What is the equation of the directrix of the parabola given by the equation y2 = -24x?

What Is The Equation Of The Directrix Of The Parabola Given By The Equation Y2 = -24x?

Answers

Answer 1

The equation of the directrix of the parabola given is x = 6, Option D is the correct answer.

What is Directrix of a Parabola ?

A parabola is a U shaped curve whose all point are at same distnace from a  point called as focus and a line called as Directrix .

The equation of the parabola given is

y² = -24x

When the standard equation of parabola is

 (y - k)² = 4p (x - h),

where the focus is (h + p, k) and the directrix is x = h - p.

here h = 0

p = -24/4 = -6

x =  0 - (-6)

x = 6

Therefore Option D is the correct answer.

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Related Questions

Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total
installation costs from two different contractors for the same style of carpet.
Contractor A charges an installation fee of $125 plus $2 per square foot for the carpet.
Contractor B charges an installation fee of $75 plus $2.50 per square foot for the carpet.
Based on this information, which system of equations could be used to determine the width of the living room, x, in feet, at which the
quote for the installation costs, y, is the same for both companies?

Answers

Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

What is the area of a rectangle?

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

In this problem, the dimensions are given as follows:

w = x, l = x + 5.

Hence the area in square feet is:

A = x(x + 5) = x² + 5x.

Then the costs are given as follows:

A(x) = 125 + 2(x² + 5x).B(x) = 75 + 2.5(x² + 5x).

The costs will be equal when:

A(x) = B(x)

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Kevin and Randy Muise have a jar containing 65 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$8.65 .How many of each type of coin do they​ have?

Answers

36 I think, I don’t really know so I’m sorry if it’s wrong.
34 quarters 3 nickels

Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help

Answers

The conversion of the following units are done below.

6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kg

What is conversion?

Conversion means to convert the same thing into different units.

We know the following unit's conversion.

1 km = 0.62 miles

6 km = 3.72 miles

    1 L = 0.26 gallons

2.5 L = 0.65 gallons

  1 lb = 0.45 kg

90 lb = 40.5 kg

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can someone please help mee(20 points and i will give brainliest!!!)

Answers

Answer:

vertex: (3,1)

y-intercept = (0,-8)

x-intercept- Smaller=2 Larger=4

Domain= all real numbers, identity, infinite

Range= 1 is greater than or equal to y

axis of symmetry=3

Step-by-step explanation:

prove that (1- cos(pi)/(8))(1-cos(3 pi)/(8))(1-cos(5 pi)/(8))(1=cos(7 pi)/(8))=(1)/(8)

Answers

Step-by-step explanation:

1&$)&(5$6$5*-_+_7&'+&-^€=%

the equation below describes a circle. what are the coordinates of the circle?
(x+5)^2 + (y+7)^2 = 21^2

Answers

Answer:

center = (-5, -7)

radius = 21

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

(a, b) is the centerr is the radius

Given equation:

[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]

Comparing the given equation with the standard equation of a circle:

center = (-5, -7)radius = 21

Hence, the coordinates of centre is (-5,-2).

What is circle ?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The given equation  of circle,

(x+5)² + (y+7)² = 21²

We know that,

Equation of a circle is:

(x-a)² + (y-b)² = r²

where:

(a, b) is the center

And r is the radius

Comparing with the given equation we have,

center = (-5,-7)

And radius = 21 units

Thus,

Coordinates =  (-5,-7).

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$50 item discounted 30%

Answers

Answer:

$15 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

$ 35.00   is what you pay     $15.00 off original price

Step-by-step explanation:

30 % discount means you pay 70 %

$ 50 * .70 = $ 35 .00

If a point is reflected over the y-axis, then the coordinates of (x, y) are changed to ______________.

Answers

Answer:

its opposite

Step-by-step explanation:

1) Which statement is needed to fill in the blank in this syllogism? If two lines are parallel, then ____________________. If the lines never intersect, then the lines have the same slope. Therefore, if two lines are parallel, then the lines have the same slope.

A) the lines have the same slope

B) the lines never intersect

C) the lines have the same equation

D) the lines are continuous

Answers

Answer:

B) the lines never intersect

Step-by-step explanation:

okay essentially, syllogism is formatted in a repetitive way

it's something like:

if "a" are "b"

and "b" are "c"

then "a" are "c"

(a = b

b = c

logically, c = a)

(idea, thing related to idea, conclusion relating the two)

hope this helps!!

Answer:

the lines never intersect

Step-by-step explanation:

Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.

HELP ASAP/NOW...NO LINKS OR JOKING PLS

Answers

Answer:

D. 0 < x < 20

Explanation:

Domain is in the x axis, Range lies in the y axis.

Here it is seen that function's domain lies between 0 to 20.

Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'

Here, as the circle's are open. Domain: 0 < x < 20

Additionally,

Range: -10 < f(x) < 0

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help

Answers

From unit conversion, it is found the following results:

6km 3.73 mi

2.5 L 0.66 gal

90 lb 40.82 kg

Unit Conversion

Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others.  Because of this, it is important to know converting them.

For solving this question you need some information as:

1 km = 0.621371 mi ( unit for length and distance)

1 L = 0.2641722 gallons (unit for volume)

1 lb = 0.453592 kg (unit for mass)

Therefore,

If 1 km = 0.621371 mi, you will have:

           1 km --------  0.621371 mi

           6 km --------  x mi

           x= 6* 0.621371

           x=3.73 mi

Thus, 6km ≈ 3.73 mi.

If 1 L = 0.2641722 gallons, you will have:            1 L--------  0.2647122 gal           2.5L --------  x gal            x= 2.5* 0.2647122            x=0.66 galThus, 2.5 L≈ 0.66 gal.If 1 lb = 0.453592 kg, you will have:            1 lb--------  0.453592 kg           90 lb --------  x kg            x= 90* 0.453592            x=40.82 kgThus, 90 lb≈ 40.82 kg.

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If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?

Answers

I am assuming you meant to write b(x) = x-4.

[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]

Since this is a linear function, the domain is all real numbers.

For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards.
There are two parallel sidelines on each side of the field. If the 50 yard line is perpendicular to one of the
sidelines, what is its relationship to the other sideline?

Answers

Answer:

Same, because they are parallel.

Step-by-step explanation:

What is the value of x in the triangle?

Answers

Answer:

45 degree=√2/2

√2/2=12√2

we use criss-cross method

√2x/√ 2=12√2/√ 2

×=24

Step-by-step explanation:

if it confused you this is (/)is dividing

hope I helped

please mark me as brainlyst

2
3
4
5
6
7
8
O They have the same slope.
O They have the same y-intercept.
9
10
TIME REMAINING
55:24
Suppose a system of two linear equations has one solution. What must be true about the graphs of the two equations
O They intersect at one point.
O They intersect at two points.

Answers

Answer:

72

Step-by-step explanation:

yhsvybybyvyyvtvvyyvvt

Answer:

number 9 is the answer for this question

Which of the following is most likely the next step in the series?

Answers

Answer:

I think the answer is B

Step-by-step explanation:

A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win

Answers

Monica win 2 games.

What is Expression?

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

According to the question,

First we  look from the perspective of one player.

How many games does this person play? 5.

Now, each or the 6 people in the tournament played 5 games,

SO,  

[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]

Therefore,

We know that there were a total of 15 games played.

This means, there were 15 losses, and more importantly, 15 wins.

Not counting Monica, there were:

4 + 3 + 2 + 2 + 2 = 13 wins.

This leaves,

15 − 13 = 2 wins for Monica.

Hence, 2 games won by monica in a tournament.

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it is about Name the property of the rational numbers in each of the following

Answers

The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property

What is the property of the rational number?

The main properties of rational numbers are:

Commutative property.Associative Property. Distributive Property.Closure property.

a) The property used here is commutative property which says that;

a + b = b + a.

This tallies with the operation used on the rational numbers.

b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.

d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

e)  The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)

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6root27+root243 simplify

Answers

Answer:

6√27 + √243

6√9 x 3 + √81 x 3  

6 x 3 √3 + 9√3

18√3 + 9√3

27√3

what is the equation?
3 + 5(2 + 7n) = 258

Answers

Answer:

n = 7

Explanation:

[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]

simply add the numbers

[tex]\rightarrow \sf 13 + 35n = 258[/tex]

subtract both sides by 13

[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]

simplify the following

[tex]\rightarrow \sf 35n = 245[/tex]

divide both sides by 35

[tex]\rightarrow \sf n = 7[/tex]

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

PLEASE HELP FAST!!!

Answers

The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

Angle of elevation and depression

From the question given, we have the following parameters

Base of the building = 7feet

Height of the building = 18 feet

Required

angle of elevation

Using the SOH CAH TOA identity

tanФ = opp/adj

tanФ = 18/7

Ф = 68.73 degrees

Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

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Question:

A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.

which property is illustrated for all expressions a and b if a=b then b=a

Answers

Answer:

Symmetric property

Find the distance between the pair of points given on the graph. Distance = √ (blank) ​

Answers

Answer:

√2.236

Step-by-step explanation:

(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236

Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?

Answers

Answer: 8

Step-by-step explanation:

We know that scale factor = (image)/(preimage).

Substituting in what we have,

[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]

Answer:

Step-by-step explanation:

We know that r's't' was formed by a scale factor of 5.

This means rst was multiplied by 5 to create r's't'.

Dividing the sides of r's't' by 5 will give us the sides of the

pre-image.  If r's' = 40 - dividing 40 by 5 = 8.

So rs is 8.

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]

Answers

The volume of the cone is V = 381.15 cu.cm

What is the Curved Surface Area of the cone ?

The curved surface area of the cone is given by

A = πrl

The slant height given in the question is

l = 10.5 cm

A = 115.5 sq.cm

radius = ?

Height = ?

Volume = ?

Using the Curved Surface Area Formula

115.5 = π * r * 10.5

taking π = 22/7

r = 3.5 cm

The slant height is given by

[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]

Therefore the height is

[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]

h = 9.9 cm

The volume of the cone is

V = π r²h

V = (22/7) * 3.5 * 3.5 * 9.9

V = 381.15 cu.cm

The volume of the cone is V = 381.15 cu.cm

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(08.01)
A new video game is expected to sell 120 copies the first hour at a local game store. After that, the sales will follow the function s(x) = 15(=
1) where x is the number of hours. What is the function that shows total sales, including the first hour?

Answers

Answer:

f(x)=15x+120

Step-by-step explanation:

trust

8y and y are like terms

true
or
false

Answers

Answer:

True

Step-by-step explanation:

Hope this helps :)

Answer: True
have a great day

Which number line represents the solution set for the inequality 3(8-4x) < 6(x - 5)?

Answers

[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]

Solution : ] 3 , + ♾️ [

PLEASE GIVE BRAINLIEST

The terms of a particular sequence are determined according to the following rule: If the value of a given term $t$ is an odd positive integer, then the value of the following term is $3t -9$; if the value of a given term $t$ is an even positive integer, then the value of the following term is $2t -7$. Suppose that the terms of the sequence alternate between two positive integers $(a, b, a, b, \dots )$. What is the sum of the two positive integers

Answers

More plainly, the sequence is defined recursively by

[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]

and some starting value [tex]a_1[/tex].

We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].

• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since

[tex]a_2 = 2a_1 - 7[/tex]

by the given rule, and 2×(even) - (odd) = (odd). So

[tex]a_2 = 2a-7 = b[/tex]

In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,

[tex]a_3 = 3a_2 - 9[/tex]

and so

[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]

[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]

Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]

• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)

Solve this system of equations algebraically:

y – 10 = 11x + x2

y – 12x = 30



The first solution is (–4, –18).



The second solution is (
,
).

Answers

Answer:

(-4,-18) and (5,90)

Step-by-step explanation:

I'll assume the first equation is supposed to be y – 10 = 11x + x^2

This is a parabola.  The second equation is a straight line:  

y – 12x = 30

We want to find the points at which these lines intersect.  They will intersect for any (x,y) that

Let's rearrange the second equation to isolate y:

y – 12x = 30

y  = 30 + 12x

Now we can take the this value of y and substitute it into the first equation:

y – 10 = 11x + x^2

(30 + 12x) – 10 = 11x + x^2

20 + 12x = 11x + x^2

0 = x^2 -x -20

We can factor this into (x+4)(x-5)

That means x can be either -4 or 5.

Find the value of y using these values of x in both original equations:

For x = -4

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y = 11(-4)+(-4)^2 +10

y = -44 + 16 + 10

y = -18    The point both lines meet is at (-4, -18) which was already given in the problem.  

For x = 5

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y  = 11(5) + (5)^2 + 10

y  = 55 + 25 + 10

y = 90

The second point both lines meet is (5,90).

We should use both solutions in the second equation to verify these values, but I'll graph them, instead.  See the attached graph to prove these points are correct.

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Which of the following is NOT true about poetry? A. Poetry often contains imagery -- language that appeals to the five senses. B. Poetry brings out the music of language through devices such as meter. C. Imagery refers to the pictures an artist draws to illustrate a poem. please help me with this problem! Which of the following questions would be answered by performing a scientific experiment? A. What type of food is the most enjoyable? B. What type of food is the most nutritious? C. What type of food looks the best? A student hears a police siren. What would change the frequency that the student hears? check all that apply A 3-column table with 3 rows. Column 1 is labeled Unit Fraction with entries StartFraction 1 Over 10 EndFraction, one-fourth, c. Column 2 is labeled Fraction with 100 in the denominator with entries StartFraction 10 Over 100 EndFraction, b, StartFraction 50 Over 100 EndFraction. Column 3 is labeled Percent with entries a, 25 percent, 50 percent.Complete the table by finding the missing equivalent form for each row.a = b = c = 100 POINTS!!!!! WILL GIVE BRAINLIEST!!!!!! PLS HELP ASAP!!!!!!!SHOW ALL WORK!!!!!!! EXPLAIN ALL WORK ASWELL!!!!!!!!!1. A theater has 20 rows of seats. If there are 4 seats in the 1st row 12 in the 2nd row, 20 in the 3rd row . How many seats are there in total? Show and explain all work. Give a specific example of how information on a social networking site can communicate negative information to a potential employer.help me within 5 min The most common use of radioactive isotopes in medicine is to diagnose disease. Typically, radioactive materials are injected into the body and then radiation-detecting cameras are used to build images of affected body parts or particular types of cells. This equation models the amount of a radioactive isotope in the bloodstream minutes after it is injected: Part EFrom the observations of the simulation, which strategy was most effective for quickly and efficiently producing ammonia? Why do you think this strategy is most effective? what type of vaccine would be most effective against tuberculosis a disease that requires a strong Why is blood glucose self-monitoring preferred over urine glucose testing? Molly wants to start a new business in collaboration with her husband and sister-in-law. the features she is looking for in the business are as follows: least possible regulatory controls, faster decision making, and ease of organization. she also wants a business in which she will not be forced to pay off any business debts from her personal assets. which type of business ownership is best suited to her needs a. s corporation b. sole proprietorship c. limited partnership d. general partnership e. c corporation 20 percent of 180 hours If the AED came equipped with adult AED pads only, Vickie should not use them. Instead, she should call for someone to bring pediatric AED pads and continue CPR until the new pads arrive. True or false Compare the origins of the common carotid arteries of the fetal pig with those of the human. Where is the humerus present? Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. You want to find out how fast she must swing the bucket to keep the glass from falling out.a. Draw the free-body diagram for the glass when it is at the top of the circle.b. What is the equation for the net force on the glass at the top of the circle in terms of w, FN, m, v, and r?c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. How fast must she spin the bucket to prevent this from happening?d. The string will break if the tension on it is more than 100 N. Over what range of speeds can she keep the glass in the bucket and prevent the string from breaking? __________ marked the transition from the end of the middle ages to the rise of nation-states. a. the treaty of tordesillas b. the treaty of paris c. the peace of westphalia d. the treaty of versailles please select the best answer from the choices provided. a b c d I need a walk through please 1 A hollow conducting sphere has an inside radius of r1 = 0.17 m and an outside radius of r2 = 0.28 m. The sphere has a net charge of Q = 4.8E-06 C. What is the magnitude of the field, in newtons per coulomb, at a distance of 0.05 m from the center of the sphere?