Answers
The equation of the parabola would be \(y = \frac{1}{4}(x + 1)^2 - 4\).
What is a parabola?
A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.
The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.
To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.
We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.
Substituting these values into the equation y = a(x - h)^2 + k, we get:
y = a(x - (-1))^2 + (-4)
= a(x + 1)^2 - 4
Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.
Substituting x = -5 into the equation, we get:
y = a((-5) + 1)^2 - 4
= a(4)^2 - 4
= 16a - 4
Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.
Substituting this value back into the equation for y, we get:
\(y = \frac{1}{4}(x + 1)^2 - 4\)
Hence, the equation of the parabola would be \(y = \frac{1}{4}(x + 1)^2 - 4\).
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The equation of the parabola would be \(y=\frac{1}{4}(x+1)^2-4\).
What is a parabola?
A parabola is a curve that is shaped like a U or a mirror image of a U. It is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone.
The equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the curve.
To find the equation of the parabola described in the problem, we can first find the values of h and k and then substitute them into the equation.
We know that the vertex of the parabola is (-1, -4). Therefore, h = -1 and k = -4.
Substituting these values into the equation y = a(x - h)^2 + k, we get:
y = a(x - (-1))^2 + (-4)
= a(x + 1)^2 - 4
Now we can use the fact that the parabola passes through the points (-5, 0) and (3, 0) to find the value of a.
Substituting x = -5 into the equation, we get:
y = a((-5) + 1)^2 - 4
= a(4)^2 - 4
= 16a - 4
Since the point (-5, 0) lies on the parabola, y must equal 0 when x = -5. Therefore, we have the equation 16a - 4 = 0. Solving for a, we find that a = 1/4.
Substituting this value back into the equation for y, we get:
\(y=\frac{1}{4}(x+1)^2-4\).
Hence, the equation of the parabola would be \(y=\frac{1}{4}(x+1)^2-4\).
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Related Questions
1. A rectangle has vertices at (0,-2), 0,3), (3,-2), and (3,3). What are the
coordinates of the vertices of the image after the translation
(x,y) (x-6, y - 3) Describe the translation.
Answers
The coordinates of the vertices of the image after the translation (x,y) (x-6, y - 3) are (-6, -5), (-6, 0), (-3, -5), and (-3, 0), when a rectangle has vertices at (0,-2), 0,3), (3,-2), and (3,3).
The given rectangle has vertices at (0,-2), (0,3), (3,-2), and (3,3). After the translation (x,y) -> (x-6, y-3), the coordinates of the vertices will be:
1. (0-6, -2-3) = (-6, -5)
2. (0-6, 3-3) = (-6, 0)
3. (3-6, -2-3) = (-3, -5)
4. (3-6, 3-3) = (-3, 0)
So, the coordinates of the vertices of the image after the translation are (-6, -5), (-6, 0), (-3, -5), and (-3, 0). The translation involves a horizontal shift of 6 units to the left and a vertical shift of 3 units down.
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Melanie buys 6 pounds of beef and 3 pounds of bacon. She pays a total of $63,
and the bacon costs $1.50 less per pound than the beef. What would be the
combined cost of 1 pound of beef and 1 pound of bacon? *
Answers
Answer:
Cost of 1 beef= $7.5
Cost of 1 bacon= $6
Step-by-step explanation:
Ok so first of organize everything:
We know she buys 6 pounds ->beef and 3 pounds ->bacon
First we need to set up an equation of how much 1 beef costs and 1 bacon costs:
Let’s say f=cost of 1 beef and b=cost of 1 bacon
Now lets make the equation:
6f+3b=63. (She buys 6 portions of beef and 3 bacon and her total comes out to 63)
Now their is another condition that the cost of one bacon is -$1.50 per pound than beef.
So we can say b=f-1.50
Do you notice anything similar? The b has a value now and so we can replace the b in our first equation with the b of the 2nd (b=b)
So hence,
6f+3(f-1.50)=63
6f+3f-4.5=63
9f=67.5
F=7.5 (This is the cost for 1 pound of beef)
Now lets find out for bacon,. Now instead of doing this equation all over again just insert it into the b=f-1.5 you know make life easier for yourself:
B=7.5-1.5
B=6
Cost of 1 beef= $7.5
Cost of 1 bacon= $6
a total of tickets were sold for the school play. they were either adult tickets or student tickets. there were 53 more student tickets sold than adult tickets. how many adult tickets were sold?
Answers
Total 250 adult tickets are sold.
Let a = number of adult tickets sold
Let s = number of student tickets sold
a + s = 553
s = a + 53
From above equations;
a + a + 53 = 553
2a = 553 - 53
2a = 500
a = 250
Total 250 adult tickets are sold.
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Simplify 4x-3x(-3x+15)
Answers
l
Ashley's bill for dinner at a restaurant was $100. She left a 15% tip. What was the amount
of the tip?
Answers
Answer:
Step-by-step explanation:
ashleys bill was 100 so by knowing any percentage times 100 is itself ashleys tip was $15
Answer:
the amount on the tip is 15.00$
but when you add the amount of the total cost and the tip it would be $115 dollar they spend
Step-by-step explanation:
For an unknown polynomial function g(x),g(-5) - 6=-6. Which binomial
is a factor of g(x)?
Answers
Answer: solve for x
x ∈ R, h = 0 and g = 0
Step-by-step explanation:
Help ASAP get 10 points
Answers
13
Solution:
Using distance formula d=squarert[(x2-x1)^2+(y2-y1)^2] and plugging in the given values. You should get 13.
Which proportion can you use to find the value of a?
Answers
The proportion used to find the value of a is a/18 = 16/a
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given are three similar triangles, (refer to attached figure to separately see the similar triangles)
We know that, similar triangle have corresponding sides in equal ratio,
Therefore,
a/18 = 16/a
Hence, the proportion used to find the value of a is a/18 = 16/a
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Select all possible solutions for 2x + 7 ≤ 3x - 5.
Answers
Answer:
x \(\geq\) 12
[12,∞]
Step-by-step explanation:
Answer:
12 ≤ x
Step-by-step explanation:
Which of the following is a function, Please i need this its due in 15 min
A= {(1, 4) (2, 5) (3, 6) (4, 7)}
B={(-3, 4) (-1, 6) (2, 4) (5, 5)}
C={(-1, 2) (3, 5) (-1, 4) (7, 12)}
D={(1, 5) (4, 5) (5, 5) (8, 5)}
Answers
Answer:
A.
Step-by-step explanation:
its A because I did this test
Find the area please
Answers
Answer:
Area = (5 * 6.5)/2 =16.25 sq.yds
Step-by-step explanation:
The area of a triangle is given by half of the product of the base and the height.
Here
base = 5 yd
height = 6.5 yd
Area = (5 * 6.5)/2 =16.25 sq.yds
an online gardening magazine wants to understand why its subscriber numbers have been increasing. what kind of reports can a data analyst provide to help answer that questio
Answers
Reports that describe how many customers shared positive comments about the gardening magazine on social media in the past year. Reports that compare past weather patterns to the number of people asking gardening questions to their social media. Reports that examine how a recent 50%-off sale affected the number of subscription purchases. Reports that predict the success of sales leads to secure future subscribers.
What is data analyst?In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data. A data analyst examines data to find significant consumer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information. Although it is recommended that data analysts have a basic understanding of statistics and mathematics, many of their tasks may be completed without it. However, data analysts often need to be familiar with statistics, linear algebra, and calculus.
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Circle Q has a circumference of approximately 50 centimeters. Circle Q with diameter d is shown. What is the approximate length of the diameter, d? Use 3.14 for . Round to the nearest tenth of a centimeter. 4.0 centimeters 8.0 centimeters 15.9 centimeters 31.8 centimeters
Answers
Answer:
The answer is 15.9 centimeters. If you work backward with the formula 2pir = circumphrence, you get diameter *pi = 50. To find diameter, you divide 50 by pi and the answer is 15.9 centimeters.
Step-by-step explanation:
The diameter to the nearest tenth of a centimeter is mathematically given as
31.8cm, option D
What is the diameter?
Question Parameters:
Circle Q has a circumference of approximately 50 centimeters.
Generally, the equation for the circumference is mathematically given as
C=2\pir
Therefore
r=C/ \pi
r=50/3.14
r=15.9cm
Therefore,
d=2r
d=2*15.9
d=31.847
In conclusion, the diameter to the nearest tenth of a centimeter. is
31.8cm
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The seventh-grade class is building target areas for a PE activity. The bases for the game will be in a circular shape. The diameter of each circle is 3 feet. Approximately, how many square feet of the turf need to be painted for a base circle? Use 3.14 for π and round your answer to the nearest tenth.
7.1 square feet
9.4 square feet
18.8 square feet
28.3 square feet
Answers
Answer:
7.1 square feet
Step-by-step explanation:
Since the diameter of a circle is twice the radius, the radius of each circle is 3/2=1.5. The area of a circle is \(\pi r^2=\pi \cdot 1.5^2=2.25\pi \approx 7.1\). Hope this helps!
Answer:
18.8
Step-by-step explanation:
which statement is true about a function f(x), where f prime of x equals 2x squared plus 4 over x
f is increasing for x < −1.260 because f ′(x) < 0 for x < −1.260
f is increasing for x < −1.260 because f ′(x) > 0 for x < −1.260
f is decreasing for x > 0 because f ′(x) < 0 for x > 0
f is decreasing for x > 0 because f ′(x) > 0 for x > 0
Answers
Function f'(X) is increasing for x< - 1.260 because f ′(x) > 0 for x < −1.260
Describe function using an example?
A unique relationship where each input only has one output. Where x is the input value, it is frequently expressed as function "f(x)".
Example: "f of x equals x divided by 2" (f(x) = x/2). This expression is a function because each input "x" has a single output "x/2": • f(2) = 1.
Given,
f'(X) = 2x² + 4/x
f'(x) = 2x³ + 4/x
So, here f'(X) is positive for x< 1.260 .
f'(X) is increasing for x< - 1.260 because f ′(x) > 0 for x < −1.260
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It cost 0.50 (cents) to download an individual song and 4 dollars to download an album, Jada has 15 dollars to spend downloading music.Part 1. complete the table showing 3 ways Jada can spend 15 dollars downloading individual songs and album's Part 2: Write an equation relating the number of individual songs (s) and the number of albums (a) Jada can download Part 3:Lastly, sketch a graph of the solutions to your equation.
Answers
Individual song : $0.50
Album : $4
Money available: $15
Equation: (Part 2)
0.50s+4a =15
The product of the number of songs and the cost per song, plus the product of the number of albums and the cost per album must be equal to the money available-
Part 1.
6 songs and 3 albums
6 (0.50)+4 a = 15
Solve for a
4a = 15-3
4a=12
a=12/4
a=3
1 album and 22 songs
0.50s+4(1)=15
0.50s =15-4
0.50s =11
s=11/0.50
s= 22
30 songs and 0 albums
0.50 (30)+4 a = 15
4a=15-15
4a= 0
Part 3.
My age is 9 years, My sister was half of my age. Now I'm 49 years, How old is my sister?
Answers
Answer:
24.5 so 24 and a half .....
please help factorise 7ab+a
Answers
Answer:
= a(7b + 1)
Step-by-step explanation:
7ab + a
a(7b + 1).
Yolanda is 4 years younger than 3 times her daughter's age. The sum of their ages is greater than 88.
What is the youngest age Yolanda's daughter can be?
Enter your answer, as a whole number, in the box.
Answers
Step-by-step explanation:
22 i think that is what it is
Answer:
23
Step-by-step explanation:
Y = Yolanda's Age
X = Daughter's Age
y = 3x - 4
x + y = 88
x + (3x-4) = 88
x + 3x - 4 = 88
4x - 4 = 88
4x = 92
x = 92/4
x = 23
Someone help me out with this question
Answers
Answer: 7
Step-by-step explanation:
\(Mean = \frac{Sum of terms}{Number of terms}\)
= \(\frac{7+6+6+7+6+9+7+8}{8}\)
= \(\frac{56}{8}\)
= 7
Hope it helps and please mark as brainiest!
A tree is 4
541 feet tall. It is expected to grow by 1 feet per year.
At this growth rate, how many years will it take for the tree to have a height greater than 40 feet? Enter the answer in the box.
years
Answers
Answer:
21 years
Step-by-step explanation:
Can you help me plz
Answers
Explanation:
Find area of 1 square:
180/5 = 36
Find the side length of the square:
Sqrt 36 = 6
Answer:
\(\boxed{\sf y=6}\)
Step-by-step explanation:
There are 5 identical squares.
The area of one square is \(\sf s^2\).
\(\sf{y^2 } \times \sf{5}\)
\(\sf 5y^2\)
The area of the whole shape is 180 cm².
\(\sf 5y^2=180\)
Solve for y.
Divide both sides by 5.
\(\sf y^2=36\)
Take the square root on both sides.
\(\sf y=6\)
The graph below shows the height of a
flower based on the number of weeks since it
was planted. What is the linear equation
representing this situation?
A. y = -x + 2
B. y = x + 2
C. y = 1/2x + 2
D. y = 2x + 2
Answers
Answer:
B. y=x+2
Step-by-step explanation:
the lines goes up by 1 for the x-intercept so you don't have to write 1x you can just write it as x
and the y intercept is at (0,2) so it would be +2
graph model for y=11/10x+76
Answers
In the world’s coldest freezer, sodium gas was cooled to a temperature of 78.5°C below zero and then cooled 194.65°C more. What was the new temperature of the sodium gas?
Answers
Answer:
-202.5 celsius
Step-by-step explanation:
Answer:
–273.15°C
Step-by-step explanation:
2.2. South African friends of the Netherlands couple departed from Pretoria at 04h30am to spend the holiday with them. Their journey is described as follows: On their way from Polokwane they took the turn-off to the R521 route. Rest for 45 minutes at Dendron and took 15 minutes to do someshopping and till up the car's fuel tank at All days. 2.2.1. If the scale of the map is given as 1: 3 000 000 and the distance measured on the map between Beitbridge and Musina is 1,3 cm. calculate (in km) the actual distance between Beitbridge and Musina. ● (3)
Answers
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.
The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.
The measured distance on the map between Beitbridge and Musina is 1.3 cm.
To find the actual distance, we can set up a proportion using the scale:
1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.
Simplifying the proportion, we have:
1 / 3,000,000 = 1.3 / x.
Cross-multiplying, we get:
x = (1.3 * 3,000,000) / 1.
x = 3,900,000 / 1.
x = 3,900,000 km.
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
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Help me please no one is helping me its due in 5 minutes
its a scientific notation not fraction.
Answers
Answer:
343
Step-by-step explanation:
Not sure how to explain it
What is the answer to 10w + 3 and 3?
Answers
Answer:
Im gonna have to say 10w + 9x?
Step-by-step explanation:
I hope this can help :,)
Answer: 30w + 9
Step-by-step explanation:
10w + 3 * 3 can be written as
3 (10w +3) and u have to distribute 3 to 10 w and the other 3
= 3*10w + 3*3
= 30w + 9
Shania bought a $1,972 drum set on the installment plan. The installment agreement included a 20% down payment and 36 monthly payments of $52. 04 each. What is the finance charge?.
Answers
Shania bought a $1,972 drum set on the installment plan. The installment agreement included a 20% down payment and 36 monthly payments of $52.04 each. So the finance charge is $295.84.
In the given question, Shania bought a $1,972 drum set on the installment plan.
The installment agreement included a 20% down payment and 36 monthly payments of $52.04 each.
We have to find the finance charge.
Down payment = 20% of drum value
Down payment = $1972 * 20%
Down payment = $394.4
Total amount of monthly payments = one month payment * Number of months
Total amount of monthly payments = $52.04 * 36
Total amount of monthly payments = $1873.44
Amount Shania will pay for drum set = down payment + total monthly payments
Amount Shania will pay for drum set = $394.4 + $1873.44
Amount Shania will pay for drum set = $2267.84
Finance charge = Total payment under installment plan - cost of drum set Finance charge = $2267.84 - $1972
Finance charge = $295.84
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Linda has $20 in her savings account Option will add to her account each month Option 2 will double the amount in her account at the end of each month PART A Write a function in terms of to model each option of saving PART B: Linda wants to have at least 800 in her account at the end of months so that she can go on vacation . Determine which option will enable her to reach her goal Justify your answer
Answers
Therefore, option 2 is the better option for Linda to choose.
Given that Linda has $20 in her savings account. The following are the two options she has for saving:
Option 1: Adding $30 to her account each month.
Option 2: Doubling the amount in her account at the end of each month.PART AThe amount in Linda's account for option 1 is given by the function:
A(n) = 20 + 30n
where n represents the number of months. This is because she has $20 initially and then adds $30 for each of the n months.
For option 2, the amount in Linda's account is given by the function:A(n) = 20 x 2^nwhere n represents the number of months. This is because she has $20 initially and then doubles this amount for each of the n months.PART BWe need to determine which option will enable Linda to reach her goal of having at least $800 in her account at the end of months.Let's start by considering
option 1:A(n) = 20 + 30nWe need to find the value of n such that A(n) >= 800. So we can write:20 + 30n >= 800Solving for n, we get:n >= 26.33Since we cannot have a fractional number of months, we need to round up to the next whole number. Therefore, Linda needs at least 27 months to reach her goal of $800 using option 1.Now let's consider option 2:A(n) = 20 x 2^n
We need to find the value of n such that A(n) >= 800. So we can write:
20 x 2^n >= 800
Dividing both sides by 20, we get:
2^n >= 40
Taking the logarithm of both sides (base 2), we get:
n >= 5.32
Again, since we cannot have a fractional number of months, we need to round up to the next whole number. Therefore, Linda needs at least 6 months to reach her goal of $800 using option 2.Since option 2 requires a shorter time to reach Linda's goal, this is the option that will enable her to reach her goal in the shortest time.
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