The parabola described by the equation -1/16(x-3)^2 + 4 = y has the directrix at y=8. What is the focus of the parabola?

Answers

Answer 1

Answer:

(3, 0)

Step-by-step explanation:

A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.

The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:

[tex]4p(y-k)=(x-h)^2[/tex]

The directrix is at y = k - p, and focus is at (h, k + p).

Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:

[tex]-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\[/tex]

Comparing with the standard form:

The center = (h, k) = (3, 4)

Also, -16 = 4p

p = -4

Directrix is at y = k - p = 4 - (-4) = 8

Directrix is at y = 8

The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)

The focus is at (3, 0)


Related Questions

can someone help? it’s 7th grade math and im finishing this project for the end of the year

Answers

Answer:

c

Step-by-step explanation:

Evaluate x2+9/x2 for each of the given values.

What is the value of the expression when x = 3?
2
3
10
undefined
What is the value of the expression when x = 1?
2
3
10
undefined
What is the value of the expression when x = 0?
2
3
10
undefined

Answers

Answer:

ok so we just substate the number in so

6+9/6

6+1 1/3 = 7 1/3

so for part a the answer is 7.33

for part b

2+9/2

3+4 1/2 =7 1/2

so the answer is 7.5

A:7.33

B:7.5

Hope This Helps!!!

Answer:

A, 2

B, 10

C, undefined

Step-by-step explanation:

Just did the assignment  E2021

How many of the following numbers are factors of 34 or multiples of 7? 1, 2, 3, 4, 8, 14, 17, 29, 56, 91

Answers

Answer:

6

Step-by-step explanation:

So here are the numbers that are factors of 34 and multiples of 7

1,2,14,17,56,91

So count the numbers, 6. And that's ur answer, believe me

I'll give brainliest to the best answer if you help me with the image down below!

Includes: an explanation please

Answers

Answer:

3 Pounds

Step-by-step explanation:

2.82 rounded to the nearest whole number is 3.

If we wanted to round 2.82 to 2, it would have to be 2.49 or less

5 - 3tan3x = 0 trên -π< x < π.

Answers

Step-by-step explanation:

the answer is In photo above

what is the constant of proportionality in the equations 3y=2X?

Answers

Answer:

the coefficient of x is 2/3 which is the constant.

I need help on this one

Answers

Answer:

just look at the constant terms...

A: 5

B: 7

C: -5

1) 11-6 = 5 thus answer A

2) -3 -2 = -5 thus answer C

3) -5 - (12) = -5 + 12 = 7 thus answer B

Step-by-step explanation:

Translate the sentence into an equation,
Three times the sum of a number and 7 equals 2.
Use the variable y for the unknown number.

Answers

Answer:

3(y+7)=2

Step-by-step explanation:

you & three friends go to the twin carnival. you have a coupon for $20 off that will save your group money! if the total bill to get into the carnival was 100$ how much does one regular price ticket cost?

Answers

Answer:

$30

Step-by-step explanation:

100+ the twenty you got off is 120 and dvide 120/4=30   I am either making this way to easy or just dont understand lol

If 5 + 2 root 3 / 7 + 4 root 3 = a - b root 3, find a and b.​

Answers

Answer:

lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]

=[35-20√3+14√3-24]/[7²-(4√3)²]

=[11-6√3]/[49-48]

=11-6√3

therefore

11-6√3 = a+b√3

compare both sides

a= 11, b= -6

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

a = 11, b = 6

Step-by-step explanation:

Given

[tex]\frac{5+2\sqrt{3} }{7+4\sqrt{3} }[/tex]

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 7 + 4[tex]\sqrt{3}[/tex] is 7 - 4[tex]\sqrt{3}[/tex]

= [tex]\frac{(5+2\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3} }[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{35-20\sqrt{3}+14\sqrt{3}-24 }{49-28\sqrt{3}+28\sqrt{3}-48 }[/tex]

= [tex]\frac{11-6\sqrt{3} }{1}[/tex]

= 11 - 6[tex]\sqrt{3}[/tex]

with a = 11 and b = 6

Find the equation of the line through point (4,−7) and parallel to =−2/3+3/2 Use a forward slash (i.e. "/") for fractions (e.g. 1/2

Answers

44 to get drops activated by ear words to get on my nerves i you

Which is another name for plane M?

Answers

the answer is YN :))))))))))

whats the inverse of f(x)=x-3/5

Answers

Answer:

inverse: f-(x)=x+3/5

Step-by-step explanation:

Set f(x)=x and x=y

x=y-3/5

isolate y by adding 3/5 to both sides

x+3/5=y

this is the inverse :)

PLEASE HELP, WILL GIVE BRAINLIEST FOR RIGHT ANSWER!
Indicate the equation of the given line in standard form, writing the answer in the equation box below.

The line that contains the point Q (1, -2) and is parallel to the line whose equation is
y − 4 = 2/3 ( x − 3)

Answers

Find gradient by changing form of equation: y = 2/3x + 4. Gradient is 2/3.

Find y intercept of other line by substituting the coordinates: -8/3

Use information to write out equation of line: y= 2/3x - 8/3

Convert to standard form: -2x + 3y = 8.

Hope this helps :)

Answer:

my previous account deleted...how r u sadie??

cos 45°×tan 60°/cot 30° find the value​

Answers

The answer should 1.4

Help with this question

Answers

Answer:

Step-by-step explanation:

First find the first radius

c=88cm

=2*22/7*r=88cm

=r=14cm

22/7 (pie as common)(R1^2+R2^2=637cm)

14^2+R2^2=637cm

196+R2^2=637cm

R2^2=637-196=441

R2=√441

R2=21

first radius =14cm

second radius  =21cm

4x=6y= 6 and 2x+5y=11 by elimination show all work

Please help me!!! I will mark brainlist !!

Answers

Answer:

ans: x= 11/4 and y= 11/8

Step-by-step explanation:

4x=6y=6 mean

4x= 6 and 6y= 6 so, 6-6=0 i.e

4x - 6y = 0 say equation ....1

and given

2x + 5y = 11 say equation ....2

to solve by eliminating methods,

multiply equation....2 by 2 and subtract from ....1

i.e

4x - 6y =0

4x + 10y= 22

(-) (-) (-)

0+ (-)16y = - 22

y = -22/-16

y = 11/ 8

to get , x put y in either equation 1 or 2

I.e x= 11/4

this value of x and y satisfy both equations

The seventh grade wants to break last year's record of 78 coats collected for the annual clothing drive. They have already collected 13 coats.

Which number line represents the graph of the solution to the inequality that represents the number of coats, c, that the seventh grade must still collect?

Answers

Answer:

The last number line or D.

Step-by-step explanation:

To find the remaining coats to be collected, subtract the coats that are collected from the total of coats needed.

So:

78 - 13= 65

They must collect a total of 65 and more to break the last year's record of 78 coats. Number line D, represents the solution of this inequality.

Hope this helps! Have a nice dayy! :)

What is infinity + infinity??

Answers

Answer:

Although this makes for a lot of potential fun with formulas, mind experiments and arguments, the answer is plain.

Infinity is already everything so there is no more to it, infinity plus infinity would be still just infinity, which is btw infinite.

Answer:

infinity + infinity =  infinity

Step-by-step explanation:

Mark brainliest please :)

Given that y is directly proportional to x. If y = 30 and x= 5, write an equation that connects y with x.

Answers

Answer: y = 6x

Step-by-step explanation:

Since this is a direct proportion, we will introduce the constant of proportionality here and this will be:

y = kx

Since y = 30 and x= 5,

30 = 5 × k

30 = 5k

k = 30/5

k = 6

Therefore, the equation that connects y to x will be:

y = kx

y = 6x

The equation that connects y to x is y = 6x.

Pls help me answer this :,(

What is the equation of the quadratic graph with a focus of (5, 6) and a directrix of y = -12?

Answers

Answer:

Step-by-step explanation:

Step-by-step explanation:

the answer is in the above image

5 6 7 8 9 10
TIME REMAINING
50:04
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?

(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y – 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36

Answers

Answer:

(x-a)(y-b)=r²

(x-(-3))(y-(-5))=r²

(x+3)2(y+5)2=36

If the area of a circle is 36 pi, what is it's circumference?

Answers

Answer:

C = 12π or 37.7

Step-by-step explanation:

A = πr²

36π = πr²

π's get divided out and you are left with:

r² = 36

if you take the square root of 'r' it will equal the square root of 36, which is 6

C = 2πr

C = 2π(6)

C = 12π or 37.7

Answer

the answer is 12*sqrt pi

2. Which equation represents a line that is perpendicular to the line
represented by y = 2/3 + 1

Answers

We need to see the graphs btw

Which of the relations below is a function? *

2 points

{(2, 3), (3, 4), (5, 1), (2, 4)}

{(2, 3), (3, 4), (6, 2), (7, 3)}

{(2, 3), ( 3, 4), (6, 2), (3, 3)}

{(2, 4), ( 3, 4), (6, 3), (3, 3)}

Answers

Answer:

{(2, 3), (3, 4), (6, 2), (7, 3)}

Step-by-step explanation:

{(2, 3), (3, 4), (6, 2), (7, 3)}

this solution has different domain values : 2, 3, 6, 7

Does anyone know the answers with big ideas!

Answers

Answer:

k = 3

Step-by-step explanation:

Parent function is f(x) = [tex]0.25^{x}[/tex]

As shown in the graph, function 'f' has been shifted 3 units upwards to form an image function 'g'.

If the given function is shifted 3 units upwards, equation of the new function will be,

g(x) = [tex]0.25^{x}+3[/tex]

Therefore, the value of k will be,

k = 3

3x^2 + 14x
how do you factories this​

Answers

Answer:

x(3x+14)

Step-by-step explanation:

what do those terms share? they share the letter "x"

therefore we multiply x by 3x^2/x + 14x/x

3x^2/x = 3x and 14x/x = 14

Recipe ingredients remain in a constant ratio no matter how many servings are prepared. Which table shows a possible
ratio table for ingredients X and Y for the given number of servings?

Answers

Answer:

Table N 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx

Verify the table 4

For x=1, y=2

so

y/x=2/1=2

For x=2, y=4

so

y/x=4/2=2

For x=3, y=6

so

y/x=6/3=2

therefore

The constant of proportionality k is equal to 2 and the equation is equal to

y=2x

The table 4 represent a direct variation, therefore is a possible ratio table for ingredients X and Y

A factory puts 2,000 picture frames in each shipment. How many picture frames will the
factory put in 2 shipments?
picture frames

Answers

4,000

I know this because 2,000 • 2 = 4,000


For the function Rx) = 1/x+1 which of these could be a value of F(x) when x is
close to -1
O A. -0.01
OB. 0.01
O c. 1
O D. -10,000

Answers

Answer:

D. -10000

Step-by-step explanation:

you really need to copy or type the question better.

I can only assume what you really mean.

I guess, you want to say that F(x) = 1/(x+1)

when the value for x gets close to -1, the whole expression gets close to 1/0, which would bring numbers with larger and larger absolute values, leading to infinity.

you also did not say from what direction we are getting closer to -1.

we could come from -2 and move closer and closer to -1.

in this case (x+1) would always be smaller than 0 (negative sign).

or we could come from +1 and then 0 and move towards -1, in which case (x+1) would airways be bigger than 0 (positive sign).

anyway, when being closer and closer to -1, the absolute value of the resulting functional values will get bigger and bigger.

the only answer option with a larger absolute value is D (-10000).

so, that had to be the solution, and it also means that we are coming from -2 to -1, and the sign is negative.

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