find the vertex, focus and equation of the directrix for the conic given by (x + 1)^2 = -20(y - 3).
sketch a graph of this conic

Answers

Answer 1

Hello,

The conic is a parabola ,

vertex (-1,3)

focus : (-1,-2)

directrix: y=8

equation: y= - 1/20x²-1/10*x+59/20

solution in picture

Find The Vertex, Focus And Equation Of The Directrix For The Conic Given By (x + 1)^2 = -20(y - 3).sketch
Answer 2

The vertex is v(-1,3) , focus is f(-1,8) and the equation of directrix is          y = -2.

What is a parabola?

A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. The equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix (x + a = 0).

For the given situation,

The standard form of equation of parabola is given by, [tex]y=\frac{1}{4p}(x-h)^{2}+k[/tex]

The vertex is given by [tex]v(h,k)[/tex]

The focus is given by [tex]f(h,k-p)[/tex]

The equation of directrix is given by [tex]y=k+p[/tex]

The given equation is [tex](x+1)^{2} =-20(y-3)[/tex]

On rearranging the given equation in standard form,

⇒ [tex](x+1)^{2} =-20y+60[/tex]

⇒ [tex](x+1)^{2} -60=-20y[/tex]

Divide by 20 on both sides,

⇒ [tex]\frac{(x+1)^{2}}{20} +4 = y[/tex]

⇒ [tex]y=\frac{-1}{(4)(5)} (x+1)^{2} +3[/tex]

On comparing the above equation with the standard form,we get

[tex]p=-5, h=-1, k=3[/tex]

⇒ [tex]k-p=3-(-5)\ =8[/tex]

Hence we can conclude that the vertex is v(-1,3), focus is f(-1,8) and equation of directrix is y=-2.

Learn more about a parabola here

https://brainly.com/question/7492359

#SPJ2

Find The Vertex, Focus And Equation Of The Directrix For The Conic Given By (x + 1)^2 = -20(y - 3).sketch

Related Questions

Can someone explain this / answer, Its a picture

Answers

Answer:

option c is the correct answer (l=1 cm and w=42cm)

Step-by-step explanation:

length(l) = 1.00cm

width(w)= 42.00 cm

ACCORDING TO FORMULA

Area of rectangle = l×w

=1 cm × 42 cm

= 42cm^2

Please help! What is 9.6=1/2b show work please!

Answers

Answer:

b = 19.2

Step-by-step explanation:

9.6 = ½b

=> 9.6 × (2/1) = b

=> 9.6 × 2 = b

=> 19.2 = b

Which label on the cone below represents the center of the base?
D
B
Ο Α
OB

Answers

Answer:

C

Step-by-step explanation:

The center of the base is the center of the circle

The center of the circle is C

can you help me please.

Answers

45 is the answer
hope this helps :)

Answer:

45

Step-by-step explanation:

1st term is 2

2nd term is 3

3rd term is 4

.

.

.

nth term is (n+1)

because common difference is 1, so 1st term = 1 + common difference = 1+1 = 2, for any term, we take n + common difference, so n+1

putting n = 44,

44th term is 44+1 = 45

Answered by GAUTHMATH

if you have a cylindrical tank that's 10 feet long and has a radius of 2 feet, what's the maximum possible capacity of the tank in gallons of water if 1 cubic foot of water = 7.48 gallons? Round your answer to two decimal places.

Answers

Answer:

Step-by-step explanation:

Volume = pi * r^2 * h

r = 2 feet

h = 10 feet

Volume = 3.14 * 2^2 * 10

Volume = 125.6 cubic feet

1 cubic foot contains 7.48 gallons

125.6 cubic feet contain 7.48 * 125.6 = 930.488

The tank contains 930.49 gallons.

Simplify to create an equivalent expression.
2(3y + 6) - 3(-4- y)
Choose 1 answer:
gy
5y + 24
9y - 24
9y + 24

Answers

Answer:

9y + 24

Step-by-step explanation:

2(3y + 6) - 3(-4 - y)

= 6y + 12 - 3(-4 - y)

= 6y + 12 + 12 + 3y

= 9y + 12 + 12

= 9y + 24

Angles A and B are complementary. The measure of angle A
is yº. What is the measure of angle B?

Answers

Answer:

D, [tex](90-y)[/tex] degrees

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees. Since angle A and angle B are complementary, they add up to 90. Since the value of angle A is y degrees, we can substitute y into the equation to get

[tex]y+B=90[/tex]

To get the measure of angle B, we must isolate B.

To isolate B, we have to remove every term from its side.

The only term on the side that B is on other than B is y. To remove y from the left side, we must subtract y from both sides. Doing this will result in the equation:

[tex]B=90-y[/tex]

The only answer option that meets this criteria is D.

Find the volume of the prism.

Answers

Answer:

11,968

Step-by-step explanation:

I'm not sure, but I think its 11,968

Find the length of side x in simplest radical form with a rational denominator.
4.
609
30°
x
C
Answer: <=
Submit Answer

attempt 1 out of
I really need help with this

Answers

Answer:

x=2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 30 = x/4

4 sin 30 =x

4 ( 1/2) =x

2 =x

4
Select the correct answer.
Simplify the expression. What classification describes the resulting polynomial?
(8x2 + 3x) – (12x2 - 1)
OA.
quadratic binomial
OB. quadratic trinomial
O C.
linear monomial
OD.
linear binomial
Reset
Reset
Next

Answers

Answer:

quadratic trinomial

Step-by-step explanation:

(8x^2 + 3x) – (12x^2 - 1)

Distribute the minus sign

8x^2+3x-12x^2+1

Combine like terms

-4x^2+3x+1

This is a quadratic since the highest power of x is 2

This is a trinomial since there are 3 terms

Define function below -5.25 and 10 equals 1+1.7 514 = 23431. Read the post I turned on the light by design

What is the answer for this question

Answers

Answer:

option d. is the correct answer

If the point (b,15) lies on the straight line with equation Y=5x fonde the value of b ?

Answers

Answer:

b = 3

Step-by-step explanation:

Substitute the y- coordinate 15 into the equation , that is

15 = 5x ( divide both sides by 5 )

3 = x

This is the x- coordinate of the point , so b = 3

Rotate the vector 3,-2 90 degrees clockwise about the origin.

Answers

Answer:

-2,-3

Step-by-step explanation:

Answer:

-2 -3

It worked for me on acellus

Step-by-step explanation:

PLS HELP ASAP


What are the possible rational zeros of f(x) = x4 + 2x3 − 3x2 − 4x − 12?

Answers

I don’t know I’m sorry I got 6x and I don’t think that’s right

On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?

Answers

Answer:

Step-by-step explanation:

The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:

by finding the slope. Remember, that slope is the same thing as rate of change.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:

[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]

A rectangular school yard has a perimeter of 114 meters and an area of 702 square meters. What are the dimensions of the school yard?

Answers

18 by 39.

Reason:
2x+2y=114 (perimeter)
XY=702 (area)
X=18
Y=39

One of the lengths of a leg on a right angled triangle is 15 ft the length of the hypotenuse is 17 ft find the length of the other leg

Answers

The length of the other leg should be 8ft

Work out the value of 10^2 - 4^3
Give your answer as a power of 6.

Answers

Answer:

6^2 = 36

Step-by-step explanation:

10^2 = 10 * 10 = 100

4^3 = 4 * 4 * 4 = 64

10^2 - 4^3= 100 - 64 = 36 = 6^2

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]6^2[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\10^2 - 4^3\\---------------\\\rightarrow 10^2 = 100\\\\\rightarrow 4^3 = 64\\\\\rightarrow 100 - 64 = \boxed{36}\\\\\text{Since we know that '36' is a perfect square, we can rewrite our answer as: } \boxed{6^2}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Evaluate the expression when x=-6.
x^2-9x+4

Answers

Answer:

- 14

Step-by-step explanation:

x = - 6

x^2 - 9x + 4

= ( - 6 )^2 - 9 ( - 6 ) + 4

= 36 + 54 - 4

= 36 - 50

= - 14

Answer:

[tex]94[/tex]

Step-by-step explanation:

[tex]x^2 - 9x + 4[/tex]

[tex](−6 {)}^{2} −9 (−6) + 4[/tex]

[tex]36 − 9 (−6) + 4[/tex]

[tex]36 + 54 + 4[/tex]

[tex]90+4[/tex]

[tex]94[/tex]

Hope it is helpful....

I need help ASAP!! Please explain how to solve the problem

Answers

Answer:

Step-by-step explanation:

Surface Area of Cylinder = 2πrh+2πr^2

2π(3)(12) + 2π(3)^2

= 282.7 yd^3

answered by g a u t h m a t h

need help with this!!!

Answers

Answer:

It's D I sure about it correspond means identical... The matching number

HELLLPPP 31 kilograms is the same as how many pounds? Hint: 1 kg = 2.2 lb Round your answer to the nearest tenth.​

Answers

Hi! I'm happy to help!

To solve this, we need to turn all the kilograms into pounds. We know that to turn 1 kg into a pound, you multiply the amount of kilograms by 2.2.

Knowing this, we can multiply our 31 kilograms by 2.2.

31×2.2=68.2

This means that 31 kilograms is equal to 68.2 pounds.

I hope this was helpful, keep learning! :D

the perimeter The area of squre Plat is 100 m² Find at the plot o a​

Answers

Answer:

perimeter=40m

Step-by-step explanation:

PERIMETER=(AREA ROOT)*4

                   =10*4=40m

The population of Greater Accra increased by 20% and became 900,7000. The original population of the city was:

Answers

Answer:

the original population of the city is 7,505,833

Step-by-step explanation:

Given;

new of the population of the city, Y = 9,007,000

the percentage increase of the city, = 20% = 0.2

Let the original population of the city = X

New population, Y = X  + 0.2X

                           Y = X(1 + 0.2)

                           Y = X(1.2)

                           Y = 1.2X

                           X = Y/1.2

                           X = (9,007,000) / 1.2

                           X = 7,505,833

Therefore the original population of the city is 7,505,833

please help me !! :)

Answers

I’m not one hundred percent but I think it’s C

Put the following equation below in function notation and evaluate, using x as the independent
variable.
3x + 5y = 15; x=2

Answers

Answer:

1st option

Step-by-step explanation:

3×2+5y=15

5y=15-6

y=9/5

Answered by GAUTHMATH

Heyyyy
Here it is
Hope it helps

please, help! i really need it !! like rnnn!

Answers

C, She can read 216 words per minute, bc 72 divided by 1/3 is 216

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!

Answers

Answer:

(-5,2)

Step-by-step explanation:

Answer:

(5 , 2)

Step-by-step explanation:

F(-5 , 2)

After reflection F'(5 , 2)

The rule for reflection over y-axis is

Original point(x , y)   :  After reflection:  (-x,y)

x-coordinate will change its sign and y-coordinate remains same

determine the quadratic equation in standard form of a parabola with a zero at x=5 and vertex ar (-3, 32). start with factored form

a)find the other zero

b) create your factored form equation

c) create your standard form equation ​

Answers

Answer:

see image...

start with Graphing Form: y = a(x-h)²+ k

knowing that h is the x value (negative of it)  of the vertex , and k is the y value of the vertex

Graphing Form Equation: y =  a(x+3)²+32

you are also given that when the x value is 5 the y value has to be 0

0 = a(4)^2 + 32

a has to be - 1/2    

   

Step-by-step explanation:

What is the slope of the line shown below?
10+
5
(9, 1)
o A. -
OB.
OC
10
15
(-3,-7) 5
10
O
D.
WIN

Answers

Answer:

D 2/3

Step-by-step explanation:

Rise over run. The x values is -3 and 9 which is the distance or run between the dots. Find the distance by finding which number is between then so -3+x=9 where x is 12. The y values are -7 and 1. Find y where -7+y=1 where y is 8. That is the rise. So the rise is 8 and that is over the run, 12, gives you 8/12 which can be simplified to 2/3.

Other Questions
Which image best supports the claim that young people can make improvements to the environment?AbelVOLUN TELERO (02.07 HC)Which of the following diets is lacking in nutrients that provide energy to the body? A diet that is rich in dairy but lacking carbohydrates A diet that is rich in vegetables but lacking protein A diet that is rich in vegetables but lacking fruits A diet that is rich in fruits but lacking dairy Light energy is part of a larger form of energy known as __________. Zero is not a real number True or False You, the manager of an electronics store, have asked the salespeople in the camera department and the computer department to come up with regular, weekly ideas about how to increase sales. However, you have asked the people in the camera department to think of ideas independently, whereas you have asked the people in the computer department to get together every week and brainstorm. You should expect, after several weeks of this, that ____. b Nobody can deny that now we have better medical facilities in the city. ( affirmative )c Where else will you get such an attractive package? ( assertive )d Everybody wants to lead a peaceful life. ( interrogative ) Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.Week Sales (1,000s of gallons)1 172 223 204 245 186 177 218 199 2310 2111 1612 23(a) Using a weight of 12 for the most recent observation, 13 for the second most recent observation, and 16 for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.) Compute four-week and five-week moving averages for the time series.Week Time Series Moving Value Average Forecast1 17 2 22 3 20 4 24 5 18 6 17 7 21 8 19 9 23 10 21 11 16 12 23 (b) Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)(c) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? MSE for the three-week moving average is 11.12. Which of the following bestdescribes what a salon wasoriginally?A. a location where everyone in the communitywould meet to have mealsB. a place where women would go and get their hairand nails doneC. a location hosted by women that was used fordiscussions and thoughts What name was given to the group of talented and educated young men who wrote plays and who, sometimes, viewed Shakespeare with jealousy?1. the duke of Cambridge2. the lord of oxford3. the collage boys4. university wits Solve using the elimination method. 2x + 7y = 36 6x - 7y = - 60 try more complete the statement1. Volume of pyramid= ________ volume of rectangular prism, V= lwhSo for pyramid, V= 1/3 (lwh) = (lwh) ________.2. The volume of the cylinder is three times the volume of the cone or the volume of the is _________ that of the cylinder.3. Volume of the cone = ________ volume of the cylinder.4. Sphere's volume is 2/3 of the _________ volume. please answer this questions because this is need to pass tomorrow!! Que diferencia haba entre los espaoles y los indgenas en la esposa de la conquista ayuda Yall pls help me out Determine the dimensions for T if T = M V^2 A / L^3 where M is a mass, V is a velocity, A is an area, and L is a length. L / TNo dimensionsM L / T^2MM / (L T^2) Evaluate the function. f(x)=x^2 6x+12 Find f(4) Match the synthetic materials with the processes used to make them. what will happen if we did not have society? Write in points ? Imagine you are celebrating a birthday in December and need balloons. The temperature in thestore where you are purchasing the balloons is approximately 25C and each balloon is filledto a volume of 2 liters to obtain maximum pressure.Use the gas laws to explain what will happen to the volume and pressure of the gas in theballoon when go outside, where the temperature is 0C. Include both Charles's Law and Gay-Lussac's Law in your answer.ILL GIVE BRAINIEST PLEASE HELP 1.) What is the domain and range of the function in the graph?2.) What is the average rate of change over the interval [1, 0]? Bob is the vice-president of a medium sized company in a suburb of Seattle. He has two new cars, a large home with a sauna, new clothes, and takes many trips with his family. He also carries $21,000 of debt on his credit cards and struggles to make his payments. Bob would be considered part of which social class What are the advantages of disulfide substitutes?