Mathematics College

What is the equation of the parabola, in vertex form, with focus at (2,-4) and directrix y=-6?

A. (X-2)^2 = 4(y+5)
B. (Y+4)^2 = 4(x-2)
C. (X+2)^2 = 1/4(y+4)
D. (X-2)^2 = -1/4(y+5)

What Is The Equation Of The Parabola, In Vertex Form, With Focus At (2,-4) And Directrix Y=-6?A. (X-2)^2

Answers

Answer 1

Answer:

A. (X-2)^2 = 4(y+5)

Step-by-step explanation:

Answer 2

Equation of parabola: (x-2)² = 4(y+5)

Thus option A is correct.

Given:

Focus at (2, -4) and a Directrix of y = -6

Here,

Let us suppose that there is a point (x, y) on the parabola.

Its distance from the focus point (2, 4) is √(x - 2)² + (y + 4)²

Its distance from directrix y = -6 is |y + 6|

Therefore, the equation will be:

√(x - 2)² + (y + 4)² = |y + 6|

Squaring on both the sides,

(x - 2)² + (y + 4)² = (y + 6)²

x² - 4x + 4 + y² + 8y + 16 = y² + 12y + 36

(x-2)² = 4(y+5)

Therefore option A is correct.

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Related Questions

Arthur has a box which contains 6 black balls and n (n ≥ 2) white balls, then at random, he takes 3 balls from the box. If the probability of taking any ball is the same and Pₙ is the probability of taking 1 black ball and 2 white balls, what is the largest possible value for Pₙ?​

Answers

Answer:

11/68 or 0.1618

Step-by-step explanation:

Balls

Black - 6White - n

Options of getting 3 balls

1. White, black, black2. Black, white, black3. Black, black, white

Probability P(n) in each option

1. WBB

P(w) = 6/(n + 6)P(b1) = n/(n + 6 - 1) = n/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)

P(n) =

P(w)P(b1)(P(b2) = 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

2. BWB

P(b1) = n/(n + 6)P(w) = 6/(n + 6 - 1) = 6/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)

P(n) =

P(b1)P(w)(P(b2) = n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

3. BBW

P(b1) = n/(n + 6)P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)P(w) = 6/(n + 5 - 1) = 6/(n + 4)

P(n) =

P(b1)P(b2)(P(w) = n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

Final equation is same for each case:

P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)

The easy way to find the maximum is to try the numbers or graph.

Both of the methods give the maximum integer n = 11 or n = 12

See attached graph

At both values n we get P(n):

P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)

Here's a graph of a linear function. Write the equation that describes that function.

Answers

Answer:

2/3x + 1

Step-by-step explanation:

The y-intercept is 1. you can see that when x increases three, y increases 2.

Find the measures of the numbered angles of the parallelogram.

Answers

Answer:

1=40

2=140

3=40

Step-by-step explanation:

We know on side

140 and side 2 are equal

1 and 3 are equal

So since 140 and 2 are equal

140*2=280

360 degrees total in any 4 sided shape

360-280=80

80/2=40

Helpppppppp.................​

Answers

What’s wrong?? ......

Which equation is equivalent to 1/5x - 3 = 2/3
A : x-15=10
B : 3x-15=10
C : 3x-45=10
D : 5x-45=3​

Answers

Yes the answer would be a

What is the standard deviation of this data set?
12, 14, 9, 11, 10, 15, 16, 12, 7, 14

Answers

Answer:

The standard deviation is 2.6832815729997

Step-by-step explanation:

SD^2=(12-12)^2+...+(14-12)^2/10

SD^2=72/10

SD^2=7.2

SD=squeare root of 7.2

SD=2.6832815729997

7.43+9.25 Show Your Work

Answers

Answer:

16.68

Step-by-step explanation:

just add them like regular numbers then just put the decimal

help me please!!!!!!​

Answers

Answer: sin(C) = 3/5

==========================================================

Explanation:

Recall that sine is the ratio of opposite over hypotenuse.

For angle C, the opposite side is AB = 24 as this leg is furthest as possible from angle C. The hypotenuse is always opposite the 90 degree angle.

So,

sin(angle) = opposite/hypotenuse

sin(C) = AB/AC

sin(C) = 24/40

sin(C) = (8*3)/(8*5)

sin(C) = 3/5

If you want to find the measure of angle C, then you apply the arcsine rule to both sides. Inverse sine is the same as arcsine.

Answer:

Step-by-step explanation:

Solution

Here,

H=40

P=32

B=24

Now,

sinC=p/h

      =32/40

      =4/5

Where, 4 is perpendicular and 5 is hypotenuse.

Hope it helped you.

Plz mark me brainliest.

Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator?

Answers

Answer:

(√17 + √2)/(√17 + √2)

Step-by-step explanation:

You need to determine the conjugate of the denominator.

√17 - √2 has conjugate of √17 + √2, when multiplied the product is going to be a rational number:

(√17 - √2)/(√17 + √2) = 17 - 2 = 15

Therefore correct choice is B or second from the top:

(√17 + √2)/(√17 + √2)

Answer:

B

Step-by-step explanation:

Because trust is a good thing in this world

Please help at answer least one question please number it!!

Answers

4. Is positive 63

I think so

Answer:

1. 88

2. -17

3. -10

4. -16

5. -14

6. 44

7. -76

8. 18

Step-by-step explanation:

Hope this helps :D

Solve the expression (w - z)²​

Answers

It will be (w-z) (w-z) hope this helps!

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, -3).
A. y−5=−109(x+3)
B. y−7=−109(x+4)
C. y+3=−109(x+5)
D. y+4=−109(x−7)

Answers

Answer:

y+4=–109(x-7)

please mark as brainliest

P+45267=87012 evaluate

Answers

Answer:

p+45267=87012

We move all terms to the left:

p+45267-(87012)=0

We add all the numbers together, and all the variables

p-41745=0

We move all terms containing p to the left, all other terms to the right

p=41745


FIND THE MEASURE OF ANGLE 2 PLEASE HELP ASAP!

Answers

Answer:

We know that the figure has a symmetry

angle 1 = angle 2

angle 1 =180°-(18°+90°) = 180° - 108°=72°

Therefore, angle 2 =72°.

Determine 0.929229222922229222229

Answers

Answer:

0.93

Step-by-step explanation:

BC -
Round your answer to the nearest hundredth.
B
?
35
A
с
2.

Answers

Answer:

BC ≈ 1.40

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA [Right Triangles Only] tanθ = opposite over adjacent

Step-by-step explanation:

Step 1: Identify

Angle θ = 35°

Opposite Leg BC = x

Adjacent Leg AC = 2

Step 2: Solve for x

Substitute [Tangent]:                    tan35° = x/2Isolate x:                                        2tan35° = xRewrite:                                          x = 2tan35°Evaluate:                                        x = 1.40042Round:                                            x ≈ 1.40

Tangent (Angle) = Opposite side / adjacent side

Tangent(35) = BC/2

Multiply both sides by 2:

BC = 2 x Tangent(35)

BC = 1.40042

Rounded to nearest hundredth:  BC =  1.40

the target temperature for a laboratory is 71° f. it can vary by up to 3°. if t is the temperature in the laboratory, which of the following inequalities represents this situation?​

Answers

Answer:

|t-71| < 3

Step-by-step explanation:

The  inequalities represents this situation is | t - 71 | < 3 .

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

According to the question

The target temperature for a laboratory = 71° f.

it can vary by up to 3°. (highest limit)

the temperature in the laboratory represented by t

Now,

inequalities represents this situation is

| t - 71 | < 3

Hence, the  inequalities represents this situation is | t - 71 | < 3

To know more about inequalities  here:

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Can someone help me with this i will give brainliest please!

Answers

Answer:

(-1, -3)

Step-by-step explanation:

Given system:

4x - 2y = 22x + y = - 5

1) Solving the second equation for y:

2x + y = - 5 ⇒y = -5 - 2x

2) Substituting y into the first equation:

4x - 2y = 2 ⇒4x - 2( -5 - 2x) = 2Correct option is a)

3) Solving for x:

4x - 2( -5 - 2x) = 24x + 10 + 4x = 28x = 2 - 108x = -8x = -1

4) Solving for y:

y = -5 - 2xy = -5 - 2(-1) = -5 + 2 = -3y = -3

5) Ordered pair is:

(x, y) = (-1, -3)

Answer:

Step-by-step explanation:

Help Please! Question on picture.

Answers

Answer:

A) 1/2x-6=-2x-1

B) x=2

Step-by-step explanation:

question A is asking to set up a system of equations

f(x)=g(x) is the original expression

substitute the equations into this to get 1/2x-6= -2x-1

for b, when you solve this equation you get x=2

sorry for the formatting I'm new here

I'm supposed to solve for PQ. it's pythagorean theorem.​

Answers

Answer:

29 i think

Step-by-step explanation:

pythagoreon thereom is a^2+b^2=c^2 so c^2 being the hypotneuse you would do 2*2=4 +5*5=25 and 4+25=29

which triangles are congruent in the figure

Answers

Answer:

Step-by-step explanation:

The two triangles that are congruent are ABE and CBD by SSS.

Two sides of a triangle have the same length. The third side measures 6 m less than twice the common length. The perimeter of the triangle is 14 m. What are the lengths of the three​ sides?
What is the length of the two sides that have the same​ length?

Answers

Answer: 5

Step-by-step explanation:

x = common side length

2x + (2x - 6) = 14

4x - 6 = 14

4x = 20

x = 5

Prove: The square of a number that is
one more than a multiple of 3 is also one
more than a multiple of 3.
n +
(3n + 1)2 = [ ? ]n? +
1([ ]n2 +
=
)n) +
- 1 more than a multiple of 3

Answers

Let 3n + 1 denote the "number" in question. The claim is that

(3n + 1)² = 3m + 1

for some integer m.

Now,

(3n + 1)² = (3n)² + 2 (3n) + 1²

… = 9n² + 6n + 1

… = 3n (3n + 2) + 1

… = 3m + 1

where we take m = n (3n + 2).

The altitude of a helicopter increases 1000 feet every 4 minutes .what is the unit rate change (feet per minute) of the altitude.(there’s no picture)

Answers

Answer:

250

Step-by-step explanation:

divide 1000 by 4 and you will get the unit rate

A rectangle has an area of 82 ft2. What is
the length if the width is 10 ft?

Answers

Answer:

187

Step-by-step explanation:

Give the ratio for sine (e) in decimal form to 4 digits.
13
11
5

Answers

.0147

I am a jedi master

Is -8 a rational number

Answers

Answer:

yes

Step-by-step explanation:

Answer:

yea

Step-by-step explanation:

because it is

John has a rectangular field that is 12 meters by 6 meters, if he wants to divide the field into 8 sections, what would the area per section be?

Answers

Answer:

9 Meters Squared

Step-by-step explanation:

First multiply 6 by 12 to find the area of the whole field:

[tex]6*12=72[/tex]

Then divide that area by 8:

72/8=9

So:

9 meters squared

Explain what method is used to solve problems involving scale drawings.
A. Use a proportion
B. Make an educated guess
C. Get a ruler or tape measure and measure the distance
D. Make a drawing on paper

Answers

The answer would be A. Use a proportion

what is the domain of the function on the graph?

Answers

Answer:

c

Step-by-step explanation: because

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