Write a quadratic function in vertex form whose graph has a vertex of (-3, 5) and passes through the point (0, -4).
Answers
In this form, "a" determines the direction of the opening of the parabola. If "a" is positive, the parabola opens upwards, and the vertex represents the minimum value of the function.
What is the quadratic function in vertex?If "a" is negative, the parabola opens downwards, and the vertex represents the maximum value of the function.
A quadratic function in vertex form is given by:
\(f(x) = a(x - h)^2 + k\)
where (h, k) represents the vertex of the parabola. We are given that the vertex is (-3, 5), so we have:
\(h = -3\)
\(k = 5\)
Substituting these values, we get:
\(f(x) = a(x + 3)^2 + 5\)
To find the value of "a", we can use the fact that the function passes through the point (0, -4). Substituting these values, we get:
\(-4 = a(0 + 3)^2 + 5\)
\(-4 = 9a + 5\)
\(-9 = 9a\)
\(a = -1\)
Therefore, the quadratic function in vertex form that satisfies the given conditions is:
\(f(x) = -(x + 3)^2 + 5\)
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Related Questions
Help me plsssssssssssssssssss
Answers
Answer:
The function that best models the given data is;
B. h(t) = -6.73·t² + 14.19·t + 0.83
Step-by-step explanation:
The data in the given table is presented as follows
\(\begin{array}{cccccc}Time, \, t(s)&0&0.5& 1.0 & 1.5& 2.0\\Height, \, h \, (m) & 1.0 & 5.42 & 9.71 & 5.9 & 2.6\end{array}\)
Where;
Time, t(s) is the independent variable
Height, h(m) is the dependent variable
Therefore, we have;
When t = 0, h = 1.0
From the given functions, we have the following table of the result of the function generated with Microsoft Excel
\(\begin{array}{cccccc}\\t & h & A & B & C& D\\0 & 1.0 & 1.22 & 0.83& 0.83& 1.22\\0.5 & 5.42 & 5.26 & 6.2425 & 9.6075 & 10.17\\1 & 9.71 & 4.39 & 8.79 & 21.75 & 24.03 \\ 1.5 & 5.9 & -1.39& 6.9725& 37.2575 &42.8\\2& 2.6 & -12.08 & 2.29 & 56.13 & 66.48\end{array}\)
By comparison, the function that nest models the given data is the function 'B', given as follows;
h(t) = -6.73·t² + 14.19·t + 0.83.
Use the drop-down menus to identify the values of the
parabola.
Vertex = (-3, -5), (-2, 0),
(0, 4), or (2, 0)
Domain = x < 0, x > 0, y > 0, or x is a real number
Range = {y| y < 0, 2, 4, or 6}
Answers
Answer:
Vertex= (0,4)
Domain= x: all real number
Range: ( - ∞, 4] or y ≤ 4
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if my avg is a 96 and my final exam is a 75 which is 25% of my whole grade what will my final grade be
Answers
Step-by-step explanation:
That means the 96 is 75% of your grade
96 (.75) + 75 (.25) = 90.75 final grade
Write number sentences using multiplication to show: A. The fraction represented in 1(a) is equivalent to the fraction represented in 1(b).
Answers
Answer: We have to write two fractions that are equivalent to 1(a) and 1(b):
1(a) Equivalent fraction to 1(b):
\(\begin{gathered} (a)\Rightarrow\frac{1}{3}=\frac{1}{3}\times\frac{2}{2}=\frac{2}{6} \\ \text{ Equivalent fraction is:} \\ \frac{2}{6}\Rightarrow1(b) \end{gathered}\)Conclusion: The two fractions are Indeed the Equivalent!
What number must you multiply the second equation by so that the sum of the x-coefficients is zero?
7x−y=55
x+3y=33
1. -7
2. 1/3
3. -1/3
4. 7
Answers
-7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are
7x−y=55..(1)
x+3y=33..(2)
We have to multiply with -7 second equation by so that the sum of the x-coefficients is zero
-7x-21y=-231..(3)
Add equation 1 and equation 2
7x−y-7x-21y=33-231
-22y=-198
Hence, -7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
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Use this area model to find One-fourth divided by 3.
One-fourth divided by 3 =
.
Answers
Answer:
1/12
Step-by-step explanation:
This answer is right
Show that at least three of any 25 days chosen must fall in the same month of the year. Proof by contradiction. If there were at most two days falling in the same month, then we could have at most 2·12 = 24 days, since there are twelve months. As we have chosen 25 days, at least three must fall in the same month.
Answers
We are to prove that at least three of any 25 days chosen must fall in the same month of the year. To prove this, we will assume the opposite and then come to a contradiction.
Let's suppose that out of 25 days, at most two days falling in the same month, then we could have at most 2 x 12 = 24 days, since there are twelve months.
As we have chosen 25 days, at least three must fall in the same month. In order to prove this, suppose that no three days fall in the same month.
It can be shown that there will be exactly two months with two days each.
Therefore, there will be 24 days in the first 11 months, and one day in the last month. This contradicts the initial assumption that there are no three days in the same month.
Hence, the proposition is true.Summary:If at most two days falling in the same month, then there could be at most 2 x 12 = 24 days, since there are twelve months. As we have chosen 25 days, at least three must fall in the same month. Let's suppose that no three days fall in the same month. It can be shown that there will be exactly two months with two days each. Therefore, there will be 24 days in the first 11 months, and one day in the last month.
Hence, This contradicts the initial assumption that there are no three days in the same month. Hence, the proposition is true.
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U3U please help me asap U3U
the question is:
How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain.
Answers
hate to be that person but what she said
if the perimeter of an equilateral triangle is 24cm, find the length of it's side
Answers
Answer:
it's side length equals to 8.
Step-by-step explanation:
Hello!An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.
Perimeter: 3 x side of equilateral triangle
\(24 = 3 \times each \: sides\)
divide both sides by 3
\(one \: of \: its \: side = 8\)
Thus, as all the three sides equals to 8.
Hope it helps!
A street fair at a small town is expected to be visited by approximately 1000 people. One information booth will be made available to field questions. It is estimated one person will need to consult with the employee at the booth every two minutes with a standard deviation of three minutes. On average, a person’s question is answered in one minute with a standard deviation of three minutes.
What percent of the day will the information booth be busy?
How long, on average, does a person have to wait to have their question answered?
How many people will be in line on average?
If a second person helps in the booth, now how long will people wait in line?
Answers
We need to find how long a person has to wait on average to have their question answered, how many people will be in line on average, what percent of the day will the information booth be busy.
The average time that each person takes is 1 minute. Therefore, 30 people can be helped per hour by a single employee. And since the fair lasts for 8 hours a day, a total of 240 people can be helped every day by a single employee. The fair is visited by approximately 1000 people.
Therefore, the percentage of the day that the information booth will be busy can be given by; Percent of the day the information booth will be busy= (240/1000)×100 Percent of the day the information booth will be busy= 24% Therefore, the information booth will be busy 24% of the day.2.
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A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters. A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters. What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter. 282.6 mm3 271.3 mm3 553.9 mm3 836.5 mm3
Answers
Answer:
its b
Step-by-step explanation:
got it right on edge
The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.
What is the volume of the cylinder?A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder = nr^2h
Where:
n = 22/7 r = radius = diameter / 2The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³
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If the point (x,y) is in Quadrant IV, which of the following must be true?
x<0 and y>0
x>0 and y<0
Answers
The statement x > 0 and y < 0 must be true for any point (x, y) located in Quadrant IV.
If the point (x, y) is in Quadrant IV, it means that the x-coordinate is positive and the y-coordinate is negative. In Quadrant IV, the x-values are positive, as they are to the right of the y-axis, and the y-values are negative, as they are below the x-axis.
Therefore, the correct statement is:
x > 0 and y < 0.
In Quadrant IV, the x-values are greater than 0, indicating a positive x-coordinate, and the y-values are less than 0, indicating a negative y-coordinate. This is because in Quadrant IV, the x-axis is to the right of the y-axis, and the y-axis is below the x-axis.
Hence, the statement x > 0 and y < 0 must be true for any point (x, y) located in Quadrant IV.
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Phillip Witt, president of Witt Input Devices, wishes to create a portfolio of local suppliers for his new line of key- boards. As the suppliers all reside in a location prone to hurri- canes, tornadoes, flooding, and earthquakes, Phillip believes that the probability in any year of a "super-event" that might shut down all suppliers at the same time for at least 2 weeks is 3%. Such a total shutdown would cost the company approximately $400,000. He estimates the "unique-event" risk for any of the suppliers to be 5%. Assuming that the marginal cost of managing an additional supplier is $15,000 per year, how many suppliers should Witt Input Devices use? Assume that up to three nearly identical local suppliers are available.
Answers
To determine the number of suppliers Witt Input Devices should use, we need to consider the probability of a "super-event" and the marginal cost of managing additional suppliers.
With a 3% probability of a total shutdown and an estimated cost of $400,000, along with a 5% "unique-event" risk per supplier, the company should aim to balance the costs and risks to make an informed decision on the number of suppliers.
Phillip Witt wants to create a portfolio of local suppliers for his keyboards. He faces the risk of "super-events" that could shut down all suppliers simultaneously for at least two weeks. The probability of such an event occurring is 3% per year, which would result in an estimated cost of $400,000 for the company.
Additionally, each individual supplier carries a "unique-event" risk of 5%. To mitigate the risks, Witt Input Devices needs to determine the optimal number of suppliers to use. However, it is stated that up to three nearly identical local suppliers are available.
To make a decision, the company needs to balance the costs and risks. Each additional supplier incurs a marginal cost of $15,000 per year. The company should evaluate the trade-off between the cost of managing additional suppliers and the risk reduction achieved by having multiple suppliers.
Considering these factors, Witt Input Devices should analyze the costs and benefits of each additional supplier and select the number of suppliers that provides an optimal balance between risk mitigation and cost management.
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Jada has been helping her younger brother practice his math facts all week. Each time they practice, Jada gives her brother 3 minutes to do as many math facts as he can. On Monday, Jada's brother completed 48 math facts. On Tuesday, he did better and completed 57 math facts. How many more math facts per minute did Jada's brother complete on Tuesday than on Monday?
Write your answer as a decimal or a whole number.
Answers
The current value of a baseball card is 50 times its original value v (in dollars). The baseball card is worth $62. Write and solve an equation to find the original value of the baseball card
Answers
Answer:
50v
Step-by-step explanation:
The equation would be 50v, because $62 is the original value, or v, and we are trying to find the value of the card now. Which is now 50 times the original price, $62.
What percent of offspring will be blue eyed?
0%
25%
50%
100%
Please I need help
Answers
Answer:
I believe the answer is 0% because the blue eye trait is recessive.
Step-by-step explanation:
Hope this helps!
✧◝(⁰▿⁰)◜✧
Answer:
25%
Step-by-step explanation:
blue eyes are the resesive gene but there is still a 25% chance.
A coordinate grid is placed over a map. City A is located at (19,22). City B is located at (-7,-2). If City C is halfway between City A and City B, Where is City C located? What is the distance between City A and City C? (Round to the nearest tenth)
Answers
Answer:
City C location: (6,10)
Distance between City A and City C: √313 or 17.69
Step-by-step explanation:
Use midpoint formula: (x2 + x1)/2, (y2 + y1)/2
Plug in the numbers, this gives you (6,10)
Use distance formula to find distance between City A and City C.
√(x2−x1)^2+(y2−y1)^2
Plug in the numbers, this gives you √313 which is also 17.69
The fraction of area model A is 4 12 . The fraction of area model B is 3 9 . Compare the two fractions and write an equation or inequality to show how the two fractions are related. Use <, >, or =. Two rectangles are shown. The left rectangle is divided into 12 equal parts and arranged in 3 rows of 4 cells each. 4 of these cells are colored yellow. The right rectangle is divided into 9 equal parts and arranged in 3 rows of 3 cells each. 3 of these cells are colored yellow.
Answers
The two fractions are related by the substitution property of equality.
How to compare fractions?Model A = 4/12
= 1/3
Model B = 3/9
= 1/3
So,
4/12 = 3/9
Each area model shows 3 rows of cells.
In each model, one of those three rows is colored yellow. That is, each model represents the fraction is equivalent to 1/3
It can be concluded that the relation between the given fractions is an application of the substitution property of equality.
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Val rented a bicycle while she was on vacation she paid a flat rental fee of $55.00 plus $8.50 each day the total cost was $123 write and equation you can use to find the number of days she rented the bicycle
Answers
Answer:
55+8.5x=123
Step-by-step explanation:
The 55 represents the flat fee, the 8.5 represents the daily charge, x represents the number of days she rented it for, and 123 is the total amount
Doing the math it adds up to 123 as your answer
Please help me ASAP
Answers
Express each of these statment using quantifires :
a) every student in this classes has taken exactly two mathematics classes at this school.
b) someone has visited every country in the world except Libya
Answers
Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.
a) "Every student in this class has taken exactly two mathematics classes at this school."
In this statement, we have two main quantifiers:
Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.
Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.
So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."
b) "Someone has visited every country in the world except Libya."
In this statement, we also have two main quantifiers:
Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.
Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.
So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."
In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.
Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.
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What is a simpler form of the radical expression sqrt 36g^6.
Answers
Answer:6|g4
Step-by-step explanation:
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
Enter your answer in the box.
Answers
Answer:
1 7/8 inches is 1.875 in decimal form.
A hiker attempting to cross a wilderness area has two GPS systems of intermittent reliability because of the areas remoteness .from past experience he estimates that at any moment the probability that system I will work is 0.85, that system II will work is 0.90 , and both will work is 0.80 . the probability that at any moment at least one of the systems will work is about:
Answers
The probability that at least one of the systems will work is approximately 0.985, or 98.5%.
To calculate the probability that at least one of the GPS systems will work, we can use the concept of complementary probability. The complementary probability is the probability that an event does not occur.
Let's denote:
Event A: System I works
Event B: System II works
The probability that at least one of the systems will work is equal to 1 minus the probability that both systems will not work.
P(at least one system works) = 1 - P(neither system works)
To calculate P(neither system works), we multiply the probabilities that each system does not work:
P(neither system works) = (1 - P(System I works)) * (1 - P(System II works))
Using the given information:
P(System I works) = 0.85
P(System II works) = 0.90
P(neither system works) = (1 - 0.85) * (1 - 0.90)
= 0.15 * 0.10
= 0.015
Therefore, the probability that at least one of the GPS systems will work is:
P(at least one system works) = 1 - P(neither system works)
= 1 - 0.015
= 0.985
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Hi Guys
Can you please help me with this?
Thanks so much!
Answers
B. 6 - 5 17/40 = 23/40 subtract total consumed from original 6
Select all of the following statements that are true four years from now, in the year 2024.
Select : 2
Submit Answer
The Thrift segment will demand 7,745 thousand units
The Core segment will demand 9,779 thousand units
The Nano segment will demand 5,406 thousand units
The Elite segment will demand 5,874 thousand units
Answers
The following statements that are true four years from now, in the year 2024 are the Thrift segment will demand 7,745 thousand units and the Core segment will demand 9,779 thousand units.
Define demand.Demand in economics refers to a consumer's readiness to pay a particular price for goods and services as well as their desire to buy them. Demand for a good or service typically declines when its price goes up. Demand describes the consumer's desire and willingness to purchase a good or service at a specific time or over an extended period of time. Additionally, consumers must be able to afford the items they want or need based on their budgeted disposable income. Demand therefore has an impact on market expansion and economic growth.
Given
The following statements that are true four years from now, in the year 2024 are:
The Thrift segment will demand 7,745 thousand units.
The Core segment will demand 9,779 thousand units.
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I NEED HELP PLEASE !!
can i also get an easy explanation so i can know how to do the other problems pls
Answers
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Expand the expression 3(1.75 + 3x)
Answers
Answer:
5.25+6x
Step-by-step explanation:
multiply 3 by both the numbers inside
(3⋅(1.75+3⋅x))
=3⋅1.75+3⋅3⋅
=3⋅1.75+3⋅3⋅x
=5.25+9⋅
The ratio of cakes to donuts in a bakery is 5:1 If there are 20 cakes, how many donuts are there?
Answers
Answer:
Should be 4.
Step-by-step explanation:
If there are 5 cakes per each donut, divide 20/5
A school lunch costs $2.50. A monthly lunch pass costs $40.00. Which inequality represents the number x of lunches you must purchase for the monthly pass to be a better deal?
Answers
Answer:
The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.
Step-by-step explanation:
Given that:
Cost of each lunch = $2.50
Cost of monthly lunch pass = $40.00
Number of lunches = x
For making the monthly pass a better deal, the cost of lunches should be greater than the cost of monthly lunches, therefore
Cost of lunch * Number of lunches > Cost of monthly lunch pass
2.50x > 40.00
Hence,
The inequality 2.50x>40.00 represents the number of lunches needed to be purchased for the monthly lunch pass to be a better deal.
Answer:
2.50x > 40.00
$2.50 times a number of lunches is greater than $40.
Step-by-step explanation: