1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yuradex [85]
3 years ago
12

Write the equation for a parabola with a focus at (-8, -1) and a directrix at y = − 4.

Mathematics
1 answer:
Sidana [21]3 years ago
4 0

Answer:

y = 1/6 x^2 + 8/3 x + 49/6

Step-by-step explanation:

This is a parabola which opens upwards.

The distance of a point (x, y)  from the focus is

√[(x -  -8)^2  + (y - -1)^2] and

the distance of the point from the line y = -4

= y - -4

These distances are equal for a parabola so:

√[(x -  -8)^2  + (y - -1)^2] = y + 4

Squaring both sides:

(x + 8)^2 + (y + 1)^2  = (y + 4)^2

x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16

x^2 + 16x + 64 + 1 - 16 = 8y - 2y

6y = x^2 + 16x + 49

y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.

You might be interested in
X + 8 + 2x <= 2x + 13
sergejj [24]

Answer:

X = 15

Step-by-step explanation:

We move all terms to the left:

<em>x+8+2x-(2x+13)=0</em>

We add all the numbers together, and all the variables:

<em>3x-(2x+13)+8=0</em>

We get rid of parentheses:

<em>3x-2x-13+8=0</em>

We add all the numbers together, and all the variables:

<em>x-5=0</em>

We move all terms containing x to the left, all other terms to the right:

<em>x=5</em>

5 0
2 years ago
What are the solutions to the expression x^2-8x=24
labwork [276]

Answer: x= 2(2+sqrt(10)) , x=2(2-sqrt(10)

Step-by-step explanation:

x^2-8x=24 <- subtract 24 from both sides

x^2-8x-24 <- take quadratic formulat (-2+/- Sqrt(b^2 - 4ac)/2a

-(-8) +/- sqrt((-8)^2 - 4(1*-24) all over (2*1) <- simplify

(-(-8) +/- 4sqrt(10) )/2 <- sepereate

(-(-8) +/4sqrt(10) )/2 ,  (-(-8) - 4sqrt(10) )/2 <- simplify

2(2+sqrt(10)) , 2(2-sqrt(10) =x

6 0
3 years ago
75 POINTS Need an immediate answer please brainliest will be given! A train left a station travelling to a city at 30 mph. The t
yaroslaw [1]

The value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

<h3>What is the rate of speed?</h3>

The rate of speed is the rate at which the total distance is travelled in the time taken. Rate of speed can be given as,

r=d/t

Here, (d) is the distance travelled by the object and (t) is time taken but the object to cover that distance.

The train traveled 1/3 of the distance at 30 mph and the remaining distance at 40 mph. Let <em>t</em> is the time the train has taken to travel and x is the distance it travelled. Thus,

t=\dfrac{\dfrac{1}{3}x}{30}+\dfrac{\dfrac{2}{3}x}{40}\\t=\dfrac{x}{90}+\dfrac{x}{60}\\t=\dfrac{2x+3x}{180}\\t=\dfrac{5x}{180}\\t=\dfrac{x}{36}

After two hour a car left the same station traveled the first 3 hours at 35 mph and the remaining distance at 51 mph. Let <em>t</em> is the time the car has taken to travel and x is the distance it travelled. Thus,

t+2=3+\dfrac{(x-3\times35)}{51}

As t is same, thus put the value of t in this equation,

\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=1+\dfrac{(x-105)}{51}\\\dfrac{x}{36}=\dfrac{(51+x-105)}{51}\\51x=36x-54\times36\\51x-36x=1944\\x=\dfrac{1944}{15}\\x=129.6

Thus, the value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

Learn more about the rate of speed here:

brainly.com/question/359790

#SPJ1

6 0
2 years ago
NEED HEELLLLPPPPPP!!
Tju [1.3M]
It looks equivalent.

Do the Pythagorean theorem on the triangle shown.
2.1^2-1.4^2

4.2-1.96=2.24

Sqrt of 2.24 is 1.496 or 1.5
Now multiply this by 2 to get the length of x

HOPE THIS HELPS
6 0
2 years ago
The sides of a triangle are 3x+ 2, 6x, and 5x. Find the expression to represent the perimeter. To find the perimeter, we ADD the
frosja888 [35]

Answer:

14x + 2

Step-by-step explanation:

Perimeter = sum of the measures of each side

If a triangle has side lengths of 3x+ 2, 6x, and 5x then the perimeter of that triangle is equal to 3x + 2 + 6x + 5x

Notice that the expression 3x + 2 + 6x + 5x has similar terms so to get the simplist version of the perimeter we would simply combine like terms

3x + 6x + 5x = 14x

The perimeter would = 14x + 2

7 0
3 years ago
Read 2 more answers
Other questions:
  • NEED DONE NOW!!!!!!
    8·2 answers
  • 70 Points!! Question!​
    7·2 answers
  • is the sum of two polynomials of degree 5 always a polynomial of degree 5? Give an example to explain your answer
    10·1 answer
  • I really need help with this before it closes
    14·2 answers
  • HELPPPPPPPPPP PLZZZZZZZZZZZZ
    5·1 answer
  • What’s the distance between (3,6) and (3,-4)
    10·1 answer
  • How do you write the fraction 6/6as a sum of fractions three different ways
    9·2 answers
  • Taking a discount of 50% off followed by a discount of 50% off results in a total discount of
    9·1 answer
  • Frank lost 5 points for not completing his homework, 3 points for talking, and 2 points for chewing gum. This happened 4 days in
    7·1 answer
  • A man works a basic week of 32 hours and earns $172.48. Find his basic rate of pay
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!