Consider we need to find the equation of the parabola.
Given:
Parabola with focus (2, 1) and directrix x=-8.
To find:
The equation of the parabola.
Solution:
We have directrix x=-8. so, it is a horizontal parabola.
The equation of a horizontal parabola is
[tex](y-k)^2=4p(x-h)[/tex] ...(i)
where, (h,k) is center, (h+p,k) is focus and x=h-p is directrix.
On comparing focus, we get
[tex](h+p,k)=(2,1)[/tex]
[tex]h+p=2[/tex] ...(ii)
[tex]k=1[/tex]
On comparing directrix, we get
[tex]h-p=-8[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2h=2+(-8)[/tex]
[tex]2h=-6[/tex]
Divide both sides by 2.
[tex]h=-3[/tex]
Putting h=-3 in (ii), we get
[tex]-3+p=2[/tex]
[tex]p=2+3[/tex]
[tex]p=5[/tex]
Putting h=-3, k=1 and p=5 in (i), we get
[tex](y-1)^2=4(5)(x-(-3))[/tex]
[tex](y-1)^2=20(x+3)[/tex]
Therefore, the equation of the parabola is [tex](y-1)^2=20(x+3)[/tex].
Which expression is equivalent to 4.4.4.4.4.4.4.4?
Answer:
your answer is D
Step-by-step explanation:
hope this helps
The school principal is designing a square courtyard outside of the school, separated into 4
equal spaces. She wants to know the total area of the courtyard.
what is the total area if each smaller space is 5 feet on each side
Answer:
Students will gain an appreciation for the study of mathematics. In ... (I.3.6) The area of the surface of a sphere is described by the formula
Step-by-step explanation:
Correct me if I'm wrong! :)
Answer:
Its 100
Step-by-step explanation:
I took the quiz and got it right
Decide which estimate is closer to the actual answer. Explain your reasoning as store bought 25lb of produce if store spent $110.90 about how much does the produce cost per pound in dollars? 0.04,0.4,4,40 (b) a 6 pack of juice boxes contains 54.6 oz of juice in total about how many ounces of juice does each juice box contain ? 0.9,9,90,900 (c) in 20 L of air there is about 0.42 L of carbon dioxide about how many liters of carbon dioxide are there in 1 L of air 0.02,0.2,2,20
2/5 divided by 1 7/8
0.21333333333
answer:
Answer:
0.213
Step-by-step explanation:
I used a calculator :)
Which unit price is the highest?
turnips for $1.51 per pound
peppers for $1.62 per pound
carrots for $1.26 per pound
celery for $1.48 per pound
Please help me out!
Answer:peppers
Step-by-step explanation:
Answer:
peppers for $1.62 per pound
Step-by-step explanation:
i took the test
you can buy 3 candy bars at the quick market for 2.17. how many candy bars can you buy with 17.36?
A school cafeteria has 30 boxes of Wheaty Squares cereal and 20 boxes of Mighty O's
cereal. Each box has the same number of ounces of cereal. Write an expression to
represent the total ounces of cereal. Then simplify it to create an equivalent expression.
Answer:
50e=t
Step-by-step explanation:
Wheaty Squares = w
Mighty O's = m
ounces in each box = e
total ounces of cereal = t
w+m=30+20=50
Please help!
Which equation has a constant of proportionality equal to 1?
Choose 1 answer:
A. Y= 10/11x
B. Y = 7/8x
C. Y= 3/15x
D. Y=x
Answer:
[tex]\huge\boxed{\sf D.}[/tex]
Step-by-step explanation:
If
Y is directly proportional to x
Then
Y ∝ x
Changing proportionality to equality
Y = k x
If k = 1 , then
Y = x
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
it's D
Step-by-step explanation:
Khan Academy
Arianna has $0.70 worth of nickels and dimes. She has 4 more dimes than nickels. By
following the steps below, determine the number of nickels, x, and the number of
dimes, y, that Arianna has.
Determine three ways to have 4 more dimes than nickels:
Who can solve this for me?
Answer:
x=2 and y=6
Step-by-step explanation:
thee isn't any other way im sorry but there isn't here is a list:
1 nickel = $0.05 and 5 dimes =$0.50 = $0.55
2 nickels = $0.10 and 6 dimes = $0.60 = $0.70
3 nickels = $0.15 and 7 dimes = $0.75 = $0.85
4 nickels = $0.20 and 8 dimes = $0.80 = $1.00
5 nickels equal $0.25 and 9 dimes equals $0.90 = $1.15
so as you can see the more you add the higher the number gets and if its any lower it won't be enough sorry if you really needed that last part
Helpppppppp pleaseeeee
Answer:
B and C; 0.5 and 4.5
Write the ratio of height of the building to the number of floors. Then, find the unit rate, and explain what it means in this situation. Fill in the correct answers to complete the sentences.
The ratio of height of the building to the number of floors is nothing. The unit rate is nothing. This means that each floor of the building is nothing ft high.
Answer:
I love a building that's nothing feet high
Step-by-step explanation:
Can that building be my new home?
i need big help because this is due today
Answer:
Step-by-step explanation:
x | y
30 | 6
60 | 12
90 | 18
120 | 24
2.25 + 65.47 + 2.333
Answer:
The answer is 70.05300.
The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d
from the source of the sound.
A person 14 feet from a jetski, it is 85 decibels loud.
How loud is the jetski when the person is 41 feet away? (Round to 3 decimal places.)
dB
Answer:
L = 9.91 decibels.
Step-by-step explanation:
The loudness, L is inversely proportional to the square of the distance, d, from the source of the sound.
i.e L [tex]\alpha[/tex] [tex]\frac{1}{d^{2} }[/tex]
L = [tex]\frac{k}{d^{2} }[/tex]
Where k is the constant of proportionality.
When d = 14 feet and L = 85 dB, then;
k = L x [tex]d^{2}[/tex]
= 85 x [tex](14)^{2}[/tex]
= 16660
k = 16660
L = [tex]\frac{16660}{d^{2} }[/tex]
Thus, when d = 41 feet, then;
L = [tex]\frac{16660}{(41)^{2} }[/tex]
= [tex]\frac{16660}{1681}[/tex]
= 9.91077
L = 9.91 dB
The loudness is 9.91 decibels.
Answer the following question please
Answer:
∠MON = 98°
Step-by-step explanation:
It is given that ∠LON is a straight line.
∠MON = 3x+89
and
∠LOM = 8x+58
If LON is a straight line. It means,
∠MON + ∠LOM = 180 (Linear pair)
Putting values,
3x+89 + 8x+58 = 180
11x + 147 = 180
11x = 180-147
11x = 33
x = 3
So, ∠MON = 3(3)+89
= 9+89
= 98
Hence, the value of ∠MON is equal to 98°.
Write the equation of a line in Point-Slope form that has a slope of -2/3 and
passes through the point (-1,3).
Answer:
The equation of a line in Point-Slope form is y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
Step-by-step explanation:
Linear equations can take various forms, such as the point-slope formula. This formula gives the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as:
y - y1= m*(x-x1)
In this equation, m is the slope and (x1, y1) are the coordinates of the point.
In this case, you know that the line has a slope of [tex]-\frac{2}{3}[/tex] and passes through the point (-1,3). This is, m=[tex]-\frac{2}{3}[/tex] and (x1;y1)=(-1;3). Replacing:
y -3=[tex]-\frac{2}{3}[/tex] *(x-(-1))
This is:
y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
The equation of a line in Point-Slope form is y -3=[tex]-\frac{2}{3}[/tex] *(x+1)
Combine like terms to simplify: H + g + h + g - g
Answer:
2h + g
Step-by-step explanation:
5. Evaluate the following expression - 12(-3) + 7
Answer:
43
Step-by-step explanation:
Someone help me please
Please friend I do not know
Make a table of values for f(x) after the given translation 3 units up
Answer:
In this case, we do not have the table, so i will answer in a general way:
First, let's describe the transformation.
Vertical shift.
If we have a function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
This will move the graph of f(x) up or down a distance of N units.
if N is positive, then the shift is upwards
if N is negative, then the shift is downwards.
Then a shift of 3 units up, is written as:
g(x) = f(x) + 3
This would be translated to the table in the next way:
You need to add 3 to all the values of y (or f(x)) in the table:
So if for example, the original table was:
x f(x)
0 5
1 7
2 10
3 15
The table of the transformation will be:
x g(x)
0 5 + 3 = 8
1 7 + 3 = 10
2 10 + 3 = 13
3 15 + 3 = 18
20 POINTS
The price of a car has been reduced from $24,000 to $14,880. What is the percentage decrease of the price of the car?
Decrease of price = $24,000 - $14,880
=> $9,120
Percentage decrease = 9120/24000×100
=> 38%
Tim flips a weighted coin 6 times and gets 2 tails. What is the experimental probability that the next flip will come up tails?
Answer:
1/3
Step-by-step explanation:
bc 2/6 reduces to 1/3
A and B are similar cuboids.
surface area of A: surface area of B = 25 : 36
Work out volume of A: volume of B
A 5:6
B 125 : 216
C 25 : 36
D 625 : 1296
Answer:
B. 125 : 216Step-by-step explanation:
Surface area of cuboid A with side a is:
6a²Same for cuboid B with side b:
6b²Ratio of surface areas:
6a² : 6b² = 25 : 36 ⇒a² : b² = 25 : 36 ⇒a : b = 5 : 6Volumes of A and B are:
a³ and b³And their ratio is:
a³ : b³ = 5³ : 6³ ⇒a³ : b³ = 125 : 216Correct option is B
Answer:
B. 125 : 216
Step-by-step explanation:
What is the value of x?
Answer:
the value of X is 10x
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x²
g(x) = ?
A. g(x) = (x - 3)2 + 1
B. g(x) = (x + 3)2 + 1
C. g(x) = (x - 3)2 - 1
O D. g(x) = (x + 3)2 - 1
The correct answer is A. g(x)=(x-3)^2+1
The equation of the blue graph is g(x) = (x - 3)² + 1.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Since the graphs of f(x) and g(x) intersect at (1.5, 2.5), we can substitute these values into the equations and solve for the constant term:
f(1.5) = g(1.5)
1.5² = g(1.5)
2.25 = g(1.5)
Therefore, we know that the vertex of g(x) is (1.5, 2.25).
Also, since the graphs have the same shape, we know that the vertex of g(x) is obtained by shifting the vertex of f(x) horizontally by the same amount, which is 3 units to the right.
So, the equation of the blue graph can be obtained by replacing x with (x-3) in the equation of the green graph:
g(x) = (x - 3)² + 1
Expanding this equation, we get:
g(x) = x² - 6x + 9 + 1
g(x) = x² - 6x + 10
g(x) = x² - 2 x 3x + 9 + 1
g(x) = (x - 3)² + 1
Therefore,
The equation of the blue graph is g(x) = (x - 3)² + 1.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ7
will give brainliest plz help me!
Answer:
II and III
Step-by-step explanation:
Please help i put max points for u!!
Marley used 7 cups of water to make 4 loaves of French bread. What equation can be used to model the total cups of water needed y for making x loaves of French bread? Write the equation in the forn y = kx. How many cups of water do you need for 6 loaves of French Bread? Express your answer as a fraction in simplest form.
Answer:
Equation: y = [tex]\frac{7}{4}[/tex] x
21/2 cups of water
Step-by-step explanation:
Plug in 7 as y and 4 as x
7 = 4k
Find k
k = 7/4
Then plug k into th equation
y = 7/4 x
For the second part of the question:
Plug in x which is 6 into the bolded equation.
y = (7/4)(6) = 42/4 = 21/2 (simplified form)
21/2 cups of water
James bought a new digital camera for $175.00. He pays a sale ax of 7.2%. What was the total of the camera
Answer:
187.6 i think
Step-by-step explanation:
Answer:
$187.60
Step-by-step explanation:
Find 7.2% of the price to figure out the sales tax:
7.2% * 175 / 100% = $12.60
Add the sales tax to the original price:
$12.60 + $175.00 = $187.60
Write the equation in exponential form.
Log3 1/9=-2
O 3=9-2
O 1/9=3^-2
O 9=3^2
O 3=3^1
Answer:
a
Step-by-step explanation:
Answer: The correct answer is B. 1/9=3^-2
Step-by-step explanation:
You go out to eat at the Outback Steakhouse. Your meal, drink and desert cost $38.56. You are
going to leave the waitress at 15% tip. How much money will you leave the waiter and what is
the total cost of the meal?
I
Answer:
44.34
Step-by-step explanation:
[tex]15 \div 100 \times 38.56 = [/tex]
[tex] = 5.78[/tex]
[tex]38.56 + 5.78 = 44.34[/tex]