Susan’s science class is performing an experiment that involves dropping objects from various heights, starting close to the ground and working upward to 8 feet. The function , where x represents the distance from the ground, represents the time it takes for the object Susan drops to hit the ground. The graph represents the function
Identify some of the key features of the graph. That is, determine if the function is monotonically increasing or decreasing, state the end behavior, find the x- and y-intercepts, find the endpoint, and state the domain and the range of the graph (without considering the context).
Answers
Answer:
1) The function is monotonically increasing
2) The end behavior of the function is x tends to infinity as t(x) tends infinity
3) The x and y -intercept is (0, 0)
4) The endpoint is (0, 0)
5) The domain is 0 ≤ x ≤ +∞
The range is 0 ≤ t(x) ≤ +∞
Step-by-step explanation:
1) The given function of the time for the object to hit the ground is t(x) = 1/4·√x
Where;
x = The distance from the ground
t = The time it takes for the object to hit the ground
Monotonically increasing function, we have;
A function that is continuous on [a, b] and it can be differentiated in the domain, (a, b) is monotonically increasing when df(x)/dx > 0 for all values of x in (a, b)
However, where df(x)/dx < 0 for all values of x in (a, b), the function is decreasing
Therefore, using an online tool, we have;
dt(x)/dx = d(1/4·√x)/dx = 1/8 × 1/√x
Therefore, the dt(x)/dx > 0, for 0 < x < +∞ and the function is monotonically increasing
2) The end behavior of the function as x tends to infinity, t(x) = 1/4·√x approaches infinity
3) From the end behavior, and the nature, of the function t(x) = 1/4·√x, where both variables are directly proportional, we have that the x and y -intercept = (0, 0)
4) The endpoint is (0, 0) given that as t(x) tends to 0, x tends to 0
5) The domain is 0 ≤ x ≤ +∞
The range is 0 ≤ t(x) ≤ +∞.
Answer:
The function is monotonically increasing since the output values are continually getting larger. This also tells us that the end behavior of the function is infinity.
The x-intercept is (0,0), the y-intercept is (0,0), and the endpoint too is (0,0).
The domain of the graph is all values greater than or equal to 0, and the range is all positive output values.
Step-by-step explanation:
Related Questions
The following table shows the total number of quizzes taken in high school. How many quizzes are taken per week?
Answers
Answer:
4
Step-by-step explanation:
y÷x
12÷3=4 and 20÷5=4
4 quizzes are taken per week.
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the total number of quizzes after x weeks.
From the table we can see that when y = 12, x = 3 and when y = 20, x = 5. Hence:
Number of quizzes per week = 12/3 = 20/5 = 4
Hence, 4 quizzes are taken per week.
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y = -8x - 24 into factored form
Answers
Answer:
Y = -8(x + 3)
Step-by-step explanation:
Divide the whole equation by -8 to get x by itself
Y = -8(x+ 3)
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
a)
Write down the mode.
b)
Work out the median.
c)
Calculate the mean.
d)
What is the range?
Answers
Answer:
Here are ten numbers:
3 7 2 4 7 5 7 1 8 8
a)
Write down the mode. 7
b)
Work out the median.
c)
Calculate the mean. add all and divide by 10
d)
What is the range? 7
Answer:
Mode: 7
Median: 6
Mean: 5.2
Range: 5
Step-by-step explanation:
For the mode you have to find which number is present the most times
For the median you have to find the middle number if the total sum of numbers is an odd number, and find the average of the two if it is an even number ,like i did here (7+5)/2=6
For the mean you have to add every number and then devide with the total number of the numbers given:
(3+7+2+4+7+5+7+1+8+8)/10=5.2
For the range you have to find the largest number and subtract the smallest number from it (8-3)=5
PLEASE HELP FAST
Let mZA = 30°. If ZB is a supplement of ZA, and ZC is a complement of 2A, what is mZB+m2c?
A. 60°
B. 150°
C. 180°
D. 210°
Answers
C should be the answer. I cant explain it because its hard to explain
Please help me with this question... please
Answers
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Convert 3500 meters into yards. Round your answer to the nearest whole number.
Answers
Answer:
yesss a 3500 = 5066
Step-by-step explanation:
this is my answer
Answer:
3828
Step-by-step explanation:
the exact no. is3827.6465
when you round it it will be 3828
Need help with this identify if its a polynomial binomial or trinomial ILL GIVE YOU THE BRAINLIEST IF U ANSWER THIS CORRECTLY
1. 2x^2 + 4x
2. 4x^4 - xy + 9
3. 16x^3
4. 9
5. xy + 9
Answers
2. Trinomial
3.monomial
4.monomial
5.Binomial
Choose the scenario below that matches this number sentence:
3 ÷ 11
A) 3 people share 11 cupcakes.
B) 11 people share 3 pounds of turkey.
Answers
Answer:
b
Step-by-step explanation:
Raul earns $37.50 for 3 hours of babysitting. He earns the same amount
per hour each time he babysits. How many hours does Raul have to babysit to earn $100
Answers
9 hours
Step-by-step explanation:
cuz that's the answer
Raul would have to babysit for 8 hours to earn $100.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To determine the number of hours Raul has to babysit to earn $100, you need to divide the amount he wants to earn ($100) by the amount he earns per hour.
The amount of Raul earns per hour by dividing the total amount he earned by the number of hours he worked.
As per the question, Raul earned $37.50 for 3 hours of babysitting,
So, he earned $37.50 / 3 hours = $12.50 per hour.
This means that to earn $100, he would have to work:
⇒ $100 / $12.50 = 8 hours.
Therefore, he would have to babysit for 8 hours to earn $100.
To learn more about the division operation click here :
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You are in charge of finding a place to have your little sister's birthday party. You
call around, but many places are already booked. You find one place, Jump and
Fun, which looks promising. Here's what you learn when you call Jump and Fun:
There is a flat fee of $120 to rent a room. There is an additional charge of $5 per
child for access to the bounce houses and miniature golf course. The more
friends your sister invites, the more the party will cost.
Write an equation to express what the cost will be for the party. Use x for the
number of kids that will attend.
Your answer
Answers
Answer:
Y=x(5)+120
Step-by-step explanation:
Y= the money you have to pay for the party
X(5)= you multiply x by 5
+120= you add the fee
I’m having problems solving this problem
Answers
D is also 55, so in the triangle there is 2 angles that are 55
To know DEF 180-55-55= 70
In a park, the locations of a drinking fountain, a streetlight and a flagpole form a right triangle. The drinking fountain is 12 yards north of the streetlight, and the flagpole is 5 yards east of the drinking fountain.
What is the shortest distance, in yards, from the streetlight to the flagpole?
A.7
B.11
C.13
D.17
Answers
Answer:
13
Step-by-step explanation:
Which Property of Addition does 3 + 0 = 3 illustrate?
a. Associative Property
b. Commutative Property
c. Identity Property
d. Distributive Property
Answers
Answer:
c identity property is illustrated by 3 + 0 = 3
does anyone know the answer to this ? (6,-2) m= -3
Answers
Answer:
Maybe
Step-by-step explanation:
I did but I forgot the answer
I am so sorry
Answer:
Point Slope Equation: Y+2=-3(x-6). Slope Intercept Equation: Y=-3x+16.
Step-by-step explanation:
If you are looking for an equation? Here you go.
Let me know if this is what you wanted!
Tom bought a radio on sale for 20% off for $68. What was the original
cost of the radio?
Answers
Answer:
88 I believe
Step-by-step explanation:
Answer:
$85
Step-by-step explanation:
20% is 1/5 of 100
68/4=17
68+17=85
Simplify the expression.
-1+1(-7+3v)-5v
Answers
Answer:
-1+1(-7+3v)-5v
Pull out like factors :
-2v - 8 = -2 • (v + 4)
Final result :
-2 • (v + 4)
In an orchard, there are 6 apple trees for every 4 pear trees. Create a ratio table to determine the number of apple trees in the orchard if there are 42 pear trees.
Answers
Answer:
........................what's the question ❓
It's in 8th grade math geometry
Answers
Answer:
sorry i have no clue
Step-by-step explanation:
Which of the following best describes the solution to the equation below? 3(x+ 7) = 3x + 21
Answers
Answer:
x = x; the solution has infinite solutions
Step-by-step explanation:
3(x+ 7) = 3x + 21; distribute the 3 on the left side
3x + 21 = 3x + 21; now subtract 21 from both sides
3x = 3x; divide by 3
x = x; the solution has infinite solutions. Since both terms are equal any value for x will be true on this equation.
9d^3+5d-8/3d-2
solve using long division monomials
Answers
Answer:
3d² + 2d + 3 remainder -2
Step-by-step explanation:
What is 41/50
as a percentage?
Answers
Answer:
82%
Step-by-step explanation:
A percent a fraction of one hundred so multiply the numbers by 2 to make it 82/100 then remove the one hundred making it 82%
Trapezoid WXYZ is shown below. What series of reflections will map the image back onto the original pre-image?
a. -axis, -axis, -axis, =
b. -axis, -axis, -axis, -axis
c. -axis, -axis, -axis, =
d. -axis, =1, -axis, =1
Answers
Answer:
d
Step-by-step explanation: i think
You spend 3 2/5 hours hiking and an additional 1/2 hour to rest.
How much time did you spend hiking and resting?
Answers
Answer:
3.9 hours
Step-by-step explanation:
3 2/5 + 1/2 = 39/10
3 9/10 =
3.9 hours
describe a system of linear equations that has no solution?
Answers
Answer:
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Step-by-step explanation:
Hope this helps - Good luck ^w
we can conclude that the system of linear equations has no solution when the graphs of equations are parallel.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The collection of one or more linear equations, such that each of those equations have same set of variables, are known as system of linear variables.
If a consistent system has an infinite number of solutions, it is dependent. When we graph the equations, both equations represent the same line.If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.Therefore, we can conclude that the system of linear equations has no solution when the graphs of equations are parallel.
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PLEASE HELP IF YOU COOL PLEASE
Answers
Answer:
B. Mark buys a pack of gum for $1.50 each
Step-by-step explanation:
The slope of the graph is 3/2 or 1.5 so x is the number of gum bought and y is the total amount he has to pay after buying the gum.
does anyone know this? URGENT!!
Answers
Answer: Y=3, X=-2
Step-by-step explanation:
Answer:
[tex]y = \frac{3}{2} x + 3[/tex]
Step-by-step explanation:
slope is a positive 3/2
y intercept is 3
2x + 5y = 16,3x-5y=-1
Answers
Answer:
the answer is [tex]x=3,\:y=2[/tex]
Step-by-step explanation:
if you want an explanation lemmie know but I rly dont feel like putting one bc its a lot to do but that is the correct answer lol
and try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations
Laura left Dunkin Donuts at 1 PM traveling 30 mph. Two hours later her friend Jen left the same Dunkin Donuts and started after her on the same route traveling 45 mph. At what time will Jen catch up to Laura?
Answers
Answer:
It took Jen 4 hours to catch up with Laura
Step-by-step explanation:
Gaining speed 45-30= 15 mph
Laura's head start 30×2=60 miles
Time for Jen to catch up 60÷15= 4 hours
In other words
30(t+2)= 45t
30t+60= 45t
60=45t-30t
60= 15t
t=4 hours
Write a triangle congruence statement!
I’ll give brainliest!
Answers
Answer:
These two are congruent because they mirror each other in size and shape.
Step-by-step explanation:
f(x) = 2x + 1 and y = 2x + 1 are the same function written in different notation
True or False?
Answers
Answer:
True
Step-by-step explanation:
2x+1 is the same both times. F(x) is just another way to write y
