Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(6, 0) and line x = −6.

Answers

Answer 1

The equation of the graph is [tex]x = \frac 1{24}y^2[/tex]

How to determine the equation?

Generally, a point is represented as:

(x,y)

The line x = -6 means that:

(-6, y)

So, we calculate the distance between (x,y) and (-6, y) as follows:

[tex]d = \sqrt{(x + 6)^2 + (y - y)^2}[/tex]

This gives

[tex]d = \sqrt{(x + 6)^2 }[/tex]

Next, we calculate the distance between (6,0) and (x, y) as follows:

[tex]d = \sqrt{(x - 6)^2 + (y - 0)^2}[/tex]

This gives

[tex]d = \sqrt{(x - 6)^2 + y^2}[/tex]

Equate both distance expressions

[tex]\sqrt{(x + 6)^2} = \sqrt{(x - 6)^2 + y^2}[/tex]

Square both sides

[tex](x + 6)^2 = (x - 6)^2 + y^2[/tex]

Expand

[tex]x^2 + 12x + 36 = x^2 - 12x + 36 + y^2[/tex]

Evaluate the like terms

[tex]12x = - 12x + y^2[/tex]

Add 12x to both sides

[tex]y^2 = 24x[/tex]

Make x the subject.

[tex]x = \frac 1{24}y^2[/tex]

Hence, the equation of the graph is [tex]x = \frac 1{24}y^2[/tex]

Read more about line equations at:

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Related Questions

sisktzkyzktRkzkKKRpyxdypzoyzitzotkg​

Answers

(Y2-y1)/(x2-x1) = gradient
Pick two points: (2,6), (4,8)
(8-6)/(4-2) = 2/2 = 1
The gradient is 1

Last year, the cost of a family-sized dinner at a picnic was $8.50. This year, the cost is $11.56. What is the percent of increase of the price? ( I need a step-by-step explanation not just the answer) ill give brainliest

Answers

to find the percentage increase, take the price increase divided by the original price :
price increase = $11.56 - $8.50 = $3.06

percentage increase = $3.06/$11.56 x 100%
= 26.47% (or 26.5%)

hope the explanation was able to help!!

indicate in standard form the equation of the line passing through the given points, in the equation box below. X(0, 6), Y(5, 6)

Answers

Answer:

0x + y = 6

Step-by-step explanation:

Equation of the Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It can be later converted to any other form of the line. For example, the standard form is:

[tex]Ax + By = C[/tex]

Let's find the equation by using the given points (0,6) (5,6):

[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]

Operating:

[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]

y - 6 = 0

Or, equivalently:

0x + y = 6

This corresponds to a horizontal line

HELP FAST ITS AN IMAGE

Answers

Answer:

3

Step-by-step explanation:

the answer is 3 because there are three units between each point of the triangle!

A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 210 feet. How long will it take to move from one end to the other?

PLEASE HELP ME WILL REPORT IF TROLL

Answers

Answer:

The answer is 1470 seconds.

Step-by-step explanation:

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Input the equation of the given line.

The line including (4, 7) and (0, 7).

Answers

Answer:

[tex]y=7[/tex]

Step-by-step explanation:

First, let's use the two given points to find the slope. Remember the slope equation:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{7-7}{0-4}[/tex]

[tex]m=\frac{0}{-4}[/tex]

[tex]m=0[/tex]

If we're following slope-intercept form, what we have so far is

[tex]y=0x+b[/tex]

Substitute one of the given points for the [tex]x[/tex] and [tex]y[/tex] values in order to find [tex]b[/tex]:

[tex]7=0(4)+b[/tex]

[tex]7=b[/tex]

Now, if we put that back into our slope-intercept equation we get

[tex]y=0x+7[/tex]

or,

[tex]y=7[/tex]

Right off the bat, we can see how we ended up with this equation because both points have the same y-values. This indicates a horizontal line.

I hope this helps!

HELP FAST I NEeD THIS

Answers

Answer:

1. x=7.16304347

2.x=11.2

Step-by-step explanation:

3x+14=2(2x-3), steps to solve

Answers

Answer:

20

Step-by-step explanation:

3x+14=2(2x-3)

3x+14=4x-6

3x-4x=-6-14

-x=-20

X=20

So the valueof X is 20


HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!

Answers

Answer: AEC = 80

              X=30

YW ;)

can somone help me pls ?

Answers

[tex]\huge\mathtt{Hello!}[/tex]

[tex](6x - 23) = (4x + 9)[/tex]

[tex]6x -4x = 9 + 23[/tex]

[tex]2x = 32[/tex]

[tex]x = 16[/tex]

It is because the sides are equal, so the angles opposite to them also are equal.

Have a nice day!

6x -23= 4x +9
-4x = -4x
______________
2x -23= 9
2x +23= + 23

2x = 32
/ 2x. /2

X = 16

First, you cancel out the x by moving the one in the right to the left. You subtract the 6 from the left to the one in the right, giving you 2x. Then you cancel out the number on the left to the right (same thing as the x, remember by cancelling a number out you make it the opposite of what it is so if it’s negative it turns to positive to cancel out). Final step is to cancel out the x so you can divide it by the number that’s left to get the x by itself !

2+4 i need help right now​

Answers

Answer:

6?

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2 + 4 =6

just add 2 by 4 than ans 6

Each big square below represents one whole,
What percent is represented by the shaded area?
%

Answers

The first square is 100% and the second square is 55% filled in

help me please somone

Answers

Answer:

Iscoccecles

Sorry if i spelled it wrong.

Step-by-step explanation:

i think that would be an isosceles triangle

6. Evaluate f(-1).

7. What value of a will make the equation f(a) = 6 true?

someone please help lol I have a test <3

Answers

Answer:

6. -f         7. f= 6/8

Step-by-step explanation:

Hope dis helps!!

Harry wants a fence around his garden.
Height: 16.7m
Length: 16.3m
What is the perimeter of the whole garden?

Answers

Answer:

66m

Step-by-step explanation:

perimeter is the distance all round a figure

perimeter(p)= 2( length(l) + width(w))  or  perimeter= 2 length + 2 width

p= 2(l + w)                                                 or      p =  2l  + 2w

p= 2(16.3 +16.7)                                        or      p=  2(16.3) + 2(16.7)

p=2(33)                                                      or     p=   32.6  +  33.4

p=66m                                                        or     p=  66m

find area of triangle formed by (1,1) (2,3) (4 ,5) using heron's formula ​

Answers

Answer:

The area of a triangle is:

A = 1 unit²

Step-by-step explanation:

Given the points of a triangle

A(1, 1)

B(2, 3)

C(4, 5)

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Distance between AB:

[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]

     [tex]=\sqrt{1+4}[/tex]

     [tex]=\sqrt{5}[/tex]

so

[tex]a=\sqrt{5}[/tex]

Distance between BC:

[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]

     [tex]=\sqrt{2^2+2^2}[/tex]

     [tex]=\sqrt{2^3}[/tex]

     [tex]=2\sqrt{2}[/tex]

so

[tex]b=2\sqrt{2}[/tex]

Distance between AC:

[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]

    [tex]=\sqrt{3^2+4^2}[/tex]

   [tex]=\sqrt{5^2}[/tex]

    [tex]=5[/tex]

so

[tex]c=5[/tex]

Semiperimeter = sum of sides ÷ 2            

                       [tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]

Area of the triangle:

[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]

[tex]a=\sqrt{5}[/tex][tex]b=2\sqrt{2}[/tex][tex]c=5[/tex]

[tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]

[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]

[tex]A=1[/tex]

Therefore, the area of a triangle is:

A = 1 unit²

A sequence of steps for solving the equation 3(x - 2) = 4 is shown. Match a property to each blank box to show the reason for each step. Question 6 options: 3(x - 2) = 4 3x - 6 = 4 3x = 10 x = 103 1. Given 2. Distributive Property 3. Addition property of equality 4. Division property of equality

Answers

Step-by-step explanation:

Given the equation;

3(x-2) = 4

A sequence of steps for solving the equation is as shown;

Step 1: Open the parenthesis by applying distributive law to distribute 3 over x and 2 as shown;

3(x-2) = 4

3(x)- 3(2) = 4

3x - 6 = 4

Step 2: Add 6 to both sides of the equation (Addition property)

3x-6+6 = 4+6

3x = 10

Step 3: Division property of equality. Divide both sides by 3;

3x = 10

3x/3 = 10/3

x = 10/3

A taxi cab charges a flat fee of $1.75 plus $0.30 for each half-mile or fraction of a half-mile.

a) Fill in the chart.

b)write and equation for the function.

Answers

Answer:

a) there is no chart but we can elaborate one:

taxi fee            half-miles driven

$1.75                      0

$2.05                     1

$2.35                     2

$2.65                     3

$2.95                     4

$3.25                     5

$3.55                     6

b) y = 0.3x + 1.75

where:

y = taxi fee

x = half miles driven

PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
Plz Answer honestly or you will be reported.

Evaluate.

(2/7)^3

A: 8/343
B: 8/7
C: 3/343
D: 6/7

Answers

Answer:

8/343

so A

Step-by-step explanation:

yler's brother earns $12 per hour. The store offers him a raise— a 5% increase per hour. after the raise,how much will tyler make per hour

Answers

Answer:

$12.60

Step-by-step explanation:

12/100 × 12 = 0.60

12 + 0.60 = 12.60

The length of a rectangle exceeds its width by 1
inch and the area is 132 square inches. What
are the length and width of the rectangle?

Answers

Answer:

Width equals 11, and length equals 12.

Step-by-step explanation: It is helpful to memorize your multiplication tables up to 12. I personally couldn't figure out a formula for this, but I knew that 12 x 11 equals 132, and the length is greater than the width, so length is 12 and width is 11. Hopefully somebody else can figure it out. P.S. I meant the formula, not the answer, my answer is correct.

Answer:

[tex]l(l - 1) = 132[/tex]

[tex] {l }^{2} - l - 132 = 0 [/tex]

[tex](l - 12)(l + 11) = 0[/tex]

[tex]l = 12 \: or \: l = - 11[/tex]

[tex]length \: must \: be \: postive[/tex]

[tex]integers[/tex]

[tex]l = 12 \: and \: w = l - 1 = 11[/tex]

plato

Can someone please help, ty!!
(Will mark brainliest)

Answers

Answer:

Yellow is correct.

You can add the valued and divide by how many values there are to find the mean

The score of 20 is an outlier and brings the mean score down by almost 10%

Step-by-step explanation:

Answer:

3: The low score causes the mean to decrease.

Step-by-step explanation:

If you add a significantly lower number, it will bring down the overall average.

Hope this helps!

Martina ordered a set of blue and orange pins. She received 96 pins in all. 24 of the pins were
blue. What percentage of the pins were blue?
Write your answer using a percent sign (%).

Answers

Answer:

25%

Step-by-step explanation:

This is like a part over whole problem, where 24 blue pens is the part and 96 pens total is the whole.

24/96 = 0.25 * 100 = 25%

Answer:

Of the 96 pins, 25% of the pins were blue.

Step-by-step explanation:

We are given that Martina ordered 96 pins in total. We are also given that she ordered 24 blue pins.

With this, we can determine how many of the pins were not blue pins by subtracting the amount of blue pins from the number of total pins.

[tex]96 \ \text{total pins} - 24 \ \text{blue pins} = 72 \ \text{orange pins}[/tex]

Now, we can divide the number of blue pins by the number of total pins to determine the fraction of blue pins to total pins.

[tex]\displaystyle \frac{24}{96} = \frac{12}{48} = \frac{6}{24} = \frac{3}{12} = \frac{1}{4}[/tex]

Then, we can convert our fraction to a decimal.

[tex]\displaystyle \frac{1}{4} = 0.25[/tex]

And finally, we can convert our decimal to a percentage by multiplying the determined decimal by 100.

[tex]0.25\times100 = 25\%[/tex]

Therefore, of the 96 pins that Martina ordered, 25% of them were blue.

Kelly currently has a checking account balance of $172.14. She makes a deposit of $27.45, and then spends $17.89 on dinner. How much money does she have now? *

Answers

Answer:

126.8 Hope this helps

2. What number is equal to five units + three tenths? Circle the correct answer.
0.53
0.35
5.3
3.5
53
35

Answers

Answer:

35

Step-by-step explanation:

5*1+3*10

5+30 = 35

Twice a number x minus 18

Answers

Step-by-step explanation:

Here is the answer...

Hope this helps you

PLEASE HELP WHO KNOWS THIS?

Answers

Answer:

I don't know how you would submit this but I do know it's a transformation. So you would move it across the x-axis 4 or 5 times depending on the shape. So I would maybe just write out each individual number like 3,4,5

Step-by-step explanation:

13. The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert.

Answers

Given:

Initial population = 45,000

Decreasing rate = 2%

Time = 5 year

To find:

The population after a period of 5 years.

Solution:

Formula used:

[tex]f(t)=ae^{rt}[/tex]

where, a is initial population, r is rate and t is time.

[tex]r=\dfrac{2}{100}=0.02[/tex]

Decreasing rate represented by -0.02.

Substitute a=45000, r=-0.02 and t=5 in the above formula.

[tex]f(5)=45000e^{-0.02(5)}[/tex]

[tex]f(5)=45000e^{-0.1}[/tex]

[tex]f(5)=45000(0.904837418)[/tex]

[tex]f(5)=40717.68381 [/tex]

Approximate the value to the previous integer.

[tex]f(5)\approx 40717 [/tex]

Therefore, the population after 5 years is 40717.

Answer:

40,718

Step-by-step ex

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:

Let the function f be defined by f(x) = 12 -5x


4. Is it true that f(0) = 0?


5. Explain why or why not?

ILL MARK YOU BRAINLIEST if you answer xx

Answers

4. It is not true
5. This is because if you substitute f(0) the equation would be f(x) = 12-0 or f(x) = 12
Hope this helps, if it does can I get brainliest ?

Q14.
Solve the simultaneous equations
2x - 3y = 24
6x + 2y = -5
landimorament

Answers

-3y=24-2x
2y=-5-6x

-y=8-2/3x y=-8+2/3x
y=-5/2-3x

-8+2/3x=-5/2-3x
-8+5/2=-3x-2/3x
-11/2= -11/3x
x=3/2
hope it helps!!!
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