Three groups of a number plus two.

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:

7

Step-by-step explanation:

x+5x<12

x+5x=12

12-5x

=7

7 divide by 1

=7

Answer:

no solutions

Step-by-step explanation:

i guess   im

Answer:

Mr Lee gets 9kg

Mrs Scarlett gets 6kg

Step-by-step explanation:

First, we have 15kg of chocolate and a total of 6 + 4 = 10 people.

We want to divide the 15kg of chocolate evenly between these 10 people, then we just need to do the quotient

15kg/10 = 1.5kg

This means that each person gets 1.5 kg of chocolate.

Now, Mr. Lee has a family of 6 people, and each one of these 6 people got 1.5 kg of chocolate, then the total amount of chocolate that Mr. Lee will bring home is 6 times 1.5kg:

6*1.5kg = 9kg

And Mrs Scarlett will get the remaining, that is:

15kg - 9kg = 6kg

Mrs Scarlett will get 6kg of chocolate.

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:

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:

B

Step-by-step explanation:

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: 16pi

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

20x+5+24x-1=180

44x=176

x=4

Answer:

The answer is 25

Step-by-step explanation:

6•5=30

30+20=50

50/-2=25

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:

40.9 - 5y

Step-by-step explanation:

25.6 - 5y + 15.3

40.9 - 5y ## ^ combine like-terms

Answer:

∠ AFE = 35°

Step-by-step explanation:

∠ EFD = ∠ BFC = 55° ( vertically opposite angles )

Since BD is a straight line , then

∠ EFD + ∠ AFE + AFB = 180°, that is

55° + ∠ AFE + 90° = 180

∠ AFE + 145° = 180° ( subtract 145° from both sides )

∠ AFE = 35°

Answer:

32 F

Step-by-step explanation:

Answer:

3/9

Step-by-step explanation:

3/9 because it goes up 3 right 9

Answer:

x = 4

Step-by-step explanation:

(7 + 2x) / 3 = 5

Cross product

7 + 2x = 5 * 3

7 + 2x = 15

Subtract 7 from both sides

2x = 15 - 7

2x = 8

Divide both sides by 2

x = 8/2

x = 4

Answer:

Y = 3 - 2x

Step-by-step explanation:

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:

(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)

Step-by-step explanation:

For a quadratic equation to have no real roots, the discriminant b² - 4ac must be negative.

For px² + 8x + 2 = 0,

We have a = p, b = 8 and c = 2.

=> (8)² - 4(p)(2) < 0

=> 64 - 8p < 0

=> 8p > 64

=> p > 8

Hence the range for p is p > 8.

Answer:

1/64

Step-by-step explanation:

Answer:

Step-by-step explanation:

4.3 °F > 4 1/4 °F

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