e^{-jwt}} \, dt\)
X(jw) = \(\int\limits^\infty_{-\infty}{e^{(-1+2 j) t} u(t)e^{-jwt}} \, dt\)
X(jw) = \(\int\limits^\infty_{0}{e^{(-1+2 j) t} e^{-jwt}} \, dt\)
X(jw) = \(\int\limits^\infty_{0}{e^{-(1-2 j+jw)t}} \, dt\)
X(jw) = \(\frac{1}{-(1-2 j+jw)}e^{-(1-2 j+jw)t}} |^\infty_0\)
X(jw) = \(\frac{1}{-(1-2 j+jw)[e^{-(1-2 j+jw)\infty}-e^0]}}\)
X(jw) = \(\frac{1}{-(1-2 j+jw)}[0-1]\)
X(jw) = \(\frac{1}{1-2 j+jw}\)
Therefore, The Fourier transform of the signal equation X(t) =\(e^{(-1+2 j) t} u(t)\) is X(jw) = \(\frac{1}{1-2 j+jw}\)
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The question is incomplete the complete question is-
Find the Fourier transform of the signal equation X(t) =\(e^{(-1+2 j) t} u(t)\)
Which FAR Part 77 imaginary surface has slopes that may range from 20:1 to 50:1?
The primary surface
The horizontal surface
The approach surface
The conical surface
Answers
The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.
The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.
Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.
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Which is the graph of the function f(x) = -√x
Answers
Answer: A
Step-by-step explanation:
Answer:
Graph A
Step-by-step explanation:
We know rootover can never be negative
So
y=√x has range [0,oo) and domain also [0,oo)So it lies in right side of y axis
for y=-√xThe range shifts to 4 th quadrant i.e [0,-oo)
So graph A is correct
Identify u and U = du dx II dx for the integral ¹ / ² (du) dx. (6 - 4x²)²(-8x) dx X X
Answers
We have u = u(x) and U =\(-1/16 ∫(du) / [(6 - 4x^2)^2x]\) as the identified substitution for the given integral.
To identify u and U for the given integral ∫(1/2) (du) dx, we can perform integration by substitution.
Let's rewrite the integral as ∫(1/2) (du/dx) dx, where u = u(x) is the function that we want to determine.
Now, we need to find the derivative du/dx and solve it for dx to obtain the substitution dx in terms of du:
\(du/dx = (6 - 4x^2)^2(-8x)\)
dx = du / (du/dx)
dx = du /\([(6 - 4x^2)^2(-8x)]\)
Now, let's substitute dx in the integral using the derived expression:
\(∫[u] (1/2) (du) / [(6 - 4x^2)^2(-8x)]\)
Simplifying the integral:
\((1/2) ∫[u] du / [(6 - 4x^2)^2(-8x)]\)
=\(-1/16 ∫[u] du / [(6 - 4x^2)^2x]\)
Therefore, we have u = u(x) and U = -\(1/16 ∫(du) / [(6 - 4x^2)^2x]\) as the identified substitution for the given integral.
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The weight of a dog in pounds can be modeled by the function f(n) where n is the number of months that have passed: f(n) = 8+3n use the function to complete the table shown
For my midterm lol
Answers
Answer:
0 = 8
5 = 23
14 = 50
Step-by-step explanation:
f(n)= 8+ 3n
when n=0
f(0)= 8+ 3(0)
f(0)= 8+0
f(0)= 8
when n=5
f(5)= 8+ 3(5)
f(5)= 8+ 15
f(5)= 23
f(n)= 50
f(n)= (50- 8)÷ 3
f(n)= 42÷3
f(n)=14
so n=14
HELP ME ASAPPPPPPPPPPPPPPP
Answers
Answer:
a because i said so trust me
Step-by-step explanation:
Answer:
The number of students that the club needs is at least 8
Step-by-step explanation:
The club would at least need 8 people.Add 15 and 8 together and you get 23.More people would be better but all the club really needs is 8.
find the value of the trigonometric ratio
Answers
tan c =opposite÷ adjacent
tan c =36÷15
tan c = 12÷5
At its highest,the elevation of a county is 5,776 feet above sea level at its lowest point the elevation of the county is 9 feet below sea level
Answers
5,776-(-9)
Positive
5,785
Write an integer that represents the elevation of county feet below sea level.
what is the measure of angle A
Answers
Answer:
a = 53
Step-by-step explanation:
Start with d
The ends of d + 53 are diameter ends. That means that d + 53 is a right angle
d + 53 = 90
d = 90 - 53
d = 37
Next, find b. The end points of b are the same end points as for 53 degrees. B is the central angle of 53 which means b = 2 * 53
b = 106
c is the supplement of b
c + b = 180
b = 106
c + 106 = 180
c = 180 - 106
c = 74
The triangle containing a and c is isosceles because 2 of the 3 angles are opposite radii. The lowest angle is also a because it is opposite one of the radii.
a + a + 74 = 180
2a = 180 - 74
2a = 106
a = 106/2
a = 53
Hard to believe, but there it is.
ument will3. Graph and investigate the following piecewise equation: (5points)f(x)={, ?for x < 2(-x + 10 for 2
Answers
We are given the following function:
\(\begin{gathered} f(x)=\lbrace x^2;\text{ x<2} \\ -x+10;2\le x\le6\} \end{gathered}\)The graph of this equation is a parabola for values of x < 2 and a line for values of 2<= x <= 6. The graph is the following:
Solve:
(a+b+c) (a+b-c)
Answers
Answer:
a²+2ab+b²-c²Step-by-step explanation:
Solve:
(a+b+c) (a+b-c)=
(a²+ab-ac+ab+b²-bc+ac+bc-c²)=
a²+ab-ac+ab+b²-bc+ac+bc-c²=
a²+2ab+0ac+b²+0bc-c²=
a²+2ab+b²-c²
Answer:
The answer is a² + 2ab + b² - c²
Step-by-step explanation:
(a + b + c) × (a + b - c)
a² + ab - ac + ba + b² - bc + ca + cb - c²
a² + ab + ba - ac + ca + b² - bc + cb - c²
a² + 2ab + b² - c²
Thus, The answer is a² + 2ab + b² - c²
-TheUnknownScientist 72
find two positive numbers that satisfy the given requirements. the sum of the first number squared and the second number is 51 and the product is a maximum.
Answers
The two positive numbers that satisfy the given requirements are 4.12 and 34
To find two positive numbers that satisfy the given requirements, we can use the concept of quadratic equations. Let's call the first number "x" and the second number "y".
From the given information, we have the equation:
x² + y = 51
To find the maximum product, we can use the formula for finding the maximum point of a quadratic function. In this case, the function is:
f(x) = xy
We can rewrite this function as:
f(x) = x(51 - x² )
To find the maximum point of this function, we need to take its derivative and set it equal to zero:
f'(x) = 51 - 3x²
0 = 51 - 3x²
3x² = 51
x² = 17
So the first number, x, is the square root of 17.
To find the second number, we can substitute x into the original equation:
x² + y = 51
17 + y = 51
y = 34
So the two positive numbers that satisfy the given requirements are approximately 4.12 and 34, with a product of approximately 140.6.
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A piggy bank has only nickels and dimes in it. There are 14 coins worth $0.95. How many nickels and dimes are in the bank?
Answers
Answer: 7 dimes 5 nickles
Step-by-step explanation:
I did the math
First she need to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days in a row. she finds her average resting heart rate to be 62 after 5 days and she remembers the last day pulse was 58 and all the others were the same
Answers
Answer: 63 She finds her average resting heart rate to be 62 after 5 days. That means, average of the 5 heart rate pulse=62 If the last day was 58 and all the other days were the same.
Step-by-step explanation
Which of the following formulas is CORRECT for finding the present value of an investment
A) FV = PV/(1 + r)^n
B) PV = FV x (1 + r)n
C) PV = FVn x (1 + r)
D) PV = FV x 1/(1 + r)^n
Answers
The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.
The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).
Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.
In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.
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3/2=12 y=
Pls help ASAP
Answers
Answer: 1/8
Step-by-step explanation:
Answer: y=8
Step-by-step explanation:
3/2=12 so first thing we want to do is multiply the bottom of the fraction and that leaves us with 3=24 then we divide and we get y=8 (that is what i beign thaught hope this helps in some way)
Will the solution x > -7 have an open or closed circle?
Answers
Answer:
Open
Step-by-step explanation:
The <, > signs will have an open circle and the greater than or equal to or less than or equal to will be a be a closed circle.
Hope this helps and I hope u have an Amazing day!!
Help explain how to solve
Answers
The value of the angle U in the triangle is 92.10 degrees.
How to find the angle in a triangle?The angle U in the triangle can be found using cosine rule as follows:
Let's use cosine formula to find the angle U
c² = a² + b² - 2ab cos C
Hence,
Therefore,
a = 58.8
b = 38.4
c = 71.4
Hence,
71.4² = 58.8² + 38.4² - 2(58.8)(38.4) cos U
5097.96 = 3457.44 + 1474.56 - 4515.84 cos U
5097.96 - 4932 = - 4515.84 cos U
165.96 = - 4515.84 cos U
divide both sides by - 4515.84
cos U = 165.96 / - 4515.84
cos U = - 0.03675063775
U = cos⁻¹ - 0.03675063775
U = 92.1032274244
Therefore,
U = 92.10 degrees
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I need help on this fast