Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.

Answers

Answer 1

Answer: $(x;\ y)-the\ coordinates\ any\ point\ on\ the \ parabola.\n\nDistance\ between\ the\ point\ (x;\ y)\ and\ the\ focus\ (-5;\ 5)\nand\ distance\ between\ the\ point\ (x;\ y)\ and\ a\ direct\ are\ equal.\n\nDistance\ between\ (x;\ y)\ and\ (-5;\ 5):\n√((x-(-5))^2+(y-5)^2)=√((x+5)^2+(y-5)^2)\n\nDistance\ between\ (x;\ y)\ and\ y=-1:\n|y-(-1)|=|y+1|\n\nWe\ equate\ the\ two\ expressions:\n√((x+5)^2+(y-5)^2)=|y+1|$

$Square\ both\ sides:\n(x+5)^2+(y-5)^2=(y+1)^2\n\nUse:(a\pm b)^2=a^2\pm2ab+b^2\n\nx^2+2\cdot x\cdot5+5^2+y^2-2\cdot y\cdot5+5^2=y^2+2\cdot y\cdot1+1^2\nx^2+10x+25+\not y^2-10y+25=\not y^2+2y+1\nx^2+10x-10y+50=2y+1\n2y+1=x^2+10x-10y+50\ \ \ \ |subtract\ 1\ from\ both\ sides\n2y=x^2+10x-10y+49\ \ \ \ |add\ 10y\ to\ both\ sides\n12y=x^2+10x+49\ \ \ \ |divide\ both\ sides\ by\ 12\n\n\boxed{y=(1)/(12)x^2+(5)/(6)x+(49)/(12)}$

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TOPIC: simultaneous linear equations

p + 2q = 3,
p - 2q = 3

Answers

Answer:

p=3 q=0

Step-by-step explanation:

p+2q=3

p-2q=3

p+2q=3

p=3-2q---------eqn i

p-2q=3

3-2q-2q=3

3-4q=3

-4q=3-3

q=0÷-4

q=0

putting the value of q in equation i

p=3-2q

=3-2×0

Answer:

p=3

q=0

Step-by-step explanation:

Adding both the equation

p+2q=3

+ p-2q=3

------------

2p=6

p=3

putting value of p in any of the above equation we will get the value of q.

3+2q=3

2q=0

q=0

mark this as brainliest!!!!

Need answer ASAP will give brainliest check out the picture the answrs: 2, 65, 69, 60, 120, 89, and 30

Answers

I think it is 120

The total of the shape is 180 so it telling us to take away 1/3 of it so 60 away from 180 is 120

Trapezoid TUVM is rotated 90 counterclockwise about the origin. After the rotation, what is the location of vertex V?A (2,-6)

B (-6,2)

C (6,-2’

D (-2,6)

Answers

Answer:

Step-by-step explanation:

Under a counter clockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

V (6, 2 ) → V' (- 2, 6 ) → D

Meredith practices the piano for 3 hours each week. How many hours will she practice in 8 weeks?

Answers

The answer is 3 the number of hours in the week, multiplied by 8 the number of weeks she will practice, so the answer is 24.

If Meredith practices 3 hours a week, and the question is asking how many hours she will practice in 8 weeks, the answer is 24. It is 24 hours because 3×8=24 :)
Hope I helped!! Please mark as Brainliest.

Write the equation of the parabola with a focus (1,2) and directrix y = 1

Answers

since the y shifted and focus is above directix, parabola opens up
4P(y-k)=(x-h)^2
distance from focus to veretx=distance from vertex to directix=P

from focus to directix is
from 2 to 1 which is 1 distance
1/2=P since 1/2of 1=1/2
4(1/2)(y-k)=(x-h)^2
vertexis 1 higher than directix so add 1/2 to 1 to get 1.5
vertex=(1,1.5)
vertex=(h,k)

equation is
4(1/2)(y-1.5)=(x-1)^2
if you want vertex form
2(y-1.5)=(x-1)^2
divide 2
y-1.5=(1/2)(x-1)^2
add 1.5
y= $(1/2)(x-1)^(2)+1.5$

20 pointsA large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Which
statements can be used to write an expression and then find the number of peanuts that ended up in each bag?
Check all that apply.
The operation is division.
The operation is multiplication.
The variable is the number of bags.
342 divided by 6 equals 57.
Write the division expression as a fraction,
To evaluate, substitute 342 for the variable.
Each bag will have 57 peanuts.
The constant is 342.

Answers

Answer:

I think the answer is A, D, E, F, and G.

Tell me if i'm right or wrong please.

Answer:

adefg

Step-by-step explanation:

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3x+6+4=6×2+10lve for x

Which algebraic expression is a polynomial with a degree of 5?3x5 + 8x4y2 – 9x3y3 – 6y5 2xy4 + 4x2y3 – 6x3y2 – 7x4 8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4 –6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5

Divide 56 in a ratio of 5:3