What is the slope of the line that passes through the points (-3, 5) and (1, 15)

Answer:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]

And, the distance from P to (0, -2) will be:

[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]

So sum of the two distances must be 6. Therefore:

[tex]d_1+d_2=6[/tex]

Now, by substitution:

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

Simplify. We can subtract the second term from the left:

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

Square both sides:

[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]

We can cancel the x² terms and continue squaring:

[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]

We can divide both sides by -4:

[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]

Adding 9 to both sides yields:

[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]

And, we will square both sides one final time.

[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]

Distribute:

[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]

The 36y will cancel. So:

[tex]4y^2+81=9x^2+9y^2+36[/tex]

Subtracting 4y² and 36 from both sides yields:

[tex]9x^2+5y^2=45[/tex]

And dividing both sides by 45 produces:

[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

Answer:

where are the equations

Step-by-step explanation:

m is how much more she needs to save

510+8+6=516+m

m=8

Answer:

Step-by-step explanation:

this system doesnt have any solutions

if you multiply the first equation by 2 you will get

2x-6y=14

second equation is

2x-6y=12

the result will -12=14

no solutions

Answer:

the middle sign

Step-by-step explanation:

Answer:

Step-by-step explanation:

50% = 1/2, 0.5

0.2 = 2%

Other = 20%, 20/100, 1/5

Answer:

I put this, Its correct.

Step-by-step explanation:

50% : 1/2, 0.5.

0.2 : 20/100, 20%, 1/5.

Other : 2%

Answer:

-4  

Step-by-step explanation:

8-10 = -2

-2^2 = -4

948.64

Subtract then multiply by itself

No offense but can't you use a calculator?

Answer:

Surface area of cuboid = 352 cm

Step-by-step explanation:

Given that:

Height of cuboid = 8 cm

Length of cuboid = 12 cm

Width of cuboid = 4 cm

Surface area = 2lw + 2lh + 2hw

Putting all the values;

Surface area = 2*12*4 + 2*12*8 + 2*8*4

Surface area = 96 + 192 + 64

Surface area = 352 cm

Hence,

Surface area of cuboid = 352 cm

Answer:

No solution

Step-by-step explanation:

1) 3(x+3y=6)

  3x+9y=72

2) 3x+9y=18

   3x+9y=72

3) 3x+9y=18

 -

   3x+9y=72

____________

       -54

Answer:

The answer is 25

Step-by-step explanation:

6•5=30

30+20=50

50/-2=25

Answer:

BOTH SIDES ARE 12

Step-by-step explanation:

Answer:

x and y is equal to 33° as x and y are the equal angles of the isosceles triangle given in the figure.

Answer:

the slope is one since the line rises once and runs once

Answer: 14, 16, 18, 20 in that order

Step-by-step explanation:

If the bottom response square is asking for a general equation, it would be y=x+7

Answer:

(C) x=50

Step-by-step explanation:

[tex]\frac{3}{5 }x -7=23[/tex]

[tex]\frac{3x}{5} -7=23[/tex]

[tex]\frac{3x}{5} -7+7=23+7[/tex]

[tex]\frac{3x}{5}=30[/tex]

[tex]3x=30* 5[/tex]

[tex]3x=150[/tex]

[tex]x=50[/tex]

Answer:

(C) X = 50

Step-by-step explanation:

(3/5)*x-7 = 23 // - 23

(3/5)*x-23-7 = 0

3/5*x-30 = 0 // + 30

3/5*x = 30 // : 3/5

x = 30/3/5

x = 50  (Sorry if it's wrong)

Answer:

32 F

Step-by-step explanation:

Answer:

What Are The Options?

Step-by-step explanation:

Answer:

0.42

Step-by-step explanation:

given:

P (penny) = 1/4

P (dime) = 1/3

since the only other possibility is to pick a nickel, hence

P (nickel)

= 1 - 1/4  - 1/3

= 5/12

= 0.4166667

= 0.42 (nearest hundredth)

Answer:

Jesse must have subtracted the 8 weeks from $40 to get $32 but the answer should be b $5

Step-by-step explanation:

Answer:

1.) -2

2.) -2

3.) -3

Step-by-step explanation:

Since we can't make a graph, we can make a table

(-5,13) and (1,1)

x       y

-5      13

1        1

From 13 to 1, you subtract 12 ( y-section)

From -5 to 1, you add 6 (x-section)

Now we can do y/x

y/x = 12/6 = -2

The slope for this first one is (-2).

(-5,14) and (12,-21)

x           y

-5          14

12         -21

From 14 to -21, you subtract 34

From -5 to 12, you add 17

Now we can do y/x

y/x = -34/17 = -2

The slope for this second one is (-2)

(1,1 )and (12,-21)​

x        y

1        12

12     -21

From 12 to 21, you subtract 33

From 1 to 12, you add 11

Now we can do y/x

y/x = -33/11 = -3

The slope for this third one is (-3)

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

Step-by-step explanation:

When you have a negative exponent, you can put a 1 over the entire thing and make the exponent positive:

[tex]\frac{1}{(\frac{1}{4}^2) }=\frac{1}{\frac{1}{16} } =16[/tex]

Answer:

198 ft/s speed

99 ft distance

Step-by-step explanation:

Answer:

7.33333ft

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

i guess   im

Answer:

mp=cp+40%of cp=140cp/100=1.4cp

discount=20%

cp=6000

mp=1.4cp=1.4×6000=8400

sp=mp-d%of mp=8400-20/100×8400=8400-1680=6720

sp with vat=sp+vat %of sp=6720+13/100×6720=6720+873.6=7593.6

Answer:

Step-by-step explanation:

4.3 °F > 4 1/4 °F

Answer:

x=4

Step-by-step explanation:

20x+5+24x-1=180

44x=176

x=4

Answer:

ANSWER:123

Step-by-step  its  very simple its puttin x+11 is how u get ur answer by adding the numbers close to that one angle

The measure of the seventh angle in the heptagon is 125 degrees.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

We are given the measures of six angles in the heptagon, which are:

95, 107, 132, 138, 145, and 158 degrees

Sum of angles in Heptagon is 900 degrees.

To find the measure of the seventh angle, we can subtract the sum of the six known angles from the sum of all the angles in the heptagon:

Measure of the seventh angle = Sum of angles - Sum of known angles

Measure of the seventh angle = 900 degrees - (95 + 107 + 132 + 138 + 145 + 158) degrees

Measure of the seventh angle = 900 degrees - 775 degrees

Measure of the seventh angle = 125 degrees

Therefore, the measure of the seventh angle in the heptagon is 125 degrees.

To learn more on Polygons click:

https://brainly.com/question/28276384

#SPJ2

Answer:

The answer is D. 110

Step-by-step explanation:

You add 8 and 3 and get 11 first because in parentheses, and then you subtract that by 14, which will give you 3. Then you multiply 3 times 5 to get 15 and add that to 95 to get your answer. Hope this helps!

Answer:

The answer is D. 110

Step-by-step explanation:

Answer:

-2 -4

Step-by-step explanation:

saying to use 20 letters lol hope that helps