Answers
Answer:
The range of g(x) is [5, ∞) ⇒ (a)
Step-by-step explanation:
The range of the function is the values of y which corresponding to the values of x (domain)
∵ [tex]g(x)=5+\sqrt{4-x}[/tex]
∵ There is no square root for negative values
∴ 4 - x ≥ 0
→ Add x to both sides
∴ 4 - x + x ≥ 0 + x
∴ 4 ≥ x
→ that means x is smaller than or equal to 4
∴ x ≤ 4
→ The greatest value of x = 4
∴ The domain of g(x) = {x : x ≤ 4} ⇒ (-∞, 4]
→ At x = 4
∵ g(4) = 5 + [tex]\sqrt{4-4}[/tex]
∴ g(4) = 5 + 0
∴ g(4) = 5
→ That means the smallest value of y = 5 because [tex]\sqrt{4-x}[/tex] is always
give a positive value which add to 5
∴ The range of g(x) is {y : y ≥ 5} ⇒ [5, ∞)
The right answer is (a)
Related Questions
A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners
at first and second base. At the moment the ball is hit, the runner at first base runs to
second base at 25 ft/s. Simultaneously, the runner on second base runs to third base
at 15 ft/s. How fast is the distance between these two runners changing 2 s after the
ball is hit?
Answers
The runner on first has distance from second of 90 -25t, where t is the time in seconds since he left 1st base.
The runner on second has a distance from second of 15t, where t is the time in seconds since he left 2nd base
Then the Pythagorean theorem tells us the distance between the runners is :
d = √((90 -25t)² +(15t)²)
The rate of change of distance between the runners is the derivative of this with respect to time.
dd/dt = 2(90-25t)(-25)+2(15t)(15) / (2sqrt(90-25t)^2 + 15t^2)
Replace t with 2 and solve to get: -31
The distance between runners is decreasing at 31 ft/s two second after they leave the bases.
Evaluate the following expression when x = -5 and y = 25.
A. -3,130
B. -630
C. 3,120
D. 620
Answers
PLEASE HELP THIS IS SERIOUS DUE IN 5 MINS
You have been saving $4.50 per week for the last several weeks.
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Answers
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hii help me pls this math test is so hard
Answers
Write the slope-intercept form for the equation of a line parallel to y = -9 and passes through the point (12, -5)
Answers
Answer:
Let's see what to do buddy...
_________________________________
Step-by-step explanation:
_________________________________
STEP (1) :
The slope of the line y = - 9 is 0(zero) because it is a Horizontal line.
So the slope of the line which is parallel to y = -9 is zero .
_________________________________
STEP (2) :
We have this equation to find the slope-intercept form of the linear functions :
[tex]y - y(given \: point) = (slope) \times ( \: x -x(g \: p) \: ) \\ [/tex]
_________________________________
STEP (3) :
Now it is time to put the slope and the given point in the equation :
given point = ( 12 , -5 )
slope = 0
[tex]y - ( - 5) = 0 \times (x - 12) \\ \\ y + 5 = 0 \\ \\ y = - 5[/tex]
_________________________________
And we're done.
Thanks for watching buddy good luck.
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Answer plz plz plz plz
Answers
The last graph best explains the rotation
Pat has 9cards. Frank has 2more cards than Steve. Steve has 3cards. How many more cards does pat have than frank ?
Answers
The bottom of a lake is 213 feet above sea level.
Short answer that best completes each statement
Answers
Answer:how will we know what your talking about if you only gave us a number
Step-by-step explanation:
She paid with a $100 bill and received $32.16 in change. If sales tax is charged at a rate of 6%, what was the price for one candle holder before taxes?
Answers
Answer:
$63.77
Step-by-step explanation:
100-32.16=67.84
67.84*0.94=63.77
Hope this helps!
Answer:
$63.76
Step-by-step explanation:
Two new wind-farm tower projects are proposed for a small company that installs them in south western Pennsylvania. Project A will cost $250,000 to complete and is expected to have an annual net cash flow of $75,000. Project B will cost $150,000 to complete and should generate annual net cash flows of $52,000. As a small company, the owner and senior management team are very concerned about their cash flow. Use the payback period method and determine which project is better from a cash flow standpoint. Show your work and include any formulas used to calculate PP.
Answers
Answer:
Step-by-step explanation:
The payback period is the time to regain the cost of the investment or DRCI. It is a risk criterion that measures the time needed for the discounted sum of the forecast cash flows to allow the recovery of the cost incurred by the investment. However, the shorter the payback period, the lower the risks associated.
Mathematically;
Payback period = Cost of the investment / Annual Net Cash Flow
From the given question:
For project A;
Cost of investment = $250,000
Annual net Cash Flow = $75000
The payback period for Project A = $250,000 / $75,000
The payback period for Project A = 3.33
For project B;
Cost of investment = $150,000
Annual net Cash Flow = $52000
The payback period for Project A = $150,000 / $52,000
The payback period for Project A = 2.88
Thus, from the calculation, we can deduce that project B is better than project A because there fewer risks associated with it because it has a shorter payback period compared to project A.
I have c candies, and my sister has twice as many. Together we have 27 candies. How many candies do I have?
Answers
Answer:
i think the answer would be 27 times two then you didved and find answer Hopes This work?
Step-by-step explanation:
I think so because it just makes since
Answer:
You have 9 candies.
Step-by-step explanation:
This is correct because if you have 9 candies, and your sister has twice as many (18), you would get 27 candies in total if you add them together.
If you could subscribe to penny_pg3d that would be great! :)
The national debt was about $6.9 trillion at the end of 2003. Express this quantity as the number of dollars per person. Assume a U.S. population of 280 million.
Answers
Answer:
$24642.85 per person.
Step-by-step explanation:
6.9T/280M
The average amount of debt on each person in U.S is $24,642.86.
What is average?An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Total debt = $6.9 trillion = $6.9 * [tex]10^{12}[/tex]
Total population = 280 million = 280 * [tex]10^{6}[/tex]
Debt per person = total debt / total population = $24,642.86 (approximately).
Learn more about average here
https://brainly.com/question/24057012
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A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. You collect the force data for 30 insulators selected for the experiment and find out that the mean force is 1670. The population mean force that you try to estimate is_______.
a. a confidence interval.
b. a statistic.
c. a point estimate.
d. a parameter.
e. an interval estimate.
Answers
Answer:
b. a statistic.
Step-by-step explanation:
the value 1670 is regarded as a statistic. this is because it is a representation of the value of a sample. from the question we get that destructive testing is being done this shows is that what we have here is a sample.
the mean force 1670 is not a parameter, a point estimate, a confidence interval or interval estimate. therefore option b is the answer.
AAAAAAAAAAAAAAAA HELP PLEASE HELP
Answers
Answer:
x=-5
Step-by-step explanation:
Answer:
x = -5
4x + 12 = -8
4x = -20
x = -5
Hope this helps
What is the value of x in the equation 6(x + 1) – 5x = 8 + 2(x - 1)?
0
7
O
o 12
Answers
Answer:
0
Step-by-step explanation:
distributive property
6x + 6 - 5x = 8 + 2x - 2
combine like terms
x + 6 = 6 + 2x
subtract x from both sides
6 = 6 + x
subtract 6 from both sides
0 = x
How do you think you could represent the number 2,300 as a number times a multiple of 10?
Answers
Answer:
23,000
Step-by-step explanation:
Sam signed up for a program that costs $12.50 per month to stream movies to her computer. She decided to cancel her service after 3/5 month. She only has to pay for the amount of time she used the service. How much does she owe?
Answers
Answer:
7.50
Step-by-step explanation:
7.50
If a=14 and b=4, then what does ab equal?
Answers
Answer:
ab=56
Step-by-step explanation:
14 x 4 = 56
Answer:
56
Step-by-step explanation:
14*4 = 56
AB = multiplication
the cost of 24 roses at Farley's flowers including the $1.74 sales tax is $34.54. Based on this information wich statement is true
Answers
eating 8 hot dogs in 1/4 of an hour
Answers
woah thats alot is that a question or you actually doing it
The graph of quadratic function f is shown on the grid. which of these best represents the domain of f?
Answers
Answer:
Domain: {x | x = -2, 2, 4}
Range: {y | y = -3, 0, 4}
Step-by-step explanation:
Domain of a function includes all possible values of x that are plotted on the x-axis on a grid.
The range includes all possible y-values.
The graph of the function given above has specific points that are marked clearly. Each specific values if x and y are clearly known.
Therefore, the domain of the function are -2, 2, and 4.
This can be written properly as {x | x = -2, 2, 4}
The domain value include -3, 0, and 4.
This can be written as {y | y = -3, 0, 4}
letter a................
Answers
Answer:
y - (18x - 6y)/3
Step-by-step explanation:
y - (2/3)(9x - 3y)
y - [(2)(9x - 3y)]3
y - (18x - 6y)/3
y + (-18x + 6y)/3
y - 6x + 2y
-6 + 3y
he length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch. Select all of the following that could be the actual length of the rectangle.
Answers
Answer:
[tex]3.65 \geq\ Length \leq 3.74[/tex]
Step-by-step explanation:
The options are not given.
However, the question is still solvable.
Given
[tex]Length = 3.7\ inches[/tex] --- Approximated
Required
What could be the actual length
The given length is approximated to nearest tenth.
So, the actual length could be any of the following range
[tex]3.65 \geq\ Length \leq 3.74[/tex]
This is so because, numbers within this range approximates to 3.7
A statistics instructor wants to see if allowing students to use a notecard on exams will affect their overall exam scores. The instructor thinks that the results could be affected by the type of class: traditional, Web-enhanced, or online. He randomly selects half of his students from each type of class to use notecards. At the end of the semester, the average exam grades for those using notecards is compared to the average for those without notecards.
Required:
a. What type of experimental design is this?
b. What is the response variable in this experiment?
c. What is the factor that is set to predetermined levels? What are the treatments?
d. Identify the experimental units.
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Answer:
Throughout the clarification section elsewhere here, the definition of the concern is discussed.
Step-by-step explanation:
This seems to be an experimental analysis where the students were purposely administered an assessment and treatment of someone using notecards towards examine a potential improvement in the answer or calculated indicator that is average scores. Overall test scores are the answer component. Through the use of notecards seems to be the explanatory component. The vector degree is 'Used' either 'Not Used.' The participants offering the test seem to be the experimental groups.pls help!!!! I will make you brainiest!!!
What is the rate of change?
Answers
Answer:
7.25
Step-by-step explanation:
21/3=7.25
29/4=7.25
and so on
The triangle has a area of 18 units find the missing side 6 x
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Answer:
6 units
Step-by-step explanation:
Area of a triangle = bh/2
6 x 6 = 36
36/2 = 18
15. A student graphed f(x) = x and g(x) = f(x) + 3 on the same coordinate grid. Which
statement describes how the graphs of fand g are related?
A. The graph of f is shifted 3 units up to create the graph of g.
B. The graph of f is steeper than the graph of g.
C. The graph of f is shifted 3 units down to create the graph of g.
D. The graph of f is less steep than the graph of g.
Answers
Answer:
The graph of f is shifted 3 units up to create the graph of g.
Here we have a problem with translations, where we define a translation as an operation that moves the graph of a function in a given direction.
We will see that the correct option is A.
"The graph of f is shifted 3 units up to create the graph of g."
To get this, we first need to describe vertical translations.
For a function f(x) we define a vertical translation (or vertical shift) of N units as:
g(x) = f(x) + N
If N is positive, the translation is upwards
if N is negative, the translation is downwards.
So here we have:
g(x) = f(x) + 3
So we can see that this is a translation of 3 units upwards, then the correct option is A, the graph of f(x) is shifted (or translated) 3 units up to greater the graph of g(x).
And the graphs of g(x) = x + 3 and f(x) = x can be seen below, where you can see this, where the grey line is g(x).
If you want to learn more, you can read:
https://brainly.com/question/24401156
What does it mean when the line of best fit dips below the x-axis?
I NEED HELP PLEASEEEEEEEE
Answers
Answer:
Decreasing line that goes below x-axisStep-by-step explanation:
This is a decreasing line that goes below x-axis
Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. When the function dips below the x-axis, it refers to negative value
How many solutions does the equation have? How do you know?
6x – 2 = 2(3x – 1)
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Answer:
infinite solutions
Step-by-step explanation:
First, solve the equation.
6x - 2 = 2(3x - 1)
6x - 2 = 6x - 2
By this point, no further work needs to be done because you have your answer. If these two equations are the exact same and are equal to each other, then there is an infinite number of solutions for x.
This is what'll happen if you continue to solve for x:
6x = 6x
x = x
This is infinite because if you substitute any real number, the equation is true.
For example: 1 = 1 or 176 + 59 = 176 + 59.
One hundred students go to the cafeteria to eat lunch. Six tables held the same amount of students while an additional 10 students stood in line. Which equation can be used to find the number of students sitting at each table?
Answers
Answer:
6x + 10 = 100
Step-by-step explanation:
Given
Six tables held the same amount of students
let the number of student held by 1 table = x
since there are 6 table holding same number of students
number of student held by 6 table = 6*x = 6x
given that
number of students held in a line = 10
therefore
total number of students = number of student held by 6 table + number of students held in a line
total number of students in cafeteria = 6x + 10
also given
One hundred students go to the cafeteria to eat lunch
6x + 10 = 100
6x = 100 - 10 = 90
x = 90/6 = 15
thus,
the number of student held by 1 table = 15
thus, required equation can be used to find the number of students sitting at each table is 6x + 10 = 100