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.
22/44 in simplest form?
Answer:
22/44, divide both sides by 22, then you would got 1/2
1/2. This is because 22 is half of 44, so we can simplify it into 1/2.
Mark wants to find the area of a circle with a diameter of 6 cm. Which expressions can he use to find the area of the circle in square centimeters? Choose all the correct answers.
a.3^2*pi
b.6*pi
c.2*3*pi
d.3*3*pi
e.6*pi
Answer:
B and C
(I'm not sure if b and e are supposed to be the same though) if they are then, b, c, and e
Answer:
The correct options are Option A and Option D
Step-by-step explanation:
Mark wants to find the area of a circle with a diameter of 6 cm.
We need to find the expressions can he use to find the area of the circle in square centimetres?
The formula used to find area of circle is: [tex]Area=\pi \:r^2[/tex]
We are given Diameter = 6 cm
Radius = Diameter/2 = 6/2 = 3 cm
We get radius = 3cm
Now, putting values and finding area
[tex]Area=\pi \:r^2\\Area=\pi \:(3)^2\\Area=3^2\:\pi[/tex]
We can also write it as:
[tex]Area=3*3*\:\pi[/tex]
So, correct options are Option A and Option D
what is a ratio and what does fractions have to do with it?
Answer:
a ratio is a comparison of two quantities, and it has to do with fractions because a ratio is just a single fraction
Step-by-step explanation:
I need yo solve y on this problem. 16x+9y-2x
Answer:
14x+9y
Step-by-step explanation:
Combine Like terms. 16x-2x=14x
dont forget the 9y
so 14x+9y
what is the answer i need help asap pleaseee
Answer:
-4 degrees C
Step-by-step explanation:
-9 + 5 = -4
What kind of triangle is this?
A) Isosceles
B) Scalene
C) Equilateral
Answer:
Scalene
Step-by-step explanation:
John placed $5000 in an account that earns interest compounded annually. His interest rate is 8.2%. If John leaves his money in the account for 10 years, what is the balance of his account? Round your answer to the nearest dollar.
In a pack of candies, Maria found that for every three blue candies, there were five red ones. Identify the correct list of ratios that compares the red candies to the blue ones.
Answer:
5/3; 5 to 3; 5:3
Step-by-step explanation:
Answer:
5/3; 5 to 3; 5:3
Step-by-step explanation:
I need some help please?
Answer:
38°
Step-by-step explanation:
hope this helps :)
help asap
if x²-2x+y²+4y+5=0
what is 2x+y??
Answer: -5
Sorry if I'm wrong
4/5p - 3/5p - 4 = 0
And I need to write out my work
9514 1404 393
Answer:
p = 20
Step-by-step explanation:
Collecting terms gives ...
(4/5 -3/5)p - 4 = 0
1/5p - 4 = 0
Multiplying by 5, we get ...
p - 20 = 0
Then, adding 20 gives the solution:
p = 20
A new car is purchased for 19000 dollars. The value of the car depreciates at 11.25% per year. What will the value of the car be, to the nearest cent, after 14 years.
Answer:
$3573. 64
Step-by-step explanation:
Convert 11.25% to the decimal fraction 0.1125. Then subtract this result from 1.0000: 0.8875.
After 14 years, the formerly $19000 car will have the value
$19000(0.8875)^14 = $3573. 64
71/3 - 21/4 (2 1/5 × 3/4) with working
How do I find the volume of a prism?
Answer:
470 cm³
Step-by-step explanation:
Decompose the prism into two rectangular prism.
Prism 1 will have the following dimensions and volume:
Length = 10 cm
Height = 8 cm
Width = 9 - 5 = 4 cm
Volume = L × W × H
Volume = 10 × 8 × 4 = 320 cm³
Prism 2:
Length = 10 cm
Height = 3 cm
Width = 5 cm
Volume = 10 × 3 × 5 = 150 cm³
✔️Volume of the entire prism = 320 + 150 = 470 cm³
x times 10% = 132 what is X
Answer:
The answer is 13.2
-n+2=7
Can sum one tell me this answer
Answer:
n= -5
Step-by-step explanation:
Answer:
Step-by-step explanation:
-n is -5
pls mark brainliest
Augie has hit the baseball 75% of the time this year. How many times will he hit the ball if
he bats a total of 32 times?
I’m need some help please! :(
Answer:
24 times
Step-by-step explanation:
75% = 0.75, so then you just do 0.75 * 32 = 24
Answer:
For this question, multiply 75% or 0.75 with 32. The result would be 24. So, Augie has hit the baseball 24 times.
Mrs.Sanchez Is taking an online test. At the bottom of the screen there is a progress bar. she has just finished 15 and on tje bar it tells her she is 25% done.
How many total questions are on the test?
A.30
B.60
C.90
D.25
Ifp * (x) = 3x ^ 2 - 4 and r(x) = 2x ^ 2 - 5x + 1 . find value r(x + 2)
Answer:
r(x+2) = 2x² + 3x - 1Step-by-step explanation:
[tex]r(x) = 2x ^ 2 - 5x +1\\\\ r(x+2) = 2(x+2)^ 2 - 5(x+2) +1\\\\ r(x+2) = 2(x^2+4x+4) - 5x-10+1\\\\ r(x+2) = 2x^2+8x+8 - 5x-9\\\\ r(x+2) = 2x^2+3x-1[/tex]
can you help me please
Answer:
Im pretty sure you divide 13 by x
Step-by-step explanation:
...................................
Answer:
1st question's answer is the 3rd option
2nd question's answer is the 2nd option
Step-by-step explanation:
Find the percent of change when 40 is increased to 83.If necessary, round your answer to the nearest tenth.
Answer:0.5
Step-by-step explanation:
Because you put the old figure over the new figure(in this case 40/83)
Answer:
107.5
Step-by-step explanation:
Hope this helps. God Bless
a
\large 140\frac{1}{2}
b
\large 140\frac{1}{3}
c
\large 141
d
\large 140\frac{3}{4}
If 1.) Gabby made a scale drawing of the Sam Houston statue in Huntsville, TX. The statue is actually 67 feet tall. Gabby's model used a scale of 1 inch = 20 feet. What was the length of her drawing?
Answer:
3.35 inches
Step-by-step explanation:
Actual height of statue = 67 feets
Scale used : 1 inch = 20 feets
Let Length of drawing = x
1 inch = 20 feets
x inch = 67 feets
Cross multiply to obtain the length of the drawing in inches
20 * x = 67 * 1
20x = 67
x = 67 / 20
x = 3.35 inches
Hence, length of her drawing is 3. 35 inches
What is the difference of the rational expressions below? 3x/x+1 minus 5/x
Answer:
B
Step-by-step explanation:
[tex]\frac{3x}{x+1} -\frac{5}{x}\\Formula=\frac{a}{b} -\frac{c}{d} =\frac{ad-bc}{bd}\\\\\frac{(3x)(x)-(x+1)(5)}{(x+1)(x)} \\\frac{3x^{2}-(5x+5) }{x^{2} +x}\\\frac{3x^{2}-5x-5}{x^{2} +x}[/tex]
Maria wants to know if the number of words on a page in her earth science book is generally more than the number of words on a page in her math book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Mean Median Mean Absolute Deviation
Earth science 48.9 41 9.2
Math 34.5 44 1.9
She claims that because the mean number of words on each page in the earth science book is greater than the mean number of words on each page in the math book, the earth science book has more words per page. Based on the data, is this a valid inference?
Answer:
No, because there is a lot of variability in the earth science book data.
Step-by-step explanation:
I just took the test and the explanation is that the earth book has more pages and more variability so that is why her answer is wrong.
Answer:
No, because there is a lot of variability in the earth science book data.
Step-by-step explanation:
will make brainliest with correct answer
Answer:
10
Step-by-step explanation:
8² = 64
6² = 36
64 + 36 = 100
√100 = 10
ANSWER ASAP WILL HIVE BRAINLIEST
Answer:
They didn't give the needed amount of evidence but let's just say it's 1/2 in width, it would then be 1/2x5/2=1 1/4 then multiply that by 27/5x1 1/4 to get 6.75! There fore the volume of the shape is 6 3/4 units other wise known as 6.75 units! Hope this helped! :D
Step-by-step explanation:
15x + 9y + 2x - 13
Answer it pleaseee
Answer:
d) 17x + 9y - 13
Step-by-step explanation:
15x + 9y + 2x - 13
15x + 2x = 17x
17x + 9y - 13
Answer:
17x+9y-13
Step-by-step explanation:
.....
✌️❤️✌️
PLEASE HELP
6x+2+3x+7