Mathematics College

A parabola can be drawn given a focus of (−5,3) and a directrix of
y=1. Write the equation of the parabola in any form.

Answers

Answer 1

Answer:

Step-by-step explanation:

y = 1 is a horizontal line

Vertex is halfway between the directrix and focus on a vertical line through x = (-5, 3).

(1 + 3)/2 = (-5, 2)

The shortest distance from the directrix to the focus is 3 - 1 = 2 units

so points (-5 - 2, 3) = (-7, 3) and  (-5 + 2, 3) = (-3, 3) are on the parabola.

The vertex form of a parabola is

y = a(x - h)² + k

y = a(x - (-5))² + 2

y = a(x + 5)² + 2

plugging in one of the other known points

3 = a(-7 + 5)² + 2      or      3 = a(-3 + 5)² + 2  

1 = a(-2)²                             1 = a(2)²

a = 1/4                                 a = 1/4

y = ¼(x + 5)² + 2

to find the standard form, expand the vertex form

y = ¼(x² + 10x + 25) + 2

y = 0.25x² + 2.5x + 6.25 + 2

y = 0.25x² + 2.5x + 8.25

or

4y = x² + 10x + 33

Related Questions

A 20-foot string of lights will be attached to the top of a 12-foot pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?

Answers

Answer:

8 feet away

Step-by-step explanation:

Because if there is 20 feet of lights, and the pole is 12 feet you subtract 20-12 which gets you 8.

In a survey of 1,900 people who owned a certain type of car, 1,045 said that they would buy that type of car again. What precent of the people surveyed were satisfied with the car?

Answers

Step-by-step explanation:

1045/1900 = .55 so 55 % of peoplr were satisfied

I need help please!!!!!!!!!

Answers

Answer:

2 x -4 = -8

Step-by-step explanation:

1.2x4=8

2.If there is one negative and one positive when multiplying the answer will be negative

Which of the following equations have infinitely many solutions?
Choose all answers that apply:
742 - 37 = 742 – 37
372 - 37 = 372 – 37
2 - 37 = 2- 37
732 - 37 = 732 - 37

Answers

Answer: Are there suppose to be Xs? All of them are equal to each other.

Step-by-step explanation:

10.
Write the equation of a line that is perpendicular to the given line and that passes through the given point.

–x + 5y = 14; (–5, –2)

A. y = 5^x – 27

B. y = -1/5x – 27

C. y = -1/5x – 15

D. y = -5^x – 27

Answers

Answer:

D. y = -5^x – 27

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  − x + 5 y = 14 .

y = − 5 x − 27                         PERPENDICULAAR

...................................................................................................................................................

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  − x + 5 y = 14 .

y = 1 /5 x − 1                             PARALLEL

An arts academy requires there to be 5 teachers for every 100 students and 6 tutors for every 48 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 72 students​?The academy has enter your response here students per teacher.

Answers

20 students per teacher.

8 students per tutor.

9 tutors needed for 72 students.

per teacher= 20 students, per tutor= 8 students , the academy needs 12 tutors for 72 students :)

whats the answer i need help with the following equations

Answers

It’s going up by fiveAnswer:

Step-by-step explanation:

Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from those waiting. Benny has assumed that both barbers would take an average of 20 minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of two per hour. Find the following information to help Benny decide if a second chair should be added: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop.

Answers

According to the information presented, Benny should decide not to add a second chair because the average number of clients waiting is 1 (very low), the average waiting time for a client is 10 minutes (very low), and the average time a customer is in the store is 20 minutes (very low).

According to the information, an average of 2 clients arrive at the hairdresser for every hour (60 min) and each cut takes a maximum of 20 minutes. Therefore, the hairdresser would have an average of 40 minutes busy and 20 minutes free for each hour.

Additionally, customers who must wait do not have to spend a long time waiting in the store because the maximum waiting time is 10 minutes (in the case that both customers arrive at the same time).

Below is a graph where the information of both cases is compared (with an additional chair and without an additional chair) and it is inferred that an additional chair is not necessary because the number of clients waiting and the waiting time is not high.

Learn more in: https://brainly.com/question/25400126

33y + 16; y = 3
PLSSS HELP MEE

Answers

i think it’s 115 because 33x3 is 99 then 99+16 is 115

Answer:

115

Step-by-step explanation:

y = 3

33y + 16

So since we know what y equals, we replace y in the equation to find our answer

33(3) + 16

33 times 3

99 + 16

115

Hope this helped! Leave a comment if it did, and try asking your teacher if it's correct :)

Write a function in any form that would match the graph shown below
f(x)=

Answers

Answer:

I think it would be

f(x) = -x² - x + 4

Hope this helps!

What is the slope of this line?

Answers

Answer:

1, -6

Step-by-step explanation:

Subtract the units on the grid from one point to the other to get the slope. You go over 1 and down 6 to get to the other point.

Write the equation of the graphed line in slope-intercept form.
The slope is a rise of 1 and over three and the y intercept is 3
Please help?

Answers

Answer:

yes the slope is 1 up 3left or 1 down 3 right

but you wrote it wrong y = 1÷3 + 3

because y intercept is 3

5.
Which equation is represented by the graph?



y = 2x2 + 1

y = 2x2 − 1

y = 1/2x^2 + 1

y = x2 − 1

Answers

Answer:

y = x^2 − 1

Step-by-step explanation:

By the look of each graph, it looks like y = x2 − 1 is the answer.

Write two equivalent ratios. 9/12

Answers

3/4 by the once we multiply 9x divide 3 times 3 will be nine 4 times 3 will be 12 we need a number that multiply’s by the same answer that’s on top

Answer:

3/4     18/24       27/36

Step-by-step explanation:

B=5 b+(bx2x3)-5 plz help

Answers

Answer:

Step-by-step explanation:

12

Who has the most money based on the table below?

Answers

If I’m correct, Russell Wilson has the most money.

Bruno cambió S/200 en tres billetes y ocho monedas. ¿De qué denominación fueron los billetes y monedas?

Answers

Answer:

Un billete de 50

Un billete de 100

Un billete de 10

8 de monedas de 5

Explicación paso a paso:

100 +50+10+8(5)=200

Step-by-step explanation:

Evaluate the determinant for the following matrix

Answers

Determinant formula ad -bc
(-5 * 4 ) - (1 * 1)
-20 - 1
-21

letter a

Step by step Explanation

-5×4-1×1

-20-1

-21

hope this help you!

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
53.8 42.2 44.0 34.3 44.0
31.6 45.8 38.8 50.5 42.0
Public Colleges
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8
(a) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)
(b) Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)
(c) What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)
We estimate that the mean annual cost to attend private colleges is $ more than the mean annual cost to attend public college
(d) Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)

Answers

Gggbztm hm finch nvm ykbtk I invincible

Write an equation in slope-intercept form for the line with slope -1/2 and y-intercept -7

Answers

Answer:

well slope intercept form is

y=mx+b

now m is slope and b is y intercept.

so just plug it in

y= -1/2x - 7

Answer:

the slope intercept form is

y=mx+b

 y= -1/2x - 7

Step-by-step explanation:


A marathon is 26.2 miles long. Jarrod is running a marathon and has completed 17.75 miles. How
many more miles to the finish line?

Answers

Answer:

Jarron has 8.45 more miles to get to the finish line.

Step-by-step explanation:

All we have to do is subtract the total number of miles by the number of miles Jarron has completed.

So: 26.20 - 17.75 = 8.45

26.2 - 17.75 = 8.45

All you need is subtraction because you are finding what is left.

You can find 8.45 by using a calculator or solving in your head, it would just take longer.

A line has a slope of 1/9 and a y intercept of 2. What is its equation in slope intercept form?

Answers

y= 1/9x + 2 that is in slope intercept form

can somebody please help me with my language arts please?

Answers

Answer: alright

Step-by-step explanation:

Whats 8*8 I'm in first grade and they give me this

Answers

um 64 lol? hope this helps.

solve the system y=6x=5 y=3x-23

Answers

Answer:

False θ·θ.................

Answer:

x = -28/3

y = -51

Step-by-step explanation:

Let's solve for X first

6x + 5 = 3x - 23

-3x            -5         (like terms)

3x = -28

/3       /3               (divide by 3)

x = -28/3

y = 6(-28/3) + 5

y = -51

(I'm having doubts with my answers, so can you check my work? Comment incorrections and I can edit)

Hope this helps! Please comment :)

PLEASE HELP
(delta math)
Triangle TUV is formed by connecting the midpoints of the side of triangle QRS.
The lengths of the sides of triangle TUV are shown. What is the length of RS?
Figures not necessarily drawn to scale.

Answers

Whatever the length of UV is. Corresponding segments are equal in congruent triangles. For example, QR would be equal to TU. Hope that helps!

what is the answer for this

Answers

Answer:

w=6.3

Step-by-step explanation:

Im too lazy to put the steps U^U

Brainliest?

HELP ME DUE IN 30mins !!!!

Find the measure of each angle indicated.

Answers

Answer:

1.50° 2.65°

Step-by-step explanation:

let x be the unknown angle

1. 32+98+x=180(sum of angles in a ∆ equal to 180°)

130+x=180

x=180-130

x=50°

2. 25+90+x=180

115+x=180

x=180-115

x=65°

i need help solving these problems!

Answers

It whould be 20 degrees in all for the first one

Which expression is equivalent to (4√a^2b)(3√b)?
A) 2ab√3
B) 3a^2b^2
C) 12ab
D) 12ab^2

Answers

Answer:

C) 12ab

Step-by-step explanation:

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