How can the equation of a parabola be derived when given the focus and the directrix?


Answers

Answer 1

Answer:

If the focus is to the right of the directrix, then the parabola opens to the right and p>0 . If the focus is to the left of the directrix, then the parabola opens to the left and p<0 .

HOPE ITS HELP


Related Questions

HELP PLEASE FASTTT !! ANYONE??!

Answers

Answer: The angled line on graphs!

Step-by-step explanation: :)

Hello I need help with this math it’s negative fractions so -7 1/5 - (-2/5)

Answers

Answer:

-36/5

- . 2/5-=+2/5

-36/5+2/5

34/5 or 6 4/5

In ΔMNO, \text{m}\angle M = (6x+1)^{\circ}m∠M=(6x+1) ∘ , \text{m}\angle N = (3x-10)^{\circ}m∠N=(3x−10) ∘ , and \text{m}\angle O = (x+19)^{\circ}m∠O=(x+19) ∘ . Find \text{m}\angle N.m∠N.

Answers

Applying the triangle sum theorem, m∠N = 41°

What is the Triangle Sum Theorem?

Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.

Given the following interior angles of ΔMNO:

m∠M = (6x+1)°

m∠N = (3x-10)°

m∠O = (x+19)°

Find the value of x:

m∠M + m∠N + m∠O = 180°

Substitute

6x+1 + 3x-10 + x+19 = 180

Add like terms

10x + 10 = 180

10x = 180 - 10

10x = 170

Divide both sides by 10

x = 17

m∠N = (3x-10)°

Plug in the value of x

m∠N = 3(17) - 10

m∠N = 41°

Learn more about triangle sum theorem on:

https://brainly.com/question/7696843

First to answer correctly will get brainiest.

How to get a number 100 by using four sevens (7’s) and a one (1)?

Answers

Answer:

read step-by-step explanation

Step-by-step explanation:

it's a trick question u can't u can get close doing (7+7)×(7+1)-7=105 but it's not 100

Joshua wanted to know the distance between two cities. The scale on the map was 1/2 in = 10 km. The distance between the cities on the map was 2 1/4 in. What was the actual distance between the cities?

Answers

Step-by-step explanation:

remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.

but let's do the exercise.

the scale says 1/2 in = 10 km

but our measurement on the map brought us quarter inches.

so,

1/2 in = 2/4 in = 10 km

therefore

1/4 in = 10/2 = 5 km

now,

2 1/4 = 9/4 in

this is 9 times 1/4.

therefore, the distance between the 2 cities is

9 × 5 = 45 km.

What is the area of the composite figure

Answers

Ok done. Thank to me :>

Plz help if understand this problem

Answers

Answer:  [tex]0.5x^7[/tex]

This is the same as typing in 0.5x^7

Other equivalent forms are (1/2)x^7 or (x^7)/2

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

Work Shown:

[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]

I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).

Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.

There are 28 girls and 21 boys in a class. What is the ratio, in simplest terms, of the number of girls to the number of boys? (show the work please)

Answers

Answer: The simplified ratio is 4:3

Step-by-step explanation:

To find the ratio of the number of girls to the number of boys, we can divide the number of girls (28) by the number of boys (21) to get:

28 ÷ 21 = [tex]\frac{28}{21}[/tex]

Next, we can simplify the fraction further to get [tex]\frac{4}{3}[/tex], which equals 4:3.

4. Tomas uses 12 gallons of water to prepare lemonade for a party. The lemonade recipe states that for every 2 quarts of water, he should add cup of lemon juice and cup 1 of sugar. How much lemon juice does Tomas need?​

Answers

Answer:

Thomas will need 24 cups of lemon juice.

Step-by-step explanation:

There are 4 quarts in every gallon.

12 x 4 = 48

2 cups of lemon juice for every 2 quarts of water.

48 / 2 = 24

Hope This Helps!

The width of a rectangle is represented by 5 1 2y.
The length is twice as long as the width. What is the
perimeter of the rectangle?

Answers

Answer:

33y

Step-by-step explanation:

since the equation of perimeter for a rectangle is lengthX2 + widthX2

and the width is given to be 5 1/2y is it? If it is so then the length will be 11y since 2X5 1/2y is 11y

and the perimeter will then be calculated as so;

11yX2 + 5 1/2yX2

so it will be 22y+11y which will give you 33y

find the answer pleasere

Answers

Answer:

b is the answer f(e) gives us b

Determine each measure. M

Answers

Check the picture below, tis corrected.

btw the picture is rather long, so the thumbnail here may not show all its size, so you may have to open the image in a new tab or window.

Evaluate (4x + 4)(7x - 3).

Answers

Answer:

28x^2+16x-12

Step-by-step explanation:

(4x+4)(7x-3)

28x^2+28x-12x-12

28x^2+16x-12

Pls look at the picture for question.

Answers

Answer:

-5, -2, 3, 4

They are in the correct order already :)

Step-by-step explanation:

They greater a negative number is the less it becomes and positive numbers are always greater than negative ones.

Good luck :)

Can someone help me please

Answers

Answer:

31.25

Step-by-step explanation:

Divide 250 by 8=31.25

Renee worked a total of 16 1/5 hours last week. She spent 1/3 of that time reviewing reports. How many hours did she spend reviewing reports?

Answers

Answer:

Step-by-step explanation:

First 1 ÷ 5 ×16

= 3.2

Then 3.2 × 1 ÷ 3

= 1.06

It takes 82 pounds of seed to completely plant 11 acre field. How many ponds of seed are needed per acre?

Answers

Answer:

7.5lbs

Step-by-step explanation:

82/11 = 7.45454545lbs

Rounded to 7.4lbs

Hope that helps

Answer:

7 5/11

Step-by-step explanation:

you divide 82 and 11 and you get 7.45454545

Ryan needs to buy some pencils. Brand A has a pack of pencils for 7.49$ . Brand B has a pack of pencils for 9.97$ .
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.

Round your answers to the nearest cent.

Answers

Answer:

Unit Price for Brand A: $0.31 per Pencil.

Unit Price for Brand B: $0.35 per Pencil.

Brand A is the better buy.

Step-by-step explanation:

Divide 7.49 by 24 to get 0.312 and round down to 0.31.

Divide 9.97 by 28 to get 0.356 and round down to 0.35 (0.36 is too much making the price $10.08)

Compare 0.31 and 0.35. (0.31 < 0.35)

Identify the slope and y-intercept of the line 4x + 2y < 3.

Answers

Answer:

Step-by-step explanation:

4x+2y<3

y<-2x + [tex]\frac{3}{2}[/tex]

For each computer Isabella sells, she earns a 5% commission. If she sells 3 computers for
$985.00 each, what is her commission?
$14.78
b. $49.25
$147.75
a.
C.

Answers

If she was to sell three computers she gets 147.75

help i want to graduate by january :,)

Answers

If the numbers inside the parentheses are greater than 1, there will be growth. Otherwise, it will decay.

1. We see that it is 1.04. This means it will increase by 4 percent. 4% growth

2. 0.6 is less than 1. We need to subtract 1 by 0.6. This gives us 0.4. It will decay by 40 percent. 40% decay

3. We need to subtract 0.86 from 1. This gives us 0.14. The decay is 14 percent. 14% decay

4. 1 - 0.96 is 0.04. The decay is 4 percent. 4% decay

5. We see that it is 1.14. So, the growth is 14 percent. 14% growth

6. It is 1.4. The growth is 40 percent. 40% growth

What is the discriminate of the following quadratic equation?
4x^2 - 2x + 6 = 0

Answers

-92

Step-by-step explanation:

If a quadratic equation has the following form:

[tex]ax^2 + bx + c =0, \;\;\;a \neq 0[/tex]

then its discriminant D is defined as

[tex]D = b^2 - 4ac[/tex]

In our given quadratic equation, a = 4, b = -2 and c = 6, so its discriminant is

[tex]D = (-2)^2 - 4(4)(6) = -92[/tex]

Note: The value of the discriminant D will determine the characteristics of the roots of the quadratic equation according to the following rules:

[tex]D > 0,\;\;[/tex] there will be 2 real roots

[tex]D = 0,\;\;[/tex] there will be 1 real root

[tex]D < 0,\;\;[/tex] there will be 2 imaginary roots

Hence our given quadratic equation will not have any real roots but only imaginary ones.

What is the value of the expression
4x+y when x = 2 and y = 4?
2y-1

Answers

4(2)+4 =
8+4= 12
Input 2 into the space of the X since it’s together it will be multiplication. Do the same with Y. Then add and you’re done :)

Chris wants to order DVDS over the internet. Each DVD costs $12.99 and shipping order costs $9.99. If he can spend no more than $100 how many DVDs can he buy?

Answers

Answer:

4

Step-by-step explanation:

I think its 4 because the max DVD's he could have bought if shipping was free was 7 but since shipping is not free,he has to equal the amount so 12.99+9.99= 22.98 and the maximum multiplication by 22.98 with the maximum number as 100 would be 91.92, thats my answer

22 loaves of bread have 506 slices of bread how many slices of bread do 6 loaves have

Answers

Answer:

138 slices

Step-by-step explanation:

506 / 22 = 23 slices per loaf

23 x 6 = 138 slices

If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?

Answers

The third ordered pair that satisfies the equation of the circle is (123, 369).

The given parameters;

[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)

The third ordered pair of the equation can be determined by using general equation of a circle;

[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]

The radius of the circle is calculated as;

[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

[tex]b < r\\\\b < 388.96[/tex]

[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]

Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).

Learn more about equation of circle here: https://brainly.com/question/11711668

A chef prepared 100 plates of shrimp. There were 8 shrimp on each plate. How many shrimp did the chef prepare?

Answers

Answer:

800 shrimp

Step-by-step explanation:

100 plates of shrimp

8 shrimp on each plate

100 × 8 = 800

= 800 shrimp were prepared by the chef

Hope this helps.

Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula l=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time

Answers

Answer:

  $900

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  I = PRT

  I = ($4500)(0.05)(4) = $900

The total interest was $900.

[tex]\large\tt\green{Answer}[/tex]

The total interest was $900

[tex]\large\tt\green{Step-by-step \: explanation}[/tex]

Step 1:

Put the numbers in the formula and do the arithmetic.

I = P × R × TI = $4500 × 5% × 4

Step 2:

Rename 5% into decimal

I = P × R × TI = $4500 × 0.05 × 4

Step 3:

Solve the problem with the full solution.

I = P × R × TI = $4500 × 5% × 4I = $4500 × 0.05 × 4I = $ 900

Therefore, the total interest was $900

y over 11 =8 .solve for y

Answers

Answer:

y=88

Step-by-step explanation:

uhh…maybe 88? Btw if I’m wrong sorry I’m really tired and just tryin to help

The mass of a an atom of helium is 6.65 x 10−24. Use scientific notation to express the mass of 250 helium atoms. A) 1.6625 x 10−21 B) 1.6625 x 10−22 C) 1.6625 x 10−24 D) 1.6625 x 10−26

Answers

Answer: its A

Step-by-step explanation:

i know this is it

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