Please help me solve this

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:

168

Step-by-step explanation:

754-586=168

Answer:

168 points

Step-by-step explanation:

subtract cruz's points by abby's so

754-586=

168 points

Answer:

•35 - 5m

•6 + 2f

Step-by-step explanation:

•5(7-m):

[5×7] - [5×m]=

35 - 5m

•2(3+f):

[2×3] + [2×f]=

6 + 2f

Answer:

A six sided number from 1 to 6 is rolled in a game.

Step-by-step explanation:

Theoretical probability of rolling a 1 or 2.

1) The cube has 6 faces so the total number of the outcome would be 6 only.

2) As per the question we need only 1 or 2 so the favorable outcome would be 2.

3) P(E) = favorable outcome/ total number of outcome

P(E)   = 2/6

P(E)   = 1/3

Theoretical probability of rolling a 1 or 2 is 1/3

Answer:

6.67625

Step-by-step explanation:

402-93-41=267/6.67625

Answer:

Please check the explanation.

Step-by-step explanation:

Given the statement:

''Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number''.

Let us break down the statement into an algebraic expression.

First Portion:

Let the number be: n

The difference of a number n and 2: n -2

Twice the difference of a number n and 2: 2(n-2)

Twice the difference of a number and 2 is added to 6 = 2(n-2) + 6

Second Portion:

3 times the number n:  3n

4 more than 3 times the number: 3n + 4

Combine the First portion and Second Portion:

Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number:

2(n - 2) + 6 = 3n + 4

Therefore, the required algebraic expression is:

BONUS SOLUTION to determine the number n

Let us solve the expression

2(n - 2) + 6 = 3n + 4

2n - 4 + 6 = 3n + 4

flip the equation

3n + 4 = 2n - 4 + 6

3n + 4 = 2n + 2

3n - 2n = 2 - 4

n = -2

Thus, the value of n = -2

Answer:

use khan academy, its a website or an app which a lot of kids which are homeschooled learn education on.

Answer:

-77/12,    -6 5/12,    or   -6.416

Step-by-step explanation:

convert

calculate

done

Answer:

150 + 17x = y

x = hours worked

y = her overall profit

Answer:

The area of the lawn is 68 [tex]m^{2}[/tex].

Step-by-step explanation:

Area of lawn = Area of garden - (Area of triangle + Area of trapezium)

Area of garden = length x width

                             = 14 x 10

                            = 140 [tex]m^{2}[/tex]

Area of triangle = [tex]\frac{1}{2}[/tex] x base x height

                          = [tex]\frac{1}{2}[/tex] x 3 x 8

                          = 12 [tex]m^{2}[/tex]

Area of trapezium = [tex]\frac{1}{2}[/tex] (a + b) h

                              = [tex]\frac{1}{2}[/tex](5 + 7) 10

                               = 60 [tex]m^{2}[/tex]

So that;

Area of lawn = 140 - (12 + 60)

                      = 140 - 72

                      = 68 [tex]m^{2}[/tex]

The area of the lawn is 68 [tex]m^{2}[/tex].

Answer:

8x-8

Step-by-step explanation:

if 2x-2 is mutiplied by 4 is 8x-8

Answer:

plssss

Step-by-step explanation:

i need your help to answer my module plsss :(

Answer:part A including SD cards, Theresa and Ruben have 2.624 x 10^11 bits of storage.

Part b :32 bits

Step-by-step explanation:sorry that's all I know

Hope I helped

The required, solution of the given numeral in scientific notation is shown.

Scientific notation is a method of writing extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation.

Here,

Part A: Including the SD cards, how many combined bits of storage do Theresa and Ruben have on their phones?

Answer: 6.4 × 10¹¹ bits

Part B: How many combined bits of storage do Theresa’s parents have on their phones?

Answer:  2.4 × 10¹¹ bits

Part C: How many combined bits of storage are there on the two tablets?

Answer: 3.6 × 10¹⁰ bits

Part D: Including the phones, tablets, and cloud, how many total bits of storage does the family have altogether?
Answer:6.9 × 10¹² bits

Part E: Theresa’s computer at home has 1 terabyte of storage. How many more bits of storage does her computer have than the combined bits available on her family’s phones, tablets, and cloud storage?
Answer:8.6 × 10¹² bits

Learn more about scientific notation here: https://brainly.com/question/13091583
#SPJ3

Answer:

오늘하루도 트친해요수고하셨습니다 ㅊ풔ㅓㅎ나지금너무배고파죽겠는데난지금바로응모하세요!

Answer: No

Step-by-step explanation:

2/4 would 1/2 and 14/16 would be 7/8 so no I think

Answer:

(0,0) is a solution to n=m and n=4m

Step-by-step explanation:

For the first equation, If u insert 0 as m into n=m

n=(0) then n will equal 0.

For the second equation, if u insert 0 as m in n=4m

n=4(0) then n will also equal 0.

So the answer is (0,0) is a solution to n=m and to n=4m

Hope this helps :)

Answer:

Step-by-step explanation:

x>-2

Becuase multiply it and divide

Answer:

The population density for city b would be 48,592 ÷ 26  

The population density for city b is more than the city c

And, the city d contains the lowest population density

Step-by-step explanation:

The computation is given below:

As we know that

Population density = Population ÷ Area

So

For city A = 2,195,914 ÷ 1,553 = 1413.98

For city B = 48,592 ÷ 26 = 1868.15

For city C = 1,257,676 ÷ 999 = 1258.93.

For city D = 196,429 ÷ 258 = 761.35.

The following are the true statements:

The population density for city b would be 48,592 ÷ 26  

The population density for city b is more than the city c

And, the city d contains the lowest population density

Answer:

A, D, E

Step-by-step explanation:

Just did it on edge!

Answer:

true

Step-by-step explanation:

the equation is exactly the same on both sides but just expressed differently

Answer:

Step-by-step explanation:

From the question, we are informed that 15⋅324=4,860. Thee exact product of 1.5⋅3.24 will be:

= 1 × 5 × 3 × 24

= 360

The answer will therefore be 360

============================================

Explanation:

The given equation y = -3x+1/2 is in slope intercept form y = mx+b

We match the terms to find that m = -3 is the slope and b = 1/2 is the y intercept.

The y intercept is where the graph crosses the vertical y axis.

Answer:

Step-by-step explanation:

The slope of the line in question is the same as the slope of the line parallel to it. Using y = mx + b, where m is the slope, we find the slope of our line is -3.

Using the pt-slope form, y - y1 = m( x - x1), we get y - (-1) = -3( x - 2) or y + 1 = -3x + 6. Which leads us to y = -3x + 5. QED

Answer:

x = 2y +10

x = -2y + 5

Step-by-step explanation:

Answer:

Least common denominator is the lowest number in similarity that a fraction can share and be divided into

Step-by-step explanation:

For example, in this example 1/5, and 1/2 the least common denominator would be 10 because when putting these fractions together you might want to find the total of what they equal. For example, think of this example as a pizza, to make one whole pizza in the first one would be 5 pieces but instead of all five pieces, all you have left is 1 piece of the five. so you only have 1/5. now just imagine you had another pizza the same size of the first one but instead of five pieces you it's only two pieces however, from this two piece pizza all you have left is 1/2. You want to find the in terms of what fraction would make them both equal each other in which you would eventually be able to find out how much pizza you would have left.  The denominator is the lower number under the fraction where that is the one most needed for a fraction to change. The least common denominator is a number that goes into both fractions that in reverse can be divided by against each other. our denominators are 5 and 2. Numbers that are divisible are 10, 20, 40 and so on since 5x2=10, 2x5=10; 5x4=20, 2x10=20; 5x8=40, 2x20=40. The least common denominator would be the lowest number which in this case would be 10.

Answer:

40.22

Step-by-step explanation:

Answer:

Row two (-4, 0)

Step-by-step explanation:

Because of the zero in the y the point does not move from the x-axis.

Answer:

volume of cuboid=l×w×h

volume of cuboid=4×5×3=60cm³