Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line. (4,-2); y=3

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]                  ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

[tex](h,k+p)=(6,-4)[/tex]

On comparing both sides, we get

[tex]h=6[/tex]

[tex]k+p=-4[/tex]                            ...(ii)

Directrix at y=-7. So,

[tex]k-p=-7[/tex]                            ...(iii)

Adding (ii) and (iii), we get

[tex]2k=-11[/tex]

[tex]k=\dfrac{-11}{2}[/tex]

[tex]k=-5.5[/tex]

Putting [tex]k=-5.5[/tex] in (ii), we get

[tex]-5.5+p=-4[/tex]

[tex]p=-4+5.5[/tex]

[tex]p=1.5[/tex]

Putting [tex]h=6, k=-5.5,p=1.5[/tex] in (i), we get

[tex]y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)[/tex]

[tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex]

Therefore, the equation of the parabola is [tex]y=\dfrac{1}{6}(x-6)^2-5.5[/tex].

Step-by-step explanation:

hope it is helpful to you ☺️

Answer:

719.24 is the correct answer

Answer:

you would divide an equation from the multiple and then you would simplify the equation for an answer

Answer:You can also use tables to represent functions. Instead of using two ovals with circles, a table organizes the input and output values with columns. ... Remember, a function can only assign an input value to one output value. If you see the same x-value with more than one y-value, the table does not represent a function.

Step-by-step explanation:

Answer:

Point A, C and D

Point B

Step-by-step explanation:

[tex]{hope it helps[/tex]

Answer:

52 in^2

Hope this helps!

Step-by-step explanation:

i think minerals and vitamins since they are micro nutrients

Answer:

Graph B

Step-by-step explanation:

The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

Answer:

Total amount of ticket free = £64.89

Step-by-step explanation:

Given:

Cost of theater ticket = £63 plus

Booking fee of theater ticket = 3%

Find:

Total amount of ticket free

Comutation:

Total amount of ticket free = Cost of theater ticket + Booking fee of theater ticket

Total amount of ticket free = 63 + 3%

Total amount of ticket free = 63 + 1.89

Total amount of ticket free = 64.89

Total amount of ticket free = £64.89

Answer:

Step-by-step explanation:

Acres of corn harvested : time taken = 8 3/4 : 5/6

How much corn can she collect in a hour. ?

Let

x = Acres of corn harvested

Acres of corn harvested : time taken = x : 1

8 3/4 : 5/6 = x : 1

35/4 : 5/6 = x : 1

35/4 ÷ 5/6 = x/1

35/4 × 6/5 = x/1

35*6/4*5 = x/1

210/20 = x/1

210 * 1 = 20 * x

210 = 20x

x = 210/20

= 10 1/2 acres

x = Acres of corn harvested = 10 1/2 acres

Answer: 19/3

Step-by-step explanation:

[tex]4x+3-x-5=30-3x\\\\3x-8=30-3x\\\\6x-8=30\\\\6x=38\\\\x=\frac{19}{3}[/tex]

Step-by-step explanation:

=> (3x-12) =(x+6)

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

Answer:

836.8

Step-by-step explanation:

Answer:

(-1,-1)

Step-by-step explanation:

Step 1 identify coordinates of A

A is located at ( -3 , -3 )

Step 2 apply dilation by multiplying the x and y values of coordinate A by the scale factor

Given:

scale factor = 1/3

Coordinates of A: ( -3 , -3 )

* Multiply the x and y values by 1/3 *

( -3 * 1/3 , -3 * 1/3 ) -------> ( -1 , -1 )

The new coordinates would be (-1,-1)

multiply the coordinates of A by the scale factor given

Answer:

11.2

Step-by-step explanation:

[tex]p =\frac{160.16}{14.3}=\frac{160.16*10}{14.3*10}\\\\p = \frac{1601.6}{143}\\\\[/tex]

p = 11.2

Answer:

The person above me is correct I just did the work and I got the same answer as them :)

Step-by-step explanation:

Answer:

$60 per ticket

Step-by-step explanation:

$215 is what it costs after the discount, so add the amount taken off, back on.

215+25

 240

Then, divide by 4 to find the cost of each individual ticket.

240/4

60

Hope it helps!

Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is [tex]140\ \text{miles}[/tex]

Speed of Emily [tex]v_e=12\ mph[/tex]

Speed of Kylie [tex]v_k=8\ mph[/tex]

Distance traveled by Emily [tex]\Rightarrow d_e=12t[/tex]

Distance traveled by Kylie [tex]\Rightarrow d_k=8t[/tex]

[tex]\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr[/tex]

They will meet after 7 hour.

Answer:

I don't understand this

Answer:

It will take 13 months for the second phone to be less expensive than the first phone.

Step-by-step explanation:

Since Sal is trying to determine which cell phone and service plan to buy for his mother, and the first phone costs $ 100 and $ 55 per month for unlimited usage, while the second phone costs $ 150 and $ 51 per month for unlimited usage, to determine how many months will it take for the second phone to be less expensive than the first phone, the following calculation must be performed:

100 + (55 x 10) = 100 + 550 = 650

150 + (51 x 10) = 150 + 510 = 660

100 + (55 x 12) = 100 + 660 = 760

150 + (51 x 12) = 150 + 612 = 762

100 + (55 x 13) = 100 + 715 = 815

100 + (51 x 13) = 150 + 663 = 813

Therefore, it will take 13 months for the second phone to be less expensive than the first phone.

Answer:

1) 100 + 55x > 150 + 51x

2) x > 12.5

3) 13

Step-by-step explanation:

Got it right on Edge :D

Step-by-step explanation:

given the geometric sequence 2, -4, 8, -16, ...

a1 = 2

r = -4/2 = -2

find : a9 and a15

solutions:

an = a1. r^(n-1)

=> a9 = 2. (-2)^(9-1)

= 2. (-2)^8

= 2. 2^8

= 2^9

= 512.

=> a15 = 2. (-2)^(15-1)

= 2. (-2)^14

= 2. 2^14

= 2^15

= 32,768

Step-by-step explanation:

Hey there!

The given geometric sequence is: 2, -4, 8, -16.

The;

a1 = 2

Common ratio (r) = T2/T1

= -4/2

= -2

Now;

Use general formula of geometric sequence;

[tex]tn = {a1.r}^{n - 1} [/tex]

Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.

Then;

[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]

or, t9 = 2*256

Therefore, t9 = 512.

Again;

[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]

or, t15= 2*16384

Therefore, t15 = 32768.

Hope it helps!

Answer:

what are the answer choice?

Step-by-step explanation:

Answer: 80 feet

Step-by-step explanation:

We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:

5 * 128 = 8x

640 = 8x

80 = x

Thus, the height of the lighthouse is 80 feet tall.

Answer:

(1,-3) and (4,-6)

Step-by-step explanation:

The solutions are where the linear line intersects the graphed parabola.

The y-coordinate of the red point is -3.

X -Y =44 will represent the number of glasses of ice tea .

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Answer:

The vertex is located at (-2,-1)

Step-by-step explanation: