An object is launched from the top of a hill and travels in a parabolic path until it reaches the ground. Write a quadratic function
that models the path of the object with a maximum height of 200 feet, represented by a vertex of (25, 200) , landing at the point
(55.0)
Answers
Answer:
Bonjour,
Step-by-step explanation:
y=k*(x-25)²+200
0=k*(55-25)²+200 => k=-2/9
y=-2/9(x-25)²+200
The a quadratic function that models the parabolic path of the object is y = -2/9(x-25)²+ 200.
What is defined as the parabolic path?A projectile's trajectory angle is defined as a parabolic path. A parabola is just a curve that represents a quadratic equation graphically. The initial velocity of a projectile is either horizontal or upward at such an angle. If a projectile starts out straight up, it will end up straight down. It's not much of a parabola because it's squished into the a straight line.For the given question;
The maximum height of the object which is launched from the top of a hill is 200 m.
The equation of the parabola is -
y=a*(x-h)²+k
(h,k) = vertex = (25, 200)
y = a*(x-25)²+200
Put (x,y) = (55,0)
0=a*(55 - 25)²+200
=> a = -2/9
Now put the value of 'a' and form the equation.
y = -2/9(x-25)²+ 200
Thus, the a quadratic function that models the parabolic path of the object is y = -2/9(x-25)²+ 200.
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Related Questions
Harriet counts 15 big boxes and 12 small boxes of notebooks. Each large box contains 189 notebooks, and each small box contains 79 notebooks. Estimate the total number of notebooks. Is your estimate an overestimate or an underestimate? Explain why it is better to have an overestimate than an underestimate. WILL GIVE 95 POINTS
Answers
Answer:15 big boxes with 189 notebooks each: 20 * 200 = 4,000
12 small boxes with 79 notebooks each: 10 * 80 = 800
4,000 + 800 = 4,800
There are approximately 4,800 notebooks, this is an overestimate as I rounded up.
Step-by-step explanation:
what is the GCF of 18 and 28?
Answers
Answer:2
Step-by-step explanation:
If , choose the line of reflection between the two congruent triangles.
Answers
The line of reflection of the given congruent angles is the y-axis.
What is the line of reflection?
A line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image
Now, from the attached image, we see that the two given congruent triangles are; ΔAHJ and ΔADB
Now, we see that the coordinates are transformed as folllows;
D(5, 2) → H(-5, 2)
B(3, 0) → J(-3, 0)
Now, this type of transformation follows the transformation rule; (x, y) → (−x, y). This means it was reflected over the y-axis.
This the line of reflection of the given congruent angles is the y-axis.
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The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 24 kg.
b) Work out the maximum number of dogs that could have a mass of more than 24 kg.
Answers
a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
What do minimum and maximum value mean?Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
The minimum of the values present in the interval 20 to 40 is 6
The maximum of the values present in the interval 20 to 40 is (12+6) = 18
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help pleaseeeeeeeeeeeeee
Answers
Answer:
400
Step-by-step explanation:
[tex]R(x)=\frac{2000x^2}{x^2+4}[/tex]
Since x represents the number of years since publication, the revenue at the end of the first year would be found by just plugging in 1 into the function.
[tex]R(1)=\frac{2000(1)^2}{(1)^2+4} \\\\R(1)=400[/tex]
Use the Distributive Property to write 2(-3 + 9) as an equivalent expression. Then evaluate.
O 2(12); 24
O2(-3) + 2(9); 24
O 2(-3) + 2(9); 12
(3 + 9)2; 24
Answers
An airplane’s altitude in feet during its descent for landing can be found using the function f(x) = −300x + 30,000, where x represents the horizontal distance in miles from where the plane begins its descent. After new government regulations become law, the airplane’s
descent will be modeled by the function g(x) = −300x + 30,500. Which statement describes this change?
A. The airplane descends 500 feet per horizontal mile slower
B. The airplane starts its descent from an altitude 500 feet higher
C. The airplane descends 500 feet per horizontal mile faster
D. The airplane starts its descent from an altitude 500 feet lower
Answers
Answer:
B. The airplane starts its descent from an altitude 500 feet higher
Step-by-step explanation:
f(x) = −300x + 30,000
the function itself represents the airplane's altitude. the y intercept, 30,000 ft, then represents the initial starting position of the plane.
when it changes
g(x) = −300x + 30,500
only the y intercept changes. it's now 30,500 ft, which is 500 more than before. that means the plane initial position is 500 feet higher.
since the term with x doesn't change, the rate will not be affected. the answers with slower or faster talks about rate, which isn't what changed.
given the first term and the term-to-term rule, write down the first six terms of each sequence.
b) first term: 2 term-to-term rule add 9
Answers
Step-by-step explanation:
a1 = 2
a2 = a1 + 9 = 2 + 9 = 11
a3 = a2 + 9 = 20
a4 = a3 + 9 = 29
a5 = a4 + 9 = 38
a6 = a5 + 9 = 47
Your yard is a mess, and you decide to hire a landscaper. The greenhouse charges a $20 consultation fee plus $11 per hour for the actual work. Garden pros does not charge a consulting fee, but charges $15 per hour for the actual work. Write an equation that will help you determine the # of hours at which the 2 companies charge the same. Clearly indicate what the variable represents.
Answers
Answer:
5 hoursStep-by-step explanation:
Let the hours of actual work be x and total charge be y.
The greenhouseTotal amount of charge is:
y = 11x + 20Garden prosTotal amount of charge is:
y = 15xSince y is same for both companies, set the equation and solve for x:
11x + 20 = 15x15x - 11x = 204x = 20x = 20/4x = 5he table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 10, negative 5, 10, 15. The second column, y, has the entries, 8, 7. 4, 3. Which equation shows how (–10, 8) can be used to write the equation of this line in point-slope form?
Answers
Equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)(x+ 10).
As given,
Given points of linear equation: (-10,8), (-5, 7) , (10,4), (15,3)
Consider (x₁, y₁)=(-10,8) and (x₂ ,y₂)=(-5,7)
Slope 'm'=(y₂-y₁)/(x₂-x₁)
=(7-8)/(-5+10)
=-1/5
Equation of line passing through (-10,8) in point slope form:
y-y₁=m(x-x₁)
⇒(y -8)=(-1/5)(x+10)
⇒y=1/5(-x+30)
Therefore, equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)( x + 10).
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How do I do this: 18 - (-21)
Answers
Answer:
39
Step-by-step explanation:
1) Remove parentheses.
18 + 21
2) Simplify.
39
Thanks,
Eddie
Quick hint:
When there is a number and then a - sign outside the parenthesis and on the inside, then it creates a figure similar to the plus sign, that is when you just make it one.
Add the two numbers (both are always positive in this instance),
and there's your answer!
Identify the key characteristics of the parent fifth-root function f(x)=x Include the following domain, range, intervals where the function is increasing, decreasing, or constant, intercepts, whether the function is even, odd, or neither, whether the function is continuous or discontinuous, asymptotes, and end behavior. (4 pts.)
Answers
From the graph of the fifth root function, we have that:
The domain and the range are all real values.The function is increasing for all real values, and never decreasing nor constant.The x-intercept is of x = 0.The y-intercept is of y = 0.The function is odd.The function is continuous.The function has no asymptotes.The end behavior is that y -> - ∞ when x -> -∞ and y -> +∞ when x -> +∞.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, since the given graph has no holes, and keeps going to infinity, we have that both the domain and the range are all real values.
Since the function has no holes, it is also continuous, and has no vertical asymptotes.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.For this problem, we have that the function is moving right and up over it's entire domain, hence it is increasing for all real values, and never decreasing nor constant.
What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.Since the graph passes through the origin, we have that:
The x-intercept is of x = 0.The y-intercept is of y = 0.What are even and odd functions?In even functions, we have that f(x) = f(-x) for all values of x.In odd functions, we have that f(-x) = -f(x) for all values of x.If none of the above statements are true, the function is neither.For this problem, looking at the graph, we have the the second statement holds true for all values of x, hence the function is odd.
What is the end behavior of the function?It is given by the values of y when x -> ∞.
Hence:
For the end behavior, y -> - ∞ when x -> -∞ and y -> +∞ when x -> +∞.
Since f(x) -> ∞ when x -> ∞, the function has no asymptotes.
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.83 and 3.39?
Answers
As a result, 95% of the students had grade point averages ranging from 1.83 to 3.39.
What exactly is a normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end.
What is the significance of the term "normal distribution"?The normal distribution is also known as the bell curve because the probability density graph resembles a bell. It is also known as the Gaussian distribution, after German mathematician Carl Gauss, who described it initially.
According to the given data:A bell-curve distribution is a normal Distribution.
Let X be the grade point averages of undergraduate students at one university.
X ~ Normal Distribution(2.61,(0.39)2)
P(1.83 < X < 3.39)
= P(X < 3.39) - P(X < 1.83)
= P((X - μ)/σ < (3.39 - 2.61)/.39) - P(((X - μ)/σ)< (1.83 - 2.61)/039)
= P(z < 2) -P(z < -2)
= P(-2 < z < 2)
Thus, given a regular normal distribution (μ=0, σ =1), z is between 2 standard deviations away from the mean.
According to the Empirical Rule, 95% of the data obtained after a normal distribution is within two standard deviations of the mean.
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you’re buying 60 acres Of farmland at a cost of 372000
What is the cost per acre
What would be the cost for 70 acres
Answers
Answer:
Per acre will cost 6200
70 acres will cost 434,000
Step-by-step explanation:
you’re buying 60 acres Of farmland at a cost of 372000
1) What is the cost per acre
solutionIn order to find the cost per acre we divide the values which is;
➟ 372000 ÷ 60
➟ 6200
∴ it will cost 6200 per acre
2) What would be the cost for 70 acres
solutionto find how much it will cost for 70 acres we will multiply the value per acre by 70 which is;
➟ 6200 × 70
➟ 434,000
∴ it will cost 434,000 for 70 acres
Jessica had $7 and her sister had $2. After their parents gave each of them an equal amount of money, Jessica had twice as much money as her sister. How much money did their parents give each of them?
Answers
Answer:
$3:00
Step-by-step explanation:
let 'x' be the money that the parents gave to Jane and her sister each
Jane will have 7+x dollars
Jane's sister will have 2 + x dollars
Jane had twice as much money as her sister thus
7 + x = 2(2 + x)
7 + x = 4 + 2x
4 + 2x = 7 + x
2x - x = 7 - 4
x = $3
the parents gave $3 to each.
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches were made?
Answers
42 bologna sandwiches were made
How many bologna sandwiches were made?The ratio is given as
Cheese : Bologna : Peanut butter = 5 : 7 : 8
Also, we have
Total = 120 sandwiches
The number of bologna sandwiches made is calculated using
Bologna = bologna ratio/total ratio * 120
So, we have
Bologna = 7/(5 + 7 + 8) * 120
Evaluate
Bologna = 42
Hence, 42 bologna sandwiches were made
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Help me pleaseeeeeeeeeeeee
Answers
You’re Welcome
Calculate the value of x that is positioned between two isosceles triangles. value of each angle is 24.
Answers
During an isosceles triangle two angles are identical, adding up to a total of 180, and its x value is 78.
Isosceles triangle: what is it?
In geometry, an isosceles triangle is one with at least two sides of equal length. There are two ways to define it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition.
The aforementioned claim states that a triangle's total number of angles is 180.
the total of all angles in a triangle is 180.
⟹24+x+x=180
24+2x=180
12+x=90
x=90−12
x=78
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Tom invites Maggie for a party. Maggie knows that on her way to Tom's house, she will come across 4 lanes. There
are five houses at the end of each lane. One of the five houses is Tom's. What is the probability that the first house
that Maggie checks is not Tom's?
Answers
Step-by-step explanation:
Given that
Tom invites Maggie for a party. Maggie knows that on her way to Tom's house, she will come across 4 lanes.There are five houses at the end of each lane. One of the five houses is Tom's.To find
The probability that the first house that Maggie checks is not Tom's?So, according to the question
we have,
There are five lanes with five houses at the end of each lane. It is clear that Tom's house is in the fifth lane because Maggie must cross four lanes to get there.Now, there are 5 homes on the first lane, and Tom's is one of them. Thus, there are 1 favorable outcomes and a total of 5 outcomes that could happen. The likelihood is therefore given as follows.We know that,
Probability P(E) = [tex]\frac{possible\;events}{no.\;of\;events}[/tex]
There is,
possible event is 1, and no. of events are 5.
So, we can say that
[tex]P(E) = \frac{1}{5}[/tex]
Answer:
The probability that the first house that Maggie checks is not Tom's is 1/5.To learn more about probability, please click on the link:
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Solve the equation
2(4-5x)=3(4x+3)
Answers
Answer:
-1 /22
Step-by-step explanation:
1his is a fraction kinda thing so put -1 at the top like a numerator and the 22 go at the bottom like the denominator
Find x for this equation
Show clear algebraic fraction
Answers
Step-by-step explanation:
cross multiply both sides
2(6x+1)=3(5x–2)
12x+2=15x–6
collect like terms
+2+6=15x–12x
8=3x
divide both sides by 3
8\3=3x\3
therefore, the final answer is
8\3
thank you
please mark as the brainliest
All of the statements are true about the barrier methods of birth control EXCEPT:
A. The female condom is inserted into the vagina before intercourse.
B. When condoms are used correctly they are 80% effective.
C. Both male and female condoms can be used as protection from an STI.
D. Another name for a diaphragm is cervical cap.
Answers
Condoms are up to 98% effective when used correctly, not 80%
Find the product.
654
×
42
=
□
A.
3
,
600
B.
3
,
824
C.
25
,
268
D.
27
,
468
Answers
Answer:
D. 27,468
Step-by-step explanation:
654
x42
--------
1,308
+26,160
---------
27,468
Use interval notation to express the following:
The set of all numbers less than or equal to 1
Answers
The interval notation that expresses the statement is (-∝, 1]
How to use interval notation to express the statement?The statement is given as:
The set of all numbers less than or equal to 1
The above can be represented as:
<= 1
Represent the set with variable x
So, we have
x <= 1
As an interval notation, we have (-∝, 1]
Hence, the interval notation that expresses the statement is (-∝, 1]
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How long, in seconds, should a bus take to travel 5000 m at an average speed of 10 m/s?
Answers
Answer:
10 분
Step-by-step explanation:
describe the magnification of a 20x ocular lens and a objective 60x lens
Answers
To identify magnification, we simply multiply the two given numbers. That’s it!
megan buys a 2-quart bottle of juice for $2.56. What is the rate unit of the cost of the juice?
Answers
The rate unit of the cost of the juice bought by Megan is $1.28 per quart.
What is defined as the unitary method?The unitary method is a methodology that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value.The unitary method's formula is to obtain the price of a single unit and afterwards multiply that value by the number of components to get the required value.For the given question;
The price of 2-quart bottle of juice bought by Megan = $2.56.
For calculating the price of 1 bottle, simply divide the total cost by number of bottles.
Price of a single quart bottle = $2.56/2.
Price of a single quart bottle = $1.28 per quart.
Thus, the price of single quart bottle of juice is 1.28 per quart.
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Hannah is the oldest of four siblings whose ages are consecutive integers the sum of their ages is 86 fine Hannah's age
Answers
Answer:
20, 21,22,23
Step-by-step explanation:
Consecutive means in order. Integers are the set of whole numbers and their opposites: ...-3,-2,-1,0 ,1,2,3...
Let x = the one sibling
Let x + 1 = the second sibling
Let x + 2 = the third sibling
Let x+4 = the fourth sibling.
If you add the four siblings together they equal 86
(x) + (x +1) + (x + 2) + (x+3) = 86 I put the parentheses in so that you can see each sibling, but it is not needed.
x + x+ 1 +x + 2 + x+ 3 = 86 Combine like terms
4x + 6 = 86 Subtract 6 from both sides
4x = 80 Divide both sides by 4
x = 20
The first sibling is 20, then 21, then 22 and finally 23
Check:
20 + 21 + 22 + 23 = 86
How to solve this math equation, a+2=5
Answers
Answer:
a = 3
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate the variable by doing the inverse operation which is in this case subtracting 2 on both sides of the equation.
a + 2 = 5
- 2 - 2
a = 3
Check:
1. Substitute a with the solution 3.
3 + 2 = 5
5 = 5 ✓
1.1.2 Show how the catering cost was determined if the cost per person is R225,00.
Answers
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
The catering cost was determined if the cost per person is R 225,00.
The cost per person = 225,00 R
To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.
Let us assume,
Suppose you can find the cost for 50 people.
Then,
We can write,
Catering cost = x
x = 225,00 * 50
x = 1,125,000 R
Therefore,
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
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