Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line F(-6,0); x=6
Answers
Step-by-step explanation:
Since we have a vertical directrix, the equation of the parabola is
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
Where p is the distance from the vertex to the directrix.
or the distance from the vertex to the focus.
Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.
[tex] \frac{ - 6 + 6)}{2} = 0[/tex]
[tex] \frac{0 + 0}{2} = 0[/tex]
So our vertex is (0,0).
So our equation become
[tex] {y}^{2} = 4px[/tex]
The distance from the focus and directrix is 6.
So p=6.
[tex] {y}^{2} = 24x[/tex]
So p is 6.
Since p is 6,
[tex] \frac{ {y}^{2} }{24} = x[/tex]
Related Questions
Determine the period
Answers
Answer:
2 units
Step-by-step explanation:
From one crest (high point) to the next crest point is one period....
this covers 2 units on this graph
The line y = 2x intersects the line y = x + 6 at the point A. Find the equation of the line that passes through A and has gradient 3
Answers
Answer:
Step-by-step explanation:
Which function represents the inverse of function f?
Answers
Answer: Choice [B]
Step-by-step explanation:
Hii, I'd love to help you out! (:
This particular problem is all about finding inverse functions.
This can be done in 3 easy steps, which are shown below.
Replace f(x) with ySwitch x and y placesSolve for yThe process is shown below.
[tex]\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y[/tex]
[tex]\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y[/tex]
Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?
Ofc not! There's just one more thing that can be done to simplify our answer.
[tex]\tt \cfrac{x}{5}-\cfrac{5}{3}[/tex]
We're getting closer!
[tex]\tt \cfrac{1}{3}x-\cfrac{5}{3}[/tex]
Voila! There's our answer, cheers! (;
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Drag the boxes to order the decimals from least to greatest from left to right.
316.011
306.324
306.359
Answers
Answer:
306.324
306.359
316.011
Step-by-step explanation:
Hope it helped!
Select the correct answer.
In the given figure, m AD = 79° and m
Answers
Answer:
2 or 3
Step-by-step explanation:
write it down dummy
can anyone help me i beggg
Answers
= 2π7(7+15)
=308pi
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
Answers
The inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The missing options are in the picture, please refer to the picture.
We have:
An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane.
Let's suppose the number of tickets is represented by x
Total number of passengers = 175
The inequality can be framed:
x + 87 ≤ 175
x ≤ 88
Thus, the inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.
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Simplify 4^3/4^8 so that it is not in fraction form.
Answers
Answer:
[tex]4^{-5}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{4^{3} }{4^{8} }[/tex] = [tex]4^{(3-8)}[/tex] = [tex]4^{-5}[/tex]
what does 5r-r-9=15 look like after combining like terms ?
and whats the answer for r?
Answers
The value of r from the expression is 6
Simplifying expressionGiven the expression below;
5r-r-9=15
Add 9 to both sides
5r - r - 9 + 9 = 15 + 9
4r = 15 + 9
4r = 24
After combining the like terms the expression will be 4r = 24
4r/4 = 24/4
r = 6
Hence the value of r from the expression is 6
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A building in a city has a rectangular base. the length of the base measures 65 ft less than twice the width. the perimeter of this base is 890 ft. what are the dimensions of the base? the width of the base is ft.
Answers
By solving a system of equations, we will see that the width is 170ft and the length 275 ft.
How to get the dimensions of the base?
For a rectangle of length x and width y, the perimeter is:
P = 2*(x + y).
Here we know that:
x = 2y - 65ft
p = 890ft = 2(x + y)
So we have a system of equations.
To solve this, we need to replace the first equation into the second one:
890ft = 2(x + y)
890ft = 2(( 2y - 65ft) + y)
Now we can solve this for y.
890ft = 4y - 130ft + 2y
890ft + 130ft = 6y
1020ft/6 = y = 170ft
So the width is 170ft, and we know that:
x = 2y - 65ft = 2*(170ft) - 65ft = 275ft
So the length is 275 ft.
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tony invest 2000 at a 4.5 percent rate.
Answers
Answer:
$2,999
Step-by-step explanation:
A = P(1 + r) ^ tA = 2000(1 + .045) ^ 9A ≈ 2999can it be solve pq(r²+1)-r(p²+q²)
Answers
Answer:
pqr²+pr-rp²+rq²
Step-by-step explanation:
pq(r²+1)-r(p²+q²)
pqr²+pr-rp²+rq²
Find one-third of the sum 9 and 12.
Answers
Answer:
7
Step-by-step explanation:
9 plues 12 = 21
21 divide by 3
= 7
Answer:
7
Step-by-step explanation:
9 + 12 = 21
one third of 21 is the same as 21 divided by 3
so 21 divided by 3
= 7
so 7 is the answer
OR
9 divided by 3 = 3
12 divided by 3 = 4
3 + 4 = 7
number machine n -5 x 4
Answers
n - 5 × 4 = 4(n - 5)
Hi, so this isn't an equation but could somebody explain what domain and range are please? I'm not doing great with understanding it for whatever reason and it would be super helpful if you could dvmb it down a little bit please
Answers
Answer:
Step-by-step explanation:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
For example, "whatis.com" could be a domain with records for "www.whatis.com" and "www1.whatis.com,"
Please help me with my math
Answers
Answer:
x = 120
y = 21
Step-by-step explanation:
Since j and k are parallel, the sum of x and 60 would be 180 because they are supplementary:
x + 60 = 180 subtract 60 from both sides
x = 120
The measure of x and (4y+36) is equal because they are alternate angles since the horizontal lines are also stated as parallel:
we know x = 120 so
120 = 4y + 36 subtract 36 from both sides
84 = 4y divide both sides by 4
21 = y
In order to determine the height of the flagpole in the school yard, Cindy is going to use similar triangles. The
length of Cindy's shadow is 5 feet. Measuring the length of the shadow of the pole at the same time, she finds
it to be 12.5 feet. Using this information and the fact that Cindy's height is 4 feet, give the height of the pole
to the nearest hundredth of a foot.
Answers
The height of the pole is 12.5 feet.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Cindy's shadow is 5 feet.
length of the shadow of the pole at the same time, she finds it to be 12.5 feet.
So,
12.5/5=x/5,
62.5=5x
x= 12.5 feet.
Hence, the height of the pole is 12.5 feet.
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which of the sentence is true?
Answers
Answer:
The graph of the circle is not a function
A box in the shape of a rectangular prism has a width that is 5 inches greater than the height and a length that is 2 inches greater than the width. Write a polynomial expression in standard form for the volume of the box. Explain the meaning of any variables used.
Answers
The volume of the rectangular prism can be express in standard polynomial as follows:
x³ + 12x² + 35x
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
let
height = x
width = x + 5
length = x + 5 + 2 = x + 7
Therefore,
volume = x(x + 5)(x + 7)
volume = x(x² + 7x + 5x + 35)
volume = x(x² + 12x + 35)
volume = x³ + 12x² + 35x
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8
the probability that a biased coin lands on heads is 0.47
13
the probability that a biased dice lands on an even number is
20
samira flips the coin and rolls the dice.
find the probability that the coin lands on tails and the dice
lands on an even number.
Answers
The probability that the coin lands on tails and the dice lands on an even number is 0.3455
How to determine the probability?Let A represents a biased coin lands on heads and B represents a biased dice lands on an even number
So, we have:
P(A) = 0.47
P(B) = 13/20
The required probability is:
P(A' and B) = P(A) * P(B)
This gives
P('A and B) = (1 - 0.47) * 13/20
Evaluate
P('A and B) = 0.3455
Hence, the probability that the coin lands on tails and the dice lands on an even number is 0.3455
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What is the completely factored form of x4y – 4x2y – 5y? y(x2 – 5)(x2 1) y(x2 5)(x2 – 1) (x2y – 5)(x2 1) (x2y 5)(x2 – 1)
Answers
Answer:
y (x² + 1) (x² - 5)
Step-by-step explanation:
Factorization:Take 'y' from each term.
x⁴y - 4x²y - 5y = y[x⁴ - 4x² - 5]
Now factorize x⁴ - 4x² - 5.
Sum = -4
Product = -5
Factors = -5 , 1
When we add (-5) + 1, it gives (-4) and when we multiply (-5)*1, gives (-5).
x⁴ - 4x² - 5 = x⁴ + x² - 5x² - 5
= x²(x² + 1) -5(x² + 1)
= (x²+ 1) (x² - 5)
x⁴y - 4x²y - 5y = y (x² + 1) (x² - 5)
A box contains
toffee, coffee, orange, mint and hazelnut
flavour chocolates.
The ratio of toffee: coffee: orange : mint chocolates is 5:4:2:3
The
probability of picking a hazelnut chocolate i5 g
How many hazelnut chocolates are in the box?
Answers
The probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1
How to determine the probabilityNote that the ratios = 5:4:2:3
toffee: coffee: orange: mint chocolates = 5:4:2:3:1
Total ratio = 15
Probability of picking a hazelnut chocolate = ratio of hazelnut chocolates/ total ratio
Probability of picking a hazelnut chocolate = [tex]\frac{1}{15}[/tex]
The number of hazelnut chocolates in the box is gotten from the ratio which is 1
Therefore, the probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1
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(-4^0) + 1 equals to ?
Answers
Answer:
zero (0)
Step-by-step explanation:
-4^0=-1
-1+1=0
HELP!!!!!
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x-6
g(x) = 3x+6
g(x)=3*-6
g(x)=3*+6
Answers
The answer is g(x) = 3x - 6
Given the function f(x) = −5x2 − x + 20, find f(3).
Answers
Answer:
123icuxxiffatjtjfug8utkxi93hkgodo c office c 8f
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(-3) = -1
B.
h(13) = 18
C.
h(2) = 16
D.
h(8) = 21
Answers
The true statement is h(2)=16.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. The range of a function is the set of values that the function assumes.
Given:
domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25,
Also, h(8) = 19 and h(-2) = 2,
Now,
2=h(-2)< h(2)<h(8) =19
h(8)=19≠21
h(13)> h(8) =19
h(-3)< h(-2) =2 [1 ≤ h(x) ≤ 25]
Hence, h(2)=16
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If a gas filled balloons rises 40 feet in the 1 minutes, 60 feet in the 2 minute, and 80 feet in the 3 minute, how many feet will the balloon rise during the 15 minute
Answers
Answer:
600
Step-by-step explanation:
15*40=600
Write the ratio using fraction notation and reduce.
HINT: Be sure to compare like units.
$5 to $35
A. 7
B. 15
C. 5
D. 17
Answers
The ratio using fraction notation of $5 to $35 would be 7.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
To convert a ratio into a fraction,
We will simply use the first number as the numerator and the second number as the denominator.
So the fraction = 35/5.
= 7
Since there are no more common factors, the fraction is in its lowest form which is 7.
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4 /3 r/ 6 start fraction, 3, divided by, 4, end fraction, equals, start fraction, 6, divided by, r, end fraction r =
Answers
The value of r is 6
Given start fraction and end fraction are 4/3,r/6 and 3 divided by 4 end fraction which is equal to start fraction 6 divided by r end fraction
We need to calculate the value of r
Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line.
It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed
According to the statement the equation formed
4/3*r/6*3/4 = 6/r
Solving the equation by 4/3*3/4 = 1
Hence 1*r/6 = 6/r
Therefore r^2 = 36
r = 6
Hence the value of r is 6
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jackie brought 9 plants
Answers
Answer:
I think its the thrid one because it is the only one with the correct top equation(I can't see the rest)
Step-by-step explanation:
