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2 years ago

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4

1 answer:

7 0

We are given with the focus coordinates of (0,-4) and a directrix equation of y=4,. we are asked for the equation of the parabola. The vertex of the parabola should lie in between the directrix and the focus. Hence, vertex should be at (0,0). the curve goes downwards. and the length of the latus rectum is 4. Hence the equation is x2=-16y

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A basket contains 15/16 pound of oranges .One serving of oranges is 1/8 of a pound.How many servings of oranges are there

nasty-shy [4]

Answer:

2/15 servings

Step-by-step explanation:

IF a basket contains 15/16 pound of oranges, then;

1 servings= 15/16 pounds of oranges

To get the number of servings for 1/8 pounds

x servings = 1/8 pounds

Divide both expressions

1/x = (15/16)/(1/8)

1/x = 15/16 * 8/1

1/x = 15/2

x = 2/15

Hence there will be 2/15 servings of oranges

7 0

2 years ago

3x + y - z= -6 2x - y + 2z = 8 4x + y - 3z = -21

Flauer [41]

Answer:

x=-1

y=4

z=7

Step-by-step explanation:

3x + y - z= -6(1)

2x - y + 2z = 8(2)

4x + y - 3z = -21(3)

(1)+(2): 5x+z=2(4)

(2)+(3): 6x-z=-13(5)

(4)+(5): 11x=-11

x=-1

so z=2-5x=7

y=-6-3x+z=4

8 0

2 years ago

Please I need to know if its true or false please lmk!!!

Papessa [141]

Answer:

False

Step-by-step explanation:

According to the complex conjugate root theorem:

if a complex number is a root of a polynomial, its conjugate is also the root of the polynomial

We are given all the roots of the polynomial and there is only one complex root

Since according to the complex conjugate root theorem, there can be either none or at least 2 complex roots of a polynomial

We can say that this set of roots of a polynomial is incorrect

7 0

2 years ago

Read 2 more answers

A textbook search committee is considering

lora16 [44]

Number of ways to select 3 books from 13 books for adoption is 286 .

Step-by-step explanation:

A Permutation is an ordered Combination. When the order does matter it is a Permutation. There are basically two types of permutation:

Repetition is Allowed: such as the lock above. It could be "333".

No Repetition: for example the first three people in a running race. You can't be first and second.

Formula is given by:

$nC_r= \frac{n!}{r! (n-r)!}$ , where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n=13 , r=3.

⇒ $13C_3 = \frac{13!}{3!(13-3)!}$

⇒ $13C_3 = \frac{13!}{3!(10)!}$

⇒ $13C_3 = \frac{13(12)(11)10!}{3(2)(1)(10)!}$

⇒ $13C_3 = 13(2)(11)$

⇒ $13 C_3 = 286$

∴ Number of ways to select 3 books from 13 books for adoption is 286 .

3 0

2 years ago

Which ordered pairs are solutions to the inequality 2x + y > 8 ? Choose all answers that are correct.

gtnhenbr [62]

Hi again!

2x + y > 8

The correct answer is option D
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Honestly I don't think we can solve the equation to find the answer. What we can do is to find the boundary line. (I think you know what that is) After that, shading the appropriate area.

y > -2x + 8

Again, credit to my beautiful graphing calculator. Here is how it looks like.

6 0

2 years ago